Advanced thermal sensing techniques for characterizing the physical properties of skin

Interest in measuring the intrinsic properties of the skin arises from the need for quantitative assessments of dermatological health and for increasing our understanding of physiological processes that occur in underlying tissues. Specifically, the physical characteristics of skin reflect basic mechanisms that occur in this organ of the human body, such as those related to blood flow, thermoregulation, homeostasis, and barrier protection. Changes in these properties can reveal immunological disorders associated with skin graft rejections, anomalous hemodynamic responses relevant to peripheral artery disease (PAD), altered healing associated with burns and ulcers, and restricted flow due to venous thrombosis/chronic venous insufficiency and arterial aneurysms. Pathologies of the skin, ranging from malignancies (e.g., melanomas), autoimmune disorders (e.g., atopic dermatitis, or AD), to infectious conditions, such as herpes simplex and cellulitis, also lead to unique types of changes. In other contexts, measurements on the surface of the skin can yield insight into the behavior of superficial implants, such as shunts/catheters for hydrocephalus patients and arteriovenous fistulas for kidney dialysis, and into underlying body processes related to cardiopulmonary activity. Interest in precision measurements primarily follow from these and other health related topics, but relevance extends to basic scientific studies of the skin and various aspects of skin care and cosmetics.

The content of this review begins with a background and motivation for studying the thermal properties of the skin, including an overview of (Sec. II) the fundamental structure of the skin and its relation to disease states, techniques for characterizing the properties of the skin, and the thermal properties of the skin. Section III highlights measurements of skin surface temperature. Section IV reviews isotropic thermal transport properties of the skin, with specific emphasis on the transient plane source and 3ω sensing techniques. Section V examines dynamic fluid flow in the skin, with emphasis on thermal anemometry, calorimetry, and time-of-flight techniques. In each of these sections, an overview of the measurement physics precedes examples that showcase applications of these techniques with clinical relevance, including the assessment and monitoring of near-surface dermatological diseases (e.g., melanoma), skin hydration, hemodynamics, wound healing, and neurological disorders like hydrocephalus. The concluding section (Sec. VI) summarizes technology trends and presents some thoughts on future opportunities for the role of engineering in the health science of the skin.

As the largest organ of the body, the skin comprises an average surface area of ∼ 2 m² and accounts for ∼12%–16% of the total weight of an adult.^1–4 The skin has multiple key functions: (1) thermoregulation, through the modulation of blood flow to the near surface regions of the skin and through the release of sweat; (2) vitamin D production, through the interaction of cholesterol precursors in the skin with UV radiation; (3) sensation to heat/cold, touch, pressure, vibration, and pain, through distributed collections of mechano- and thermoreceptors; (4) absorption of gases and medications through transcellular diffusion; (5) excretion of waste through the release of sweat; and (6) immunological functions providing resistance to microorganisms and noxious external agents.^3,5,6 The three main layers of the skin—the epidermis, dermis, and hypodermis—act together in supporting these essential roles.

An overview of the essential structural features of the skin are described in Table I. The epidermis is thinnest on the eyelids and thickest on the soles of the feet.⁷ This outermost layer of the skin is avascular and is comprised primarily (∼95%) of cells that produce the keratin protein, known as keratinocytes.⁵ Corneocytes and an associated lipid matrix define the outermost layer of the epidermis, known as the stratum corneum. Corneocytes naturally retain water while lipids impede the escape/evaporation of water from the surface of the skin. Together, these components hinder water loss from the underlying tissues to the surroundings. Epidermal water resides both within the cells and within this extracellular lipid matrix. Loss of water can occur from this and underlying layers of the skin.

The dermis is a highly vascularized layer that lies beneath the epidermis, comprised of connective tissue formed from collagen. The dermis is typically 1–4 mm in thickness across most body locations.⁷ Beneath the dermis lies the hypodermis, a 2- to 7-mm-thick layer comprising of fatty connective tissue that cushions the internal organs from external impacts and provides some thermal insulation against the surroundings.⁸ Blood flow through vessels in the dermis accounts for ∼5%–10% of the total cardiac output volume.⁹ This flow can occur as capillary microcirculation (microvascular flow or perfusion) or as macrovascular flow through veins and arteries. Capillaries are small blood vessels that support diffusive exchange with surrounding cells.¹⁰ Branched capillaries connect to veins and arteries through small corresponding vessels, called “venules” and “arterioles” that lead to superficial veins and arteries. Microcirculatory perfusion is the rate of isotropic, volumetric blood flow through a given mass or volume of tissue.¹¹ In the dermis, perfusion (denoted by w) is typically 1.25 $×$ 10⁻³ m³ s⁻¹ m⁻³ tissue.¹¹ 

The deeper layers of the epidermis and the entire dermis include both lymphatic and circulatory channels, aiding in blood delivery and immune response. Both lie within the extracellular matrix (ECM), a network of supportive connective tissue, and are surrounded by interstitial fluid (ISF). ISF constitutes 60%–70% of the overall fluid content of the body.^12,13 In bulk tissue, volumetric ISF flow is largely isotropic; typical anisotropic lymphatic flow rates in vessels (>20 μl/h) are negligible compared to those of blood. Depending on the diameter of the vessel, blood flow rates range from 0.1 ml/min (i.e., retinal vessels) to 600 ml/min (i.e., coronary arteries and jugular veins). These rates can, however, increase dramatically, for example, up to 6–8 l/min during episodes of hyperthermia.^14,15 The dermis contains other important physiological features (appendages) including hair follicles, sweat glands, sebaceous glands, and cutaneous nerves.^4,5,16–18

Skin diseases can affect one or multiple layers depending on their pathology and severity, ultimately impairing the key functions of the skin. The underlying pathologies of skin diseases that cause physiological changes to each of these layers can be broadly classified as autoimmune/inflammatory, infectious, cancerous, and/or related to wound formation. Diseases that span the range of these categories appear in Fig. 1. Some of the most prevalent global skin disorders—acne, AD, urticaria, psoriasis, lupus, tinea pedis, melanoma, and herpes simplex virus (HSV)—are shown in bold text.¹⁹ To illustrate the impact of skin diseases on its properties, consider the example of AD, a common inflammatory disorder affecting 3% of adults, marked by thickening of the epidermis (lichenification) in chronic cases, and erythema with edema, formation of vesicles, and weeping in the acute stage.^20,21 Psoriasis, on the other hand, is characterized by epidermal thickening (hyperkeratosis) forming raised, scaley plaques on the skin surface.²² Both of these can often have similar morphological features. As illustrated by this example, dermatological diseases are difficult to diagnose due to ambiguous symptoms—such as dryness, erythema, and edema—and require interaction with trained medical personnel for accurate assessments. Visual inspection is inherently subjective and provides little information on the affected layer of tissue. The inability to quantitatively identify and track skin disease etiology has important ramifications and motivates the need for advanced characterization techniques. Quantitative detection and monitoring of skin disease are crucial to the development of accurate diagnostics and effective therapeutics. Section II B overviews quantitative techniques for monitoring of skin health.

Various techniques are available to assess the characteristics of the skin through measurements of its mechanical, thermal, electrical, chemical, and/or optical properties, each with different relationships to the structure, function, health, and appearance of the skin (Fig. 2). A brief overview of well-established modalities is useful as context for the main focus of this review on thermal methods. Measurements of electrical properties of the skin are perhaps the most common, where the skin can be approximated as a simple, parallel resistance-capacitance (R_p-C_p) model.²³ The dielectric constant and electrical impedance of the skin depend on its water content and on concentrations of electrolytes.²⁴ Skin temperature and skin conductance exhibit a positive monotonic relationship and can lend insight into sweat gland activity.²⁵ Measurements typically involve application of an alternating voltage (f ∼ 20 Hz–3.5 MHz) to the skin surface through concentric ring (outer diameter ∼600 μm–4 mm) or interdigitated electrodes, in direct contact or separated by a thin insulating layer.^24,26,27 Traditional “dry” metal electrodes rely on bulk, rigid components that form contacts to the skin via applied pressure, with typically poor electrode/skin interfacial impedance and limited repeatability. “Wet” electrodes avoid these shortcomings by use of soft, conformal coatings of electrolyte, hydrogel, or ionic liquid gels to realize low interfacial impedance, improved physical contact and minimized artifacts from motion; however, drifts can arise due to changes in conductivity and/or contact impedance that follow from absorption of electrolytes/ions from the gel into the skin or vice versa, or from dehydration of the electrolyte or hydrogel [Fig. 2(a)].^28–30 A recent work shows that thin, soft, skin-conformable, breathable classes of electrodes, sometimes referred to as “epidermal” electrodes, can form attractive approaches. Here, networks of conductive elements in random or deterministic layouts adhere to the surfaces or distribute into the bulk regions of elastomeric polymer matrices to yield conductive composites that interface to the skin via nonspecific adhesive interactions, without applied pressure and with low interfacial impedances for extended periods of wear. Such electrodes can adhere to curved regions of the body in ways that prevent constraints on natural motions or perturbations to the intrinsic rates of transepidermal water loss (Refs. 24, 26, 31, and 32).

Skin impedances at high and low f can provide insight into the concentration of free and bound water in the skin, across sensing depths that are tunable with measurement f and electrode spacing.^26,31 Variations in electrical impedance can correlate with time dependent changes in the hydration of the skin and/or to spatial variations, of use, for example, in identifying malignant and benign cancerous tissues.³³ The effective measurement depths are typically in a range that corresponds to the uppermost layers of the skin, the stratum corneum (∼15–20 μm) and sometimes the upper epidermis (20 μm–1 mm), due to the small electrode sizes/spacing and high f (∼100 kHz–>3.5 MHz) that are commonly used.^23,26,34 As a result, the density of capillary beds and the influence of capillary blood flow have negligible effect. While depths can reach the millimeter-scale (0.5–2.5 mm) at low frequencies (e.g., 15 kHz) with electrode sizes in the range of centimeters (1–2.2 cm), the spatial resolution is poor.^26,34

Optical measurements performed on the skin provide a means to evaluate the chemistry and dynamics associated with tissue water and blood,^35,36 along with other properties that affect optical absorption and/or scattering. Illuminating the skin with single or multiple wavelengths of light and measuring the intensity and/or spectral characteristics of transmitted or reflected light can yield data relevant to the constituents of the skin, near surface tissue metabolic processes, flow properties, blood oxygenation,^37,38 and many others. The most widely used types of such sensors determine pulse oximetry associated with blood flow within the dermis via measurements at two optical wavelengths performed using rigid finger-mounted devices. A recent work demonstrates possibilities for epidermal embodiments that rely on organic or hybrid organic/inorganic optoelectronic technologies.³⁹ Specific examples include multi-wavelength sensors to assess dermal water content, optoelectronic architectures for the measurement of pulse rate/arterial blood oxygenation, and NIRS sensors to monitor tissue oxygen saturation [Fig. 2(b)].^{35,36,40–43} Such devices can be placed onto the skin at nearly any anatomical location, for measurements with reduced sensitivity to motion induced artifacts due to absence of relative motions between the devices and the surface of the skin. Additional improvements may follow from efforts to further miniaturize these devices, include dynamic digital filtering techniques, and compensate for physical motions, actively or passively. Challenges that follow from sensitivities to motions are intrinsic to all optical approaches, due to the heterogeneous structures of the skin and the relative movements of constituents of the skin during natural activities.

Measurements of the mechanical properties of the skin, such as hardness, viscosity, and tissue modulus, provide complementary information. The viscoelastic properties of the skin can be used to monitor tissue edema, tissue growth/regeneration (e.g., in wound healing), signs of aging, and reactions to exogenous substances.^44–48 Nanoindentation, mechanical suction, torsion, and ultrasound dynamic elastography represent established techniques. These approaches are typically applied to small, approximately planar regions of the body for spot measurements, with limited ability for continuous data collection.^47,49–53 The most recent technologies adopt wearable designs, using thin flexible sheets of piezoelectric or electromagnetic actuators and sensors [Fig 2(c)]. Oscillating forces imparted to the skin by these devices yield displacements that can be sensed to determine intrinsic modulus values. The effective depths of the measurements can extend from the upper regions of the epidermis to the dermis and below, depending on the device configuration. The results provide unique insight for diagnosis/monitoring of cutaneous disorders (e.g., psoriasis, ulcers), muscular activity, and signs of tissue ageing for applications in cosmetics.^47,48,54

Measurements of biochemical characteristics of the skin can complement those of biophysical parameters discussed in preceding sections. Here, skin pH and the concentrations of biomarkers in sweat are of growing interest^55–59 due to their relationship to physiological health, hydration status, and electrolyte balance.^55,57,58 For example, chloride concentrations in sweat serve as clinical indicators for detecting and monitoring cystic fibrosis [Fig. 2(d)].^55,59,60 Some studies suggest that glucose concentrations in sweat correspond approximately to those in blood, of relevance to screening and tracking of conditions related to diabetes. Other sweat biomarkers can lend insight into nutritional health (e.g., electrolytes such as Na⁺ and K⁺) and metabolic activity (ethanol, uric acid, and lactate), with good correlations to concentrations in blood for certain cases (similar to glucose). Similarly, the presence of substances, such as heavy metals (e.g., Cu, Zn, Hg, and Cd) and drugs (e.g., methylxanthine and nicotine), in sweat can be important indicators of health. Commercial devices exist for using sweat alcohol concentrations as approximate measures of alcohol levels in the blood.^61–64 Sensing in these various scenarios involves electrochemical, colorimetric, or fluorometric methods applied to sweat at the surface of the skin or to microliter volumes captured in skin-compliant microfluidic reservoirs and channels.⁵⁸ Water can also escape from the skin in the form of vapor due to permeation through the stratum corneum. Known as transepidermal water loss (TEWL), this process is widely used to characterize the efficacy of the barrier function of the stratum corneum.⁶⁵ TEWL, with units of g m⁻² h⁻¹, is inferred from measurements of water vapor flux using clinical instrumentation. While portable meters exist to measure skin TEWL, these instruments are expensive and rigid, preventing continuous measurements.^66,67

Skin pH is also relevant to barrier function, as an acidic stratum corneum (pH ∼ 4–6) is responsible for maintaining the mechanical integrity and the homeostasis of the epidermal barrier.^68–70 Inflammatory diseases, such as atopic dermatitis, contact dermatitis, ichthyosis, rosacea, and acne, as well as dry and aged skin all exhibit a relative increase in pH compared to that of healthy skin.⁷¹ Glass planar electrode instruments are commonly used to measure skin surface pH, but require precise and frequent calibrations in standard buffers for accurate measurements.⁷² 

The final type of skin measurement summarized in this section involves thermal properties, the primary focus of the remainder of this article. Spatiotemporal distributions of temperature at the surface of the skin, along with thermal transport properties both in the near surface regions and at underlying depths, represent additional, complementary sets of characteristics that can yield important insight. Recent advances in devices and approaches for rapid, accurate measurements of thermal characteristics form the basis of growing interest in this area.^31,73–80 Temperature measurements performed on the surface of the skin are important as a surrogate for, or extrapolation of, core body temperature, one of the six clinical vital signs used to assess overall health status.^81–83 Measurements of local skin temperature can also be used to assess dermatological disease severity, presence of melanoma, and other conditions.^84,85 Body temperature is also instrumental in monitoring circadian rhythms and sleep quality.^46,86 Within the last decade, development of high-precision, high-resolution (∼0.03 °C) temperature sensors with fast response times (5–30 ms), with designs that do not disrupt the skin's natural physiological processes, such as TEWL, enable observations of physiological phenomena, such as changes in cognitive state and microcirculation to the skin [Fig. 2(e)].^76,80 Aside from surface temperature, the thermal transport properties of the skin, such as the thermal conductivity k and thermal diffusivity α, relate directly to changes in subsurface microvascular/macrovascular blood flow and tissue water content. Some of the most advanced devices for measuring thermal transport are reusable, nondestructive, tunable (to sense tissue properties at varying depths, ∼0.5–6 mm), multimodal, and applicable to nearly any region of the body.^{76,78,79,87,88} The ability to create arrays of thermal sensors with small lateral dimensions (∼0.25 mm² or smaller) and with relatively large measurement depths (∼0.5–2 mm) allows for high-resolution spatial mapping of the thermal transport properties of the skin and determination of degree of anisotropy of microvascular and macrovascular blood flow in superficial veins and arteries.^75,76 Reported investigations on subjects with neurological disorders and common dermatological diseases highlight the relevance and applicability of this field of research to real-world clinical cases.^79,87,88

The two main thermophysical properties associated with heat transport are the ability of a material to store and to transfer heat.⁸⁹ The former is given by its heat capacity c, where the temperature increase dT caused by the addition of heat dQ to a thermally isolated material of mass m is given by⁸⁹ 

Equation (1) is a statement of the first law of thermodynamics. We ignore the distinction between heat capacity at constant pressure (c_p) and constant volume (c_v) as solids and liquids—the relevant constituents of the skin—can be considered “incompressible” (material volume is constant for variations in pressure, so c_p = c_v = c).^89,108 In simple terms, the heat capacity of a material describes the amount of heat required to raise the temperature of a sample of mass m by one unit of temperature. For skin modeled as a mixture of spherical droplets of water embedded within a matrix of tissue, the product of tissue density and c_p is linear with respect to the volume fraction of water in skin.³¹ Data show that this model of the skin provides a reasonable approximation through studies of in vitro porcine skin models.³¹ To aid theoretical discussions, a list of key variables used in this paper appears in Table II.

Heat transport through conduction is the primary method of heat transport in solid bodies like skin and occurs predominantly through molecular interactions. Thermal conduction is described through Fourier's Law as follows:

where q is the heat flux density in W m⁻², and $∇$T is the local temperature gradient. The coefficient k is a second-order tensor and describes the thermal conductivity, which can vary with temperature and relative position within the material.¹⁰⁸ This review largely considers skin and/or its individual layers as isotropic and homogeneous, with values of k that have negligible dependence on temperature (without considering the effects of perfusion), consistent with ex vivo studies of tissue models.⁹³ Thus, the tensor k reduces to a scalar, k. Thermal conductivity describes both transient and steady-state conduction.⁸⁹ For human skin, values of k of the epidermis and dermis lie in between the literature reference for dry skin and for blood and water, as illustrated in Table III. The value of k of the hypodermis is lower than that of the epidermis/dermis, as this layer is primarily composed of fatty tissue. Dermatological diseases result in changes of the water content, vascular blood flow, barrier properties, and composition of one or more layers of the skin (e.g., induce thickening of the epidermis). In turn, changes in the water content and blood flow can be reflected in measured values of the thermal transport properties of the skin.

Typically, both heat conduction and storage occur simultaneously.⁸⁹ The transient heat conduction equation describes the “competing” nature of heat conduction and storage as follows:

Equation (3) applies for an isotropic, incompressible material. The diffusivity, α, is the ratio of the thermal conductivity to the product of the tissue density ρ and c,

Physically, α is the ratio of heat conducted to heat stored within a material and denotes the speed of heat propagation through a material subject to a temperature gradient.⁸⁹ Unlike k which describes both transient and steady-state heat conduction, α is only defined during transient heat conduction. Like k, α of human skin lies in between values of dry skin, blood, and water, but it has a non-monotonic relationship with respect to blood and water content.³¹ 

Convection, another mechanism of heat transport, occurs via the movement of a fluid away from a surface. Convection can be natural, due to local variations in fluid temperature, or forced by an external agent, such as a pump.¹⁰⁹ For applications in skin, convection of blood through veins/arteries is “forced” by the heart. The Newton rate equation, or the rate equation for convective heat transfer, defines the heat transfer coefficient h as follows:

where $q̇$ is the rate of convective heat transfer per unit area normal to the direction of heat flow in J/s/m² (W/m²), and ΔT is the difference in temperature between the surface and the fluid. The heat transfer coefficient denotes the rate of heat transfer between a solid surface and a moving fluid. The skin cannot be treated as a pure solid body, as it contains fluids, such as blood and water, which can dissipate heat through convection. The rate of perfusion, w, or the blood flow velocity per unit volume of tissue, can be derived from thermal transport measurements by detecting convective heat losses, which will be described in Sec. V. The avascular epidermis naturally has w = 0 while the dermis and hypodermis are both vascularized and, therefore, have finite w > 0; the hypodermis experiences more blood flow than the dermis. On the other hand, the directional flow rate of blood (v) in the skin (e.g., through veins) can vary from 10 ml/min (metacarpal vein) to 500 ml/min (portal veins) and can change based on cardiac output.¹¹⁰ The flow of water in the skin (e.g., interstitial fluid) is much lower, ∼0.2 ml/min, and is typically isotropic.¹¹¹ Section V describes experimental methodologies to distinguish between the isotropic and anisotropic flows.

Radiative heat loss occurs through electromagnetic radiation between two bodies. The Stefan–Boltzmann law describes the rate of energy emission from the skin to the environment as follows:^109,112,113

where $q̇$ is the rate of radiant energy emitted per unit area of the exposed skin surface; T_skin and T_air are absolute temperature of the skin and air, respectively; ε_skin and ε_air are the emissivity of the skin and air, respectively; and σ is the Stefan–Boltzmann constant. Equation (6) illustrates that radiative effects are dominant at large differences in skin/air temperature and are negligible for the physiologically relevant temperatures (∼310 K or 37 °C) with respect to room temperature (∼298 K or 25 °C).

Skin temperature arises from thermal energy balance within the body, an additive combination of the body's metabolic heat production and the heat lost/gained by various heat transfer processes,¹¹⁴ 

where ΔE is the rate of energy storage in the body, M is body's metabolic energy produced, W is the external work performed by the body, and Q represents heat gain/loss, with various subscripts indicating the different heat transfer mechanisms (conv = convection, cond = conduction, rad = radiation, evap = evaporation and resp = respiration). Pennes' bioheat transfer equation, derived from this energy balance equation, can be used to predict temperature distributions inside the skin and other tissues:^114,115

where T_a represents the arterial blood temperature, and T is the surrounding tissue temperature. This model describes the effect of metabolism and blood perfusion on the energy balance within the tissue. While Eq. (8) relies on many simplifying assumptions (e.g., isotropic, homogeneous tissue properties), advanced models can be used to capture additional details.¹¹⁶ 

Simple, accurate measurements of skin surface temperature, particularly performed with wearable devices, are of growing interest given their physiological significance. Chung et al. demonstrate the use of compact, wearable devices that interface gently and noninvasively with the skin of neonates for the measurement of the full suite of vital signs in the intensive care unit (ICU), including clinical grade thermometry on the skin of as a surrogate for measuring core body temperature.^81,82 Wearable temperature sensors can also be used to monitor mental and physical activity,⁷⁶ emotions,¹¹⁷ sleep cycles, and menstrual cycles.^86,118,119 Furthermore, skin temperature has applications in monitoring of skin injury, such as wound healing, viability of skin flaps, and ulcer formation (e.g., diabetic ulcers, bed sores), and the onset of disease, such as breast cancer.^46,120–122

Critical criteria for characterizing wearable temperature sensors are temperature resolution, response time (low thermal mass), and hysteresis-free behavior, each of which can be addressed with appropriate device designs and materials selections. In addition, intimate thermal contact with the skin is vital for all of these types of measurements.¹²³ To minimize thermal contact resistance, the devices must conform to the nonplanar, rough surface of the skin without air gaps. From an analysis of the contact mechanics, this scenario occurs when¹²⁴ 

where $E¯skin$ is the plane-strain modulus of the skin; h_rough and λ_rough are the amplitude and wavelength of the roughness of the surface of the skin, respectively; $EI¯device$ is the bending stiffness of the device; and γ is the work of adhesion between the surface of the device and the skin. Equation (9) assumes that λ_rough ∼ 7h_rough, as shown in experimental measurements of skin roughness.¹²⁴ This scaling law demonstrates that devices with low effective modulus and bending stiffness (i.e., soft and thin), and strong adhesion to skin promote conformal contact. Establishing such contact becomes increasingly difficult as the roughness and modulus of the skin increases. The amplitude of features in the skin like wrinkles, creases, and pits are 15–100 μm and their sizes are 40–1000 μm, and the Young's modulus of the skin is 140–600 kPa for the epidermis and 2–80 kPa for the dermis; in practice, for typical filamentary serpentine epidermal devices (silicone/PI/Au) reported in Ref. 124 with d_silicone = 30, d_PI = 0.3, and d_gold = 0.2 μm, γ = 0.16 Ν/m, and $EI¯device$ = 0.27 $×$ 10⁻⁰ N m, devices have conformal contact with the skin when h_rough$≤$56 μm.^124,125

Sensing mechanisms typically involve electrical or optical means. The former exploit resistive temperature detectors (RTDs), positive temperature coefficient (PTC) or negative temperature coefficient (NTC) thermistors, or thermocouples.^{76,79,126–130} RTDs for measurements of skin temperature, often constructed using inert, biocompatible metals, such as Au or Pt, exhibit a change in electrical resistance with temperature. For most metals, at small values of ΔT,

where $ΔR=R−R0$⁠, R₀ is the nominal resistance and β is the temperature coefficient of resistance (TCR) of the metal. Values of β and resistivity for copper, gold, and platinum are β = 43 × 10⁻⁴/K, resistivity = 1.67 × 10⁻⁸ Ω m, β = 39 × 10⁻⁴/K, resistivity = 2.30 × 10⁻⁸ Ω m), and β = 39.2 × 10⁻⁴/K, resistivity = 10.6 × 10⁻⁸ Ω m, respectively.^131,132 While the highly linear relationship between R and T for RTDs is appealing, these small values of TCR typically demand the use of amplification electronics for reliable measurements.^76,79

Soft, ultrathin devices, sometimes referred to as “epidermal” devices, represent the most attractive construction of RTDs (and other temperature sensing mechanisms),^76,125 where winding traces (∼20 μm wide) of thin films (∼50–100 nm thick) of an inert metal, such as Au, serve as the heaters and sensors [Fig. 3(a)].^73,76 Encapsulation above and below using biocompatible polymers (e.g., polyimide (PI), with thicknesses d_PI between ∼1 and 6 μm) form chemically resistant, electrically insulating, mechanically robust (∼2.8 GPa elastic modulus) protective layers that isolate these traces from the surroundings (e.g., from environmental humidity, water/fluids). With appropriate choices in thickness, these layers can also place the metal features at the neutral mechanical plane to enhance the bendability of the resulting structure.^76,124 An elastomer backing material (typically poly(dimethyl)siloxane (PDMS), ∼50–100 μm thick) allows repeated application and removal of the device from the skin, as a soft, conformal physical interface.^76,78 Such devices have small thermal mass (7.2 mJ cm⁻² K⁻¹), fast response times (4–13 ms), and high levels of elastic stretchability (∼10%, can be > 50%).^74,76 The polymer encapsulants and their thicknesses (d_PI, d_silicone), furthermore, are key in defining the thermal mass and ultimately the response times of the RTD devices. Typical silicone elastomer backing materials increase the thermal mass per unit area by 48 $×$ over that of the PI/metal/PI structures alone (150 μJ cm⁻² K⁻¹).⁷⁶ The response time for a device structure with d_PI = 3.6 μm, t_silicone = 50 μm is 4.2 ms. Increasing the d_PI to 6 μm leads to a threefold increase in response time.⁷⁶ Ultrathin backing layers, in perforated or non-perforated forms, can be highly gas/water vapor permeable, thereby accommodating natural physiological processes like TEWL (i.e., skin hydration) without perturbing the natural temperature of the surface of the skin across most scenarios of interest.⁷⁶ Commercial, surface-mount components (SMD/SMT) (∼0.9 $×$ 0.9 mm²) can also serve as heating and sensing elements, but accurate measurements require calibration to account for their heat capacities.^79,87 Thin metal films are attractive for their relatively small heat capacities (e.g., gold, c = 0.13 kJ kg⁻¹ K⁻¹) compared to those of ceramics (e.g., silicon carbide, c = 0.67 kJ kg⁻¹ K⁻¹) and for their ease of patterning into small features and/or desired geometries.⁷³ 

NTC thermistors (as well as PTC thermistors), in contrast with RTDs, exhibit much larger variations in resistance as a function of temperature, as given by¹³³ 

where R_T is the resistance at temperature T, R_∞ is the reference resistance of the thermistor, and B is the “B-value,” also known as the “thermistor value.” While NTC/PTC thermistor responses are typically nonlinear with respect to T, for small ranges, the dependence can be approximated as linear with a corresponding value of TCR. Conventional thermistors are typically ceramic materials based on sintered semiconducting oxides (e.g., transition metal oxides like NiO, FeO, CoO, and MnO). Polymers/polymer composites are increasingly popular, due to their ease of processing and their mechanical flexibility.^134,135 At T ∼ 25 °C, the TCR for the flexible, sintered 30-μm-thick NiO NTC thermistor fabricated on a thin PET substrate (25 μm) from Ref. 133 is −9.2% C⁻¹, much larger than values for RTDs [Fig. 3(b)].¹³³ The thin PET substrate enables a response time of < 50 ms for this sensor structure. These flexible NiO NTCs can be used for applications in artificial skin (touch sensitivity to heat/cold) or as monitors of changes in the temperature of the skin associated with activity (e.g., cycling). Additional possibilities are in tracking respiratory rate when placed in physiologically relevant locations, such as under the nasal cavity.¹³³ Sang et al. demonstrate Au-doped silicon nanomembrane (SiNM) NTC thermistors with relatively fast response times (<9 ms due to ∼300 nm Au-doped SiNM thickness and ∼1.5 μm PI encapsulation on either side) compared to materials which exhibit phase-change mechanisms (i.e., polymer-based thermistors) and a TCR 22 $×$ higher than that of thin film RTDs.¹³⁶ The magnitude of the TCR of the Au-doped SiNM increases with decreasing doping temperature and dopant concentration¹³⁶ according to

where E_D is the donor level energy of Au, E_V is the highest energy level of the valence band, K_B is Boltzmann's constant, N_a is the concentration of acceptors (Boron) in Si, and N_Au is the Au dopant concentration. Experiments demonstrate improved signal to noise ratios (SNR) in body-worn applications, where the Au-doped SiNM sensor can detect appreciable changes in signal due to temperature fluctuations on the body during alternating periods of rest and exercise. By comparison, conventional metal-based RTDs exhibit very low percentage changes in resistance in similar conditions.¹³⁶ 

Yokota et al. report classes of flexible, printable PTC thermistors comprised of a composite of graphite (2–3 μm diameter particles) and semicrystalline acrylate copolymers with resistance changes of six orders of magnitude over temperature changes of only 4 °C, response times of < 100 ms, and temperature sensitivities of 20 mK [Fig. 3(c)]. These properties address the challenge of developing PTC thermistors with sensitivity at physiological temperatures.¹³⁵ The “PTC” mechanism arises from an increase in specific volume of the composite as a function of temperature through the melting point (T_M = 36 °C). The density of the polymer composite is reported to decrease by ∼5% above T_M as the polymer undergoes a phase transition from semicrystalline to amorphous.¹³⁵ For applications on skin, the response must be immune to bending and thermal cycling. Characterization results show that the devices are unaffected by bending radii to values as small as < 700 μm. Negligible changes occur over 200 cycles of bending to radii of 1 mm and 1800 thermal cycles from 29.8 to 37 °C. These excellent performance characteristics follow, at least partly, from the use of a “lateral-type” structure where the PTC film lies between two neighboring electrodes on the x–y plane, instead of between electrode films above and below in the vertical z-direction.¹³⁵ 

Thermocouples operate on the principle of the thermoelectric effect, where an electromotive force (EMF) results from the junction between two dissimilar conductors upon heating.¹³⁷ The Seebeck coefficient S, analogous to TCR, describes the induced voltage change V with respect to change in temperature:

The two constituent materials for thermocouples must have a sufficiently large difference in electronic work function, Φ. The Seebeck coefficient for two commonly used metals in thermocouples—copper and constantan—is 40 μV K⁻¹. Reference 126 reports a flexible thermocouple for use in electronic-skin applications that combines silver nanoparticles (Φ ∼ 4.2 eV) and multiwalled carbon nanotubes (Φ ∼ 4.6 eV) inkjet-printed onto a flexible indium-tin-oxide (ITO)-coated PET substrate. For this system, S = 8 mV K⁻¹ for 25–150 °C [Fig. 3(d)].¹²⁶ Thermocouples are attractive for certain applications, but they can undergo baseline drift in wearable devices due to the difficulty in maintaining a precise reference temperature at one side of the metal junction.^134,138

Apart from traditional temperature sensing mechanisms (RTDs, thermistors, thermocouples), colorimetric temperature sensing systems comprising pixelated thermochromic liquid crystal (TLC) arrays on thin, soft elastomeric supports represent an additional option with demonstrated utility in the thermal characterization of the skin.⁸⁰ Gao et al. report a patterned TLC ink (∼25 μm thickness, 250 or 500 μm diameter and spacing), on black poly(dimethyl) siloxane (PDMS) with < 30 ms response times [Fig. 3(e)].⁸⁰ Hue and saturation extracted from digital camera photos using computer vision algorithms quantitatively relate the colorimetric response to temperature.

Infrared thermography is the most common, non-contact optical technique used for noninvasive temperature mapping of the skin surface. The sensitivity of IR cameras is 0.01–0.05 °C, and spatial resolution can be < 2 mm over large fields of view: 200 $×$ 200 mm²–500 $×$ 500 mm².¹³⁹ The images provide information about local cutaneous perfusion, metabolism, and environmental temperature.¹²² The temperature sensed by the IR camera (T_sensed) is given by¹²² 

where ε is the emissivity of the skin, T_skin is the true skin temperature, and T_∞ is the ambient room temperature. For radiative emission with wavelengths in the range of 3–14 μm, ε is independent of pigment, and for skin at 303 K and a room temperature of 293 K, a variation in ε of $±$ 0.01 (from the literature on in vivo and in vitro subjects) corresponds to an apparent variation of temperature of $±$ 0.01 °C.^122,140 Infrared thermography requires instrument calibration, and measurements often rely on symmetric sites on the body as points of reference. Surface curvature and viewing angle also can lead to measurement errors, thereby frustrating studies on complex geometries of the body and requiring subjects to remain stationary during image recording.¹³⁹ 

Simple, point measurements, or spatiotemporal mapping of skin surface temperature (T_skin) can be valuable in many applications. Table IV highlights a few key examples. Epidermal or skin-mounted temperature sensors have garnered interest, at the most basic level, as a surrogate for measurements of core body temperature (T_core). Zhang et al. demonstrate differential measurements from RTD sensors at different distances away from the skin, separated by layers of silicone [Fig. 4(a)].⁷⁷ Through an approximated 1D heat conduction analysis, theoretical analysis indicates that the temperatures at these distances depend on T_core, the thermal properties of the underlying tissue, and the ambient conditions, such as temperature and air convection. Extraction of the unknowns (i.e., T_core, t_tissue/k_tissue where t_tissue is tissue thickness, and convection coefficient h) occurs through numerical error minimization analysis. Uncertainties that result from this fitting process can be minimized by increasing the total number of sensors.⁷⁷ The published results include the impact of various environmental conditions, including those that involve air convection, on differential measurements to determine of T_core. A disadvantage of this approach is the relatively long response times (∼474 to ∼1030 s) that follow from the thicknesses of the separating silicone layers in this device architecture.⁷⁷ 

Ota et al. developed a wireless, 3D-printed device mounted on the ear for the measurement of T_core [Fig. 4(b)]. The device consists of a thermistor, which measures environmental temperature (T_E) and an infrared detector which measures the differential temperature between T_E and the tympanic membrane inside the ear. The tympanum is less susceptible to environmental changes compared to the skin, making it an ideal location for sensing T_core.¹⁴¹ Tests on a subject during exercise demonstrate excellent agreement between the device developed in this work and a commercial tympanic membrane temperature sensor, while skin-mounted temperature sensors exhibit no such correlation. Experimental demonstrations of varying environmental temperature have significant impact on skin temperature, but no significant changes in tympanic temperature. The authors integrate the device with a bone-conduction hearing aid, illustrating multifunctional use and ease of integration with conventional medical/wearable devices (e.g., hearing aids, headphones).¹⁴¹ 

Spatiotemporal mapping of the temperature of the skin surface can lend insight into a subject's health status and cognitive state. Webb et al. introduced arrays of epidermal temperature sensors to map the surface of the skin, with examples in measuring blood flow and/or detecting subtle spatiotemporal fluctuations [Fig. 5(a)]. Low frequency oscillations (0.005–0.5 Hz) of magnitudes of 0.1–1.0 °C detected by these sensors on the skin of the palm follow from changes in blood perfusion due to the sympathetic activity of arteriovenous anastomoses, relevant for conditions, such as congestive heart disease and tissue hypoxia.⁷⁶ A reactive hyperemia test with a sensor array placed above the ulnar artery demonstrates the use of temperature as a metric for changes in blood flow [Fig. 5(a)]. The experiment involves a blood pressure cuff placed on the upper arm to temporarily occlude blood flow. During occlusion, the temperature decreases due to the absence of blood flow (⁠$≈$ –0.4 °C). After the release, the temperature exceeds the baseline value (⁠$≈$ +0.8 °C) before returning to normal. Sensors placed near the artery exhibit the greatest change while locations away from the artery show no significant change (∼0–0.2 °C), illustrating the importance of temperature mapping to detect spatiotemporal variations.

Cognitive state can contribute to changes in local skin temperature. Epidermal temperature sensors placed on the skin of the palm can detect changes from mental stimuli (mental math), in good agreement with conventional, high-precision infrared cameras.⁷⁶ Another study highlights changes in facial temperature using infrared imaging (n = 40) while presenting subjects with various positive, neutral, and negative visual stimuli [Fig. 5(b)].¹¹⁷ A significant change in temperature (−0.85 °C) appears on the tip of the nose compared to the neutral condition (p < 0.001) for images with negative, low emotional impact, while a significant increase in temperature (+ 0.96 °C) occurs for images with negative, high emotional impact (p < 0.003). Images with strong, positive emotional arousal leads to a + 1.66 °C change in nasal temperature (p < 0.001). Similar procedures can assess other emotions, such as empathy and love, of interest in applications in mental health.¹¹⁷ 

Techniques to measure the isotropic, effective thermal transport properties of the skin involve some combination of thermal power delivery to the skin and sensing the spatiotemporal patterns of temperature that result. Heating methods, like sensing techniques, typically exploit electrical (resistive, or Joule) or optical (absorption) means in a constant mode over the course of the measurement (direct current, DC) or in a time variant (e.g., alternating current, AC) fashion. During Joule heating, a current passes through a resistive heating element in physical contact with the surface a sample of interest for a well-defined time, often on the order of ∼1 s to a few 100 s.^{31,73,76,78,79} Techniques like the 3-omega method involve AC sinusoidal Joule heating, typically with frequencies between 1 and 1000 Hz.⁷⁴ The measurement time (DC) or frequency (AC) and the heater geometry can be used to tailor the effective sensing depth.⁷⁸ 

A combination of heating and sensing components like those described in previous paragraphs form basis for thermal transport measurements. Heating induces spatial and temporal changes in the distribution of temperature across the sample surface and into its depth. Sensors, typically interfaced to the surface at one or more spatial locations, measure these changes to allow, with suitable models of heat flow, determination of the intrinsic thermal properties. In many thermal transport measurement techniques, a single element serves as both the heater and the sensor. Self-heating induces a change in temperature, the magnitude of which depends on the thermal properties of the surrounding materials. This change in temperature leads to a change in resistance due to the temperature coefficient of resistance of the constituent material. Transient plane source (TPS) measurements in their simplest embodiment exploit a single RTD component that serves simultaneously as a heater and sensor. A recent work demonstrates the use of the TPS technique for evaluations of the skin to a range of characteristics depths (∼50 μm–6 mm), defined by the geometry and the timescales of the measurement, typically with DC power for Joule heating (∼10–60 mW for heater r = 0.5–4.5 mm that lead to maximum increases in temperature, ∼1–5 K) that fall far below the thresholds for damage.^75,78 Another version of this approach relies on one or more separate sensors.⁷⁹ The pulsed decay technique is analogous to TPS but instead observes the temperature decay of the heater after a short (∼3 s) DC heating pulse,^88–143 most often used to characterize skin at shallow depths (∼0.9 mm).⁸⁸ 

The 3-omega technique uses a resistive heater with a linear geometry for simultaneous AC heating and sensing. In comparison to DC approaches, measurements made using the 3ω technique are less sensitive to radiative and convective heat loss mechanisms (e.g., air convection) and are less affected by boundary conditions between the sample under consideration and its substrate.⁷⁴ The measurement depth is continuously tunable based on adjustment of the heating frequency (< 100 μm for high frequency heating to ∼2 mm for low frequency heating, depending on heater geometry) and enables relatively short measurement times (< few s to tens of s) compared to DC approaches (several seconds—hours); hence, measurements can be collected even with drifts in the baseline temperature associated with the sample or environment.^{74,120,144,145} There are far less constraints for sample size using the 3ω technique as compared to TPS owed to the ability to highly confine the measurement depth—the limiting factor is the minimum feature size of the line heater that can be patterned using standard lithographic techniques.¹⁴⁵ In contrast, DC techniques like TPS typically involve measurement times chosen such that the sample can be treated as a “semi-infinite solid,” where the sample size is sufficiently larger than the thermal penetration depth in each dimension.¹⁴⁶ Table V summarizes the differences between TPS and 3ω.

Photothermal techniques can replace the resistive heating/sensing approaches outlined above for remote, non-contacting measurements. In many examples of this approach, heating of the skin occurs with a laser. Sensing occurs through optical imaging of the skin temperature or by detecting changes in characteristics of the light scattered from the surface of the tissue due to temperature modulation of the refractive index and/or local thermal expansion.^147–149 Examples of photothermal beam deflection (PBD) methods applied to samples of biological tissue use a λ = 632.8 nm “probe” laser to detect changes in the angle of scattered light using a phase sensitive photodetector following local heating from a λ = 8–10 μm “pump” laser.^147,148 Reports show that PBD can probe superficial layers of the skin (∼17–44 μm) with high temporal (few ms to a few 100 ms) and spatial (10–300 μm) resolution.^147,148 Complex optical setups, dependence on skin tone/pigmentation and sensitivity to motion artifacts represent key disadvantages.¹⁴⁷ Of these various schemes, electrical methods are generally most practical for continuous measurements of conscious subjects, particularly for use outside of clinical or laboratory settings.^74,79,88,149 The remainder of this section, therefore, focuses on electrical measurement techniques—TPS and 3-omega—in detail.

In all cases, safe thresholds of heat must be maintained to prevent thermal injury of the subject. The United States Food and Drug Administration (FDA) recommends medical equipment/devices conform to the International Electrotechnical Commission (IEC) standards for maximum allowable temperatures and time for contact of medical electrical equipment with skin. The IEC 6061–1 guideline states that for medical equipment composed of molded material, plastic, or rubber (of relevance in wearable thermal devices) in contact with small areas (< 10%) of the total body area, for applied time t < 1 minute, the maximum allowable applied temperature T_max is 60 °C, for 1 min $≤$ t < 10 min, T_max = 48 °C, and t $≥$ 10 min, T_max = 43 °C. For applied parts intended to supply heat to a patient, if the applied T > 41 °C, additional justification is required.

For most applications to the skin, TPS involves injecting a direct current I through a thin film metal (or SMD) heater of resistance R and radius r for a fixed time t, causing Joule heating with power P [Fig. 6(a)].

The change in R of the heater (ΔR) recorded during the heating period relates to the change in temperature through the TCR [Eq. (10)]. Qualitatively, ΔT increases rapidly at short times and then approaches a quasi-steady state value ΔT_sat, reflecting the transient temperature response of the material to the applied thermal power, followed by the quasi-steady state behavior of the material after a sufficiently long time, t > t_sat.⁷⁸ The average temperature change for a spiral-shaped disk of radius r is given by¹⁴⁶ 

where $τ=tα/r2$⁠, and

where τ is a dimensionless measure of time, and I₀ is the second-order Bessel function of the zeroth kind. The parameters u and v represent 2D Fourier space. Equations (16) and (17) can be solved using Finite Element Analysis (FEA). Simplified scaling laws [Eqs. (18) and (19)], with analytical solutions solved through FEA relate the ΔT and k:⁷³ 

where

J₁ is the first-order Bessel function of the first kind. Equations (18) and (19) assume a solid disk shape, as compared to Eqs. (16) and (17), which assume a spiral geometry. The difference between these two cases can be neglected in most instances.⁷³ Eqs. (18) and (19) demonstrate that ΔT, q, k, and r have linear co-dependence, while t and α have non-linear relationship to the measured ΔT. For applications to skin, q is chosen such that ΔT < 10 °C (typically < 5 °C), the threshold for sensation of pain and for compliance with IEC6061–1.^76,78,150

Representative TPS data collected from three materials (water, air, and the skin of the forearm) appear in Fig. 6(b). The results display the expected inverse relationship between ΔT and the measurement time t.⁷⁶ The gray region of the graph indicates the full range of ΔT observable for skin with a 1 mm² square heater at q = 1 mW for t = 0–2 s.⁷⁶ Figure 6(c) summarizes modeling results for the change in the temperature of the heater ΔT_heater with respect to thermal contact resistance R_t with the skin. ΔT_heater increases monotonically with respect to R_t, as expected, as air gaps fill voids between the skin and the heater.¹²³ The presence of air, due to its low thermal conductivity (k_air = 0.02 W/m K) leads to an increase in ΔT_heater. The ΔT can be used to compute k of the skin using FEA or the simple scaling law presented in Eqs. (18) and (19), as graphically represented in Fig. 6(d) for known q, R, and t.⁷³ Here, the extraction of k assumes the skin across the measurement depth can be considered as an isotropic, homogenous medium. This scaling law also assumes an estimated α_skin = 0.15 mm² s⁻¹ $±$ 20%.⁷³ For large values of t and small values of R, the value of α has minimal impact on ΔT, and $ΔTkqR$ is nearly constant. Figure 6(e) illustrates that the error in fitted values of k due to uncertainties in α is minimized in this quasi-steady state regime.⁷³ The blue region of the contour plot (where FEA fitting error is minimum) is vertical, indicating that an accurate value of k (in this case, ∼0.21 W/m K) can be extracted independently of the value of α (0.05–0.2 mm² s⁻¹) at t = 40 s.

Drift of baseline temperature T₀ of the skin represents an additional source of error for measurements of ΔT.¹⁵¹ In the case of inflammatory diseases, such as urticaria, lesions can develop over the course of minutes. Changes in the temperature of the environmental temperature can vary over similar timescales. Pulsing the heater allows for re-calibration of T₀ for every pulse, but this approach effectively reduces the duty cycle and the effective measurement depth [Fig. 6(f)].¹⁵² Measurements of the temperature of adjacent, unheated, regions of the skin can, in certain cases, be used to eliminate these drifts via a differential mode of detection.

Understanding the effective measurement depth, h, is important because the skin is a layered structure with depth-dependent properties, as discussed in Sec. II. For the TPS technique, this measurement depth is comparable to the thermal penetration depth, h ∼ $αt$⁠, where α_skin ≈ 0.15 mm² s⁻¹.^75,146 Examples of the TPS technique applied to skin involve depths between ∼100 μm and ∼6 mm, dictated by the sizes of the heaters and the timescales for the measurements.^75,78 This range spans the stratum corneum, the epidermis, dermis, and hypodermis.

Models that account for the skin as bi-layer systems allow the extraction of the approximate thermal properties of the individual layers. Recent research (2018) treats the skin as a bi-layer made up of the epidermis/dermis (depicted as layer A, with thickness h) and hypodermis (depicted as layer B) [Fig. 7(a)] in series of TPS measurements with different heater sizes and measurement times. Increasing the size and the time increase the measurement depth [Fig. 7(b)]. For a single-layer model, the k can be denoted as “k_eff,” as a weighted, volumetric average of k_A, the thermal conductivity of the epidermis/dermis, and that of the hypodermis, k_B. Figure 7(c) illustrates a constant C₁ that defines the weight fraction of the volume of heat that penetrates through layer A.

Fitting measurements to FEA results can determine the thermal properties of the epidermis and dermis, using devices and measurement parameters to restrict the characteristic depth to ∼1 mm.⁷⁹ One reported approach uses a small (∼1 $×$ 1 mm²) heater and an analysis of the dependence of ΔT on t. At short times (t = 2 s), the heat propagates mostly into the epidermis and at longer times (t = 13 s), a larger portion of the heat propagates into the dermis [Fig. 7(d)]. A micromechanics model treats the thermal properties as a composite of pure dry tissue and water to determine the volumetric water content φ in the skin. Contour plots of ΔT for varying φ_E (epidermal water content) and φ_E (dermal water content) at different times enable separate the extraction of the water content of the epidermis and dermis, respectively [Figs. 7(e) and 7(f)].

The 3-omega technique involves injection of an alternating current (AC) i at angular frequency ω = 2πf into a one-dimensional (1D) heater of length l:

Typically, f ranges between 1 and 1000 Hz. This alternating current induces Joule heating:

where

P_rms represents the root mean square (RMS) power dissipated over one heating cycle, and I_rms is the corresponding RMS heating current. The total power can be separated into two Joule heating components, the DC component P_rms and the AC component $Prmscos2ωt$⁠.

From the literature, the steady-state harmonic temperature oscillations in the metal heater produce harmonic variations in the resistance of the metal line given by the following equation:¹⁵³ 

where β is the TCR of the metal heater, ΔT_DC is the temperature change due to the RMS power dissipated by the 1D line heater, |ΔT_AC| is the magnitude of the temperature oscillations due to the AC Joule heating component, and $ϕ$ is the phase delay between the temperature oscillations and the injected current i. The voltage across the 1D heater is the product of the heater resistance and the current injected into the heater:¹⁵³ 

The 3ω component of the voltage arises from the product of the resistance change due to Joule heating at 2ω and the input current oscillating at frequency ω. The amplitude of the third harmonic voltage is given by¹⁵³ 

where V₀ = i₀R₀ and T_2ω is the complex AC temperature oscillation at 2ω. The average temperature of the line heater is given by⁷⁴ 

where l and b are the length and half-width of the line heater, respectively, v represents 1D Fourier space, and 1/q = h which is the thermal penetration depth. h is given by⁷⁴ 

For typical values of ω (2πf where f = 1–1000 Hz), line heaters of metal width = 5 μm, thickness = 100 μm, and L = 1.5 mm, and for α_skin = 0.15 mm² s⁻¹, h does not exceed 100 μm. The 3-omega technique is ideal for sensing across shallow depths of the epidermis, with potential applications in skin hydration. At very low frequencies (e.g., 0.1 Hz), h = 1 mm can be achieved. In such cases, however, boundary conditions become significant, and the substrate (t_substrate) and sample thicknesses (t_sample) must satisfy a semi-infinite condition: t_substrate/h > 5, t_sample/h > 5 for < 1% error in measured k of the sample.¹⁴⁴ 

Tian et al. demonstrated soft, stretchable 3-omega sensors for use on the skin.⁷⁴ Fig. 8(a) illustrates the AC temperature oscillations of the Joule heating at 2ω frequency. The magnitude of ΔT changes with the physiological properties of the skin, such as water content. The out-of-phase (imaginary) component of ΔT (V_{3ω, ip}) directly relates to k¹⁴⁴ 

where

The in-phase component (V_{3ω, ip}) of the measured ΔT represents, however, a more reliable measure of k [Fig. 8(b)]:^144,154

Equation (30) illustrates that k_total is directly proportional to the slope of the measured ln(ω) vs V_3ω,_ip curve—all other parameters are constant/pre-determined within the measurement setup. The thermal diffusion length for the line heater is small for various relevant ω; thus, the thermal penetration depth does not surpass ∼100 μm for most line heater geometries investigated in the work of Ref. 74 [Fig. 8(c)]. The 3-omega technique can, however, allow depth profiling of the epidermis. Theoretical simulations reveal that epidermis at various water concentrations can be visualized as a function of measurement depth at different excitation frequencies [Fig. 8(d)].¹⁵⁵ The backside boundary condition can be exploited to measure tissue thickness below a characteristic excitation frequency, where h is no longer confined within the sample.¹⁴⁴ 3ω sensors can also be used to sense tissue contact, where V_3ω has a value 22% lower than air when in contact with skin, which is 20 $×$ higher than the difference sensed using V_1ω.⁷⁴ 

A key point of interest in Ref. 74 is the use of a serpentine geometry for the line heater (width of Au = 5 μm, width of PI = 20 μm) for stretchability (54% and 71% latitudinal and latitudinal elastic strain, respectively).⁷⁴ These heaters, unlike those with straight-line geometries, are subject to proximity effects typically at low frequencies (<10 Hz), where local thermal oscillations in one part of the heater can impact neighboring sections [Fig. 8(e)].⁷⁴ The effect can be illustrated by two parallel line heaters at a separation distance D, where thermal oscillations measured across one line heater are a superposition of its own oscillations and parallel line heater:⁷⁴ 

where A is the magnitude of the thermal oscillation determinable from Eq. (26) and B depends on the oscillation strength as a function of distance from the heater, which can be computed using numerical analysis. Another reported study describes 3ω measurements of k using 2D fractal heaters (Peano curve motif), likely also exhibiting proximity effects.¹²⁰ 

Measurements of isotropic heat transport based on the methods discussed in Secs. IV A and IV B are of increasing interest for uses in wearable and non-wearable devices. Table VI highlights several representative applications. A recent study (2020) introduces wireless, battery-free sensors that infer hydration (φ) based on thermal conductivity measured through interfaces to the skin that exploit near field communication (NFC) links to smart phones [Fig. 9(a)]. These sensors are thin (∼2.1 mm), flexible, and compact (3.1 $×$ 4.5 cm²) with the ability to gently mount across multiple body locations. The measurement determines the water content of the epidermis and dermis using the TPS technique. A micromechanics model which treats the skin as a composite of water in a tissue matrix relates the effective thermal properties of the skin to water content:⁷⁹ 

where

Here, k_dry and k_w are the thermal conductivities of dry skin and water, respectively. The sensing electronics and NFC receiving coils define the overall size of the device. The sensor dimensions (comprised of two SMD resistors, ∼0.9 × 0.9 mm² and one NTC thermistor 0.6 × 0.3 mm²) are limited by the SMD components.⁷⁹ Thin, patterned metal traces can circumvent these limitations and improve measurement sensitivity.⁷⁶ The results enable assessments of patients with various inflammatory diseases, including atopic dermatitis, psoriasis, urticaria, rocasea, and xerosis cutis. Figure 9(b) showcases measurements captured from patients with atopic dermatitis, a disease of the epidermis. The data reveal differences (average of ∼20%) in epidermal hydration levels of diseased sites (denoted by “L”) in comparison to sites of normal skin (denoted by “N”).⁷⁹ Some patients also display differences in dermal hydration level, indicating possible epidermal thickening. These and other insights can be important in guiding protocols for care of these diseases.

Alternative versions inspired by Ref. 79 replace NFC powering/communication with Bluetooth Low Energy (BLE) for wireless data transfer, powered by a lithium polymer battery.¹⁵⁶ A modified sensing structure uses NTC thermistors placed above the heater, thermally coupled together through a 75-μm-thick layer of PI, the insulating “body” of the flexible printed circuit board. The heater was embedded in a 180-μm adhesive silicone gel layer, compared to afore-mentioned structures where the heater is exposed to air on one side. Because this sensing platform contains the same materials and corresponding thermal masses (PI, copper traces, silicone adhesive), the top/bottom heater/thermistor structure offers no improvement in sensitivity to the lateral structure (i.e., for a given q, both structures exhibit the same range of ΔT for φ = 0% –100%). Additional thermistors used in the system to decouple the effects of changes in skin and environmental temperatures on ΔT do not assist in improving the system response time, which is dependent upon the thermal masses of the heating/sensing components and encapsulation layers.

Crawford et al. demonstrate soft, epidermal TPS sensors can be used for quantitative assessment of erythema recovery time from (1) solar radiation, causing sunburn, (2) heating of the skin with a source of thermal power, and (3) cooling of the skin with an ice pack [Fig. 9(c)].⁷³ The authors used two metrics, k and skin surface temperature T, to quantify erythema with a TPS sensor with r_heater = 2 mm and measurement t = 60s for q = 2 mW/mm². In case (1), prior to exposure to direct sunlight (UV index = 9) for one hour, the values of k and T for the skin were 0.46 W/m K and 36.5 °C, respectively, with only minor changes immediately after exposure [Fig. 9(d)]. When visual redness was greatest (t = 5 h after exposure), k = 0.57 W/m K and T ≈ 37.5 °C, due to elevated levels of near-surface blood flow. The values returned to baseline ∼4 days after exposure. The measured k of the skin showed similar correlations with the visual appearance of the skin for heat-induced erythema in case (2) but not in case (3). Reference 78 reports a similar experiment to case (3) using the application of a cold pack to the skin for ∼10 min to four subjects, resulting in lower measured k after the cold pack is removed using two sensors at different measurement depths (1.42 and 2.66 mm). The difference in agreement between the experiments in Refs. 73 and 78 may be due to subject-to-subject variations. This work provides a foundation for further investigations of thermal sensing as a quantitative basis for evaluating erythema recovery on a large population scale.

Cutaneous wound healing represents an additional application where thermal transport sensing offers quantitative information compared traditional practices for the assessment and care of wounds (e.g., clinical visual inspection). Hattori et al. developed multimodal thermal sensors (measurements of both skin surface temperature and k) that laminate gently and reversibly to the perilesional site of a cutaneous wound without causing irritation compared to conventional medical tape [Fig. 10(a)]. The 3ω technique at two different angular frequencies (1 and 3 Hz) allows for sensitive measurements of k for both the epidermis and dermis, important in detecting changes in blood flow during tissue healing. Studies conducted on patients with incisional cutaneous wounds over a 30-day period using an array of six equidistantly spaced sensors (total length = 45 mm) reveal that both skin surface temperature and k at different distances from the wound are useful in detecting inflammation during the healing process, resulting from increased blood flow and enzymatic reactions [Fig. 10(b)].¹²⁰ In contrast, the contralateral location on the body, serving as a reference to the wound site, does not exhibit significant variations in temperature. On-going work focuses on device layouts that allow direct lamination over the sensitive and complex geometry of the wound site, along with options for incorporating additional, complementary sensing techniques (e.g., pH, TEWL).¹²⁰ 

Another sensing approach for quantitative monitoring of wounds utilizes infrared imaging. As noted in Sec. III B, imaging techniques are attractive as they are completely noninvasive, without requiring contact of any material to the wound site. The FLIR ONE thermal camera, used as an attachment to a smartphone, allowed for the assessment of healthy and damaged tissue in patients with diabetic foot ulcers.¹⁵⁷ Analytical models were used to extract k from the infrared images. The authors detected temperature changes of up to 6.9 °C between the wound and adjacent tissue and associated reductions in k of up to 84.3%.¹⁵⁷ While imaging techniques are clearly attractive for a multitude of applications, there are drawbacks related to cost and the requirement of patient immobilization for accurate measurements.⁷⁶ 

Okabe et al.'s work on a guard-heater thermistor probe in a pen-like format for characterization of malignant melanoma lesions represent another example of thermal sensing as the basis for assessing the health of the skin [Fig. 11(a)].⁸⁸ The device utilizes a pulsed power decay technique (similar to the TPS method) whereby a constant DC voltage (initial power 3 mW) delivers thermal power in the form of a pulse (∼3 s duration) to the surface of the skin.⁸⁸ Recordings of the temperature and power during heating and the temperature during cooling occur continuously, to allow determination of k through an energy balance equation. The result depends on the integral of the temporal change in temperature during cooling and the integral of the power across the thermistor during heating.¹⁴² The authors demonstrate the use of this scheme to show that the effective k of melanoma lesions are consistently higher than those of non-lesional areas [Fig. 11(b)]. In addition, the data indicate a positive, linear relationship between tumor thickness and k. The findings suggest a fast, simple, and noninvasive basis for characterizing melanoma tumors, with the potential to avoid cumbersome imaging techniques or invasive skin biopsies.

Through schemes in adjusting the measurement depth with the operating frequency, the 3ω method can determine the k of single, cancerous biological cells with volumes as small as ∼10 pl, where the effective depth is less than 10 μm.¹⁵⁸ In this setup, a nanoscale heater (half-width = 200 nm, allowing h < 5 μm) defined using electron-beam lithography rests below a micro-well that confines a cell [Fig. 11(c)].¹⁵⁹ Studies demonstrate that normal human skin cells (k = 0.593 W m⁻¹ K⁻¹) have k 2.2% higher than that of basal cell carcinoma cells (k = 0.579 W m⁻¹ K⁻¹) with high significance (p = 0.0031) [Fig. 11(d)]. Possible explanations for the difference in k between cancerous and normal skin cells are increased protein content in cancer cells, reduced water content in cancer cells, and an increase in glycogen content in conjunction with an increase in lipid content.¹⁵⁹ 

Tian et al. report soft, skin-conformal 3ω sensors for detecting the thermal properties of the skin, with capabilities in accurate measurements of subtle changes in k and α of the skin, with the ability to adjust the effective depth of sensing through the operating frequency.⁷⁴ This platform can monitor subtle changes in perfusion, for instance, through slap-induced hyperemia. Increased surface perfusion leads to increases in the thermal conductivity and diffusivity by ∼32% and ∼13.3%, respectively, indicating effusion of water out of the skin cells of the epidermis and increased microvascular blood flow in the dermis, consistent with visual reddening of the skin [Fig. 6(c)].

Son et al. demonstrate applications of heat therapy and associated increases in k and α, thereby further establishing the dependence of the thermal properties of the skin on physiological parameters, such as blood flow and water content. These studies utilize thin film metal Joule heaters operated at high thermal power densities to heat the skin to different values based on the thermal diffusivity of the underlying tissue.¹⁶⁰ In this work, the authors develop a wearable integrated memory unit to store data and trigger therapy [Fig. 12(a)]. The heat from the heaters accelerates diffusion of drug-loaded m-silica nanoparticles by first degrading the physical bonding between the nanoparticles and the drugs and next, increasing the transdermal drug diffusion rate [Fig. 12(b)]. Skin temperature is monitored during the drug delivery process. Thus, heat therapy and closed-loop feedback represent attractive options that can be useful in the diagnosis, monitoring, and therapy of skin diseases and tracking skin health for a multitude of applications.

Section IV focuses on “static” conditions where convective fluid flow in the skin can be neglected entirely or can be considered time invariant. As discussed earlier, volumetric blood perfusion, w describes omni-directional capillary/volumetric blood flows through a volume of tissue. Unlike perfusion, blood flow velocity through a vein or artery is a vector quantity, with magnitude v (expressed in mm/s or ml/min). Assessments of this quantity can be important for evaluations of vascular and tissue health.^161–163 The following presents a brief overview of traditional measurements of near-surface w and v in the skin.

Conventional, noninvasive flow sensors (e.g., strain gauge plethysmography) rely on mechanical effects to measure v over a wide range (7–268 ml/min) via changes in volume of a particular body location (typically the limbs) during periods of occlusion and release by one or more pressure cuffs. Such approaches are, however, cumbersome for continuous tracking of changes in flow and they are susceptible to motion artifacts related to respiratory mechanics (movements of the thoracic cage).^164–166 Acoustic techniques, such as contrast-enhanced ultrasound imaging, can evaluate blood flow/perfusion through the skin and other organs.^167–169 Contrast-enhanced ultrasound is similar to conventional Doppler ultrasound, but with the addition of intravenous injection of contrast agents that perfuse through the bloodstream to other blood vessels and organs. The contrast agents are 1 – 7 μm diameter microbubbles of air or perfluoro gas encased in a phospholipid, surfactant, or denatured albumin shell, designed to exhibit resonant frequencies in the range of 2–17 MHz, aligned with ultrasound used in clinical environments.¹⁷⁰ Upon exposure to the ultrasound, the microbubbles oscillate, causing echo-enhancement and increased contrast.^{168,170–172} Continuous data cannot be obtained with this technique, however, due to the need for patient immobilization and intake of contrast agents for quantifying w and v.^171–174 

Optical sensing methods, such as laser doppler flowmetry (LDF) and photoplethysmography (PPG), avoid some of these limitations. LDF operates by illuminating a local surface area of tissue with a single wavelength of light (most commercial systems use a 780 nm laser source) and evaluating the resulting frequency shift in the light backscattered by red blood cells.¹⁷⁵ The measurement typically uses an optical fiber probe, placed in contact with the skin, to emit the source wavelength and receive the backscattered signal. The spacing between the emitting and receiving fibers, along with the source wavelength dictate the measurement depth: e.g., for a 780-nm source wavelength, LDF can probe the skin at a depth of ∼0.73 mm and volume of 2.7 mm³.¹⁷⁵ High temporal resolution (milliseconds) allows for rapid, continuous measurements.^176–178 The net flux of red blood cells (the product of the red blood cell concentration and v) is directly proportional to the magnitude of the wavelength shift, thereby yielding an estimate of microcirculatory blood flow in arbitrary units, not perfusion units.¹⁷⁹ LDF is sensitive to a wide range of w (0–300 ml/min per 100 g tissue).^180–186 Disadvantages include poor spatial resolution and measurement artifacts related to deformation of the probe fibers and pressure applied to the skin by the probe.¹⁸⁷ Laser speckle contrast imaging (LCSI) is a similar alternative to LDF, with the added advantage of large surface-area measurements.¹⁸⁸ A red- or near-infrared laser source that illuminates the surface of tissue generates a random speckle pattern (varying spatial intensity) that is detected by a silicon charge coupled detector (CCD).¹⁸⁹ In the presence of flow, the speckle pattern is “blurred” resulting in reduced contrast in the corresponding region of the image. The degree of contrast reduction depends on the blood velocity.¹⁸⁹ While this technique does not require physical contact, the required optics cannot be integrated into a compact wearable device.

PPG relies on similar underlying measurement physics. An infrared (800–960 nm) LED is the most common illumination source, selected for absorption of hemoglobin in this range of wavelengths.¹⁹⁰ A photodiode captures some of the backscattered light. PPG is most commonly used to measure heart rate, as the AC component of the backscattered light relates to pulsatile flow through the arterioles and arteries, independent of source wavelength.¹⁹¹ In contrast, the DC component of this signal represents non-pulsatile, average blood volume in the tissue at depths up to 3 mm, depending on the illumination wavelength and the distance between the LED and photodiode.^{165,191–194} Like LDF, PPG only yields qualitative estimates of w. Cycles of respiration, processes associated with thermoregulation, activity of the sympathetic nervous system, and overall motions of the body also affect the DC component of the PPG signal, as further complications to interpreting the response.¹⁹⁵ 

Thermal sensors are attractive alternatives for noninvasive, quantitative measurements of both near-surface cutaneous w and v. These thermal flow sensors can easily be rendered into wearable and epidermal form factors, thereby removing measurement sensitivity to body motions (e.g., nonconformal contact/delamination of the sensor from the skin), the need for application of pressure to the skin (e.g., with a rigid probe), and bulky, wired electronics, allowing free motion of the user.^{76,80,87,151,196} Heaters and temperature sensors arranged in specific geometries allow for measurements of v at different depths into the tissue. For example, recent work illustrates a 4 $×$ 4 array of small-area (1 mm²) thermal sensors for quantitative measurements of venous blood flow in the skin by way of multiple parameters—w, v, k, α, and T_0.⁷⁶ Subsequent sections detail different thermal flow sensing techniques, followed by wearable architectures and their applications to skin and other important physiological health conditions.

Thermal techniques to measure perfusion involve the same components as those for simple sensors of the skin's intrinsic thermal properties. A heater locally induces a temperature change (ΔT) on the surface of the skin, and one or more temperature sensors capture the resultant spatiotemporal changes in temperature. The main differences lie in analysis approaches and models of the transient and steady state thermal responses.⁹⁰ Valvano et al. (Ref. 210) used an electrically resistive, spherical thermistor mounted at the tip of a needle, or catheter for measurements of w in a scheme known as the step-temperature technique, where (i) the initial temperature of the tissue T₀ is measured and (ii) the thermistor is self-heated to a fixed, pre-determined temperature T > T₀ while the power through the thermistor q is varied to maintain the constant T, for a measurement time on the order of ∼10–20 s, depending on the geometry of the probe.^90,197 The thermal power q required to maintain T varies according to⁹⁰ 

where Γ is the steady state, volume-average power (W/ml) of the thermistor, B is the slope of the transient power rise (in W s^−1/2/ml), and f(t) is the transient power function given by⁹⁰ 

where c_bl is the specific heat capacity of blood, and k_m and α_m are the thermal conductivity and diffusivity of unperfused tissue matrix, respectively. An effective thermal conductivity (k_eff) and diffusivity (α_eff) model can be used to determine perfusion. The effective values combine the contributions of perfused and unperfused tissue. Equations (34) and (35) can be used to find the relationship between k_eff and q, through a closed solution to the well-known bioheat equation.⁹⁰ The value of k_eff is⁹⁰ 

T is the pre-determined temperature change during the measurement, a is the radius of the bead, and k_b is the thermal conductivity of the thermistor. When w = 0, k_eff = k_m. The value of Γ can be determined by a linear regression of values of f(t) as a function of t^−1/2. The value of α_eff is derived from the solution of the transient model and is given by⁹⁰ 

B/Γ can be computed from least squares regression of the measured values fit to (Γ+Bt^−1/2), where B is the slope of the transient power curve. Perfusion can be isolated for the steady-state solution:⁹⁰ 

where w can also be calculated from the transient solution (w₂):⁹⁰ 

Reference 90 provides a measurement procedure for calculating w with this model. With this approach, reproducibility in k_eff is better than 0.6% and that for α_eff is better than 2%, resulting in a 5% reproducibility in computed w. Systematic studies show that the measurement error for w from the k_eff model [Eq. (38)] determined by comparing true (acquired using radioactive tracing techniques) and computed values with tissue samples was 10.6%, while that from α_eff [Eq. (39)] was 24%. In addition, the sensitivity to changes in perfusion was ∼7% using Eq. (38). The use of α_eff to determine tissue perfusion, thus, requires further study.

An alternative approach known as the pulsed decay technique can also be used to measure w. Here, a short current pulse of constant q is applied to a thermistor or RTD.¹⁹⁷ ΔT rises to a maximum value and then decays at a rate dependent on w, the geometry of the heating/sensing element and other factors. The analytical solution for the temperature decay at the center of a sphere is given by¹⁹⁷ 

where z is the axial variable in meters, τ is dimensionless time, given by $τ=αt/a2$⁠, and γ is dimensionless blood flow parameter given by $γ=wcbla2/k$⁠. The values k and α represent the thermal transport properties of the tissue. The measurement sensitivity depends on w, k and sensor geometry. This sensitivity is given by¹⁹⁷ 

where $ΔTunperfused(t)$ is the response when w = 0, $ΔTperfused(t)$ is the response when w > 0, for a time window t_w (the length of time where the pulsed decay response is largely influenced by perfusion). Equation (41) represents a 10% difference between $ΔTunperfused(t)$ and $ΔTperfused(t)$⁠. For example, for tissue density ρ = 1000 kg/m³, c_bl = 4000 J/kg K, k = 0.5 W/m K, the time window for a spherical probe of r = 3 mm and w = 10 kg/m³ s do detect an appreciable difference is 30 s, but for r = 6 mm and same w would be hundreds.¹⁹⁷ The smallest measurable w (w_min) depends on the sensor size. For a sensor with r = 2 mm, w_min = 30 kg/m³ s and for one with r = 8.6 mm, w_min = 1.6 kg/m³ s.¹⁹⁷ Lower values of w require larger heating elements, a trend that applies to most heated thermistor approaches, including the step-temperature and constant power measurement schemes.

The closed analytical solutions described here and in Ref. 90 do not include tissue inhomogeneities due to large blood vessels or due to local variations in perfusion and tissue properties. In cases where such effects are significant, other analytical or numerical approaches may be required.¹⁹⁷ Apart from these step-temperature and pulsed-decay techniques, other thermal methods for the measurement of perfusion include the heat-washout method (described in a later section)^198,199 and combined heat flux/temperature sensor measurements.^200,201

In addition to measurements of non-directional, microvascular flow, determining the flow velocity through large vessels is of great importance. Macrovascular flow sensors also rely on a heater and one or more temperature sensors distributed along the flow channel. Figure 13 illustrates heater/sensor geometries for three thermal flow sensing techniques: (i) anemometry, (ii) calorimetry, and (iii) time-of-flight (ToF). In each of these methods, the heater operates in one of two modes: (i) to deliver constant heating power q, with variable temperature at the heater T_heater or (ii) to ensure a constant T_heater, with variable q.

Anemometric sensors offer the simplest geometry for the measurement of v, comprised of a single heating/sensing structure (the heater and sensor can be the same element, or two thermally coupled elements) [Figs. 13(a)–13(c)]. Most thermal anemometers use a single fine, cylindrical wire (∼1–15 μm diameter) as both the heater and sensor²⁰² for measurements over a wide range of v (< 2 μl/min–10 l/min), with low noise (<0.01% of the mean value) and high-frequency responses (>100 kHz possible).^202–205 The heater typically operates in a constant T mode, though operation in constant q mode is also possible. For the former, the current is adjusted, using sensing circuitry, to maintain a constant T_heater. Underlying fluid flow causes convective heat loss.^202,206 The resulting change in voltage V required to maintain constant T_heater can be used to determine v. The relationship between V and v for a hot wire anemometer can be analytically represented with a combined form of King's Law:^207,208

where μ and k are the fluid viscosity and thermal conductivity, respectively; T_w is the temperature of the wire; and T_a is the ambient fluid temperature. A, B, and n are empirical constants that depend on the sensor dimensions and fluid properties and can be obtained through calibration with known materials and fluids.^207,209 In constant T mode, the expression (T_w – T_a) is constant and V is a function of v alone, while in constant q mode, V is constant, and T_w is a function of v. Measurement accuracy of v using hot-wire anemometry can be affected by calibration accuracy and drifts in the values of A, B, and n in Eq. (42) related to change in fluid temperature and pressure.^210–213 The above analysis is valid for anemometers embedded within the flow channel, typically for implanted devices in arteries, such as the aortic artery,²¹⁴ or for the measurement of skin flap viability.²¹⁵ The authors in Ref. 215 demonstrate a small probe (smaller than a 2-mm diameter biopsy needle) containing a heater, and four temperature sensors (one thermally coupled to the heater, similar to anemometry) for the measurement of microvascular flow velocity through skin flaps in porcine models [Figs. 14(a) and 14(b)]. This sensor operates in constant q mode, where a stable baseline T_w – T_a is achieved before inducing ischemia (clamping of the deep superior epigastric artery), reperfusion (release of the clamp), and congestion (clamping of the deep and superficial superior epigastric veins) of the flap [Fig. 14(c)]. The convective fluid flow changes the magnitude of T_w – T_a according to

where r is the circular radius of applied heat (using a copper ring heat spreader to improve the overall device sensitivity), $χ$ is the volume fraction of blood, and x is the distance to the center of the heater, and $Fxr$ is

J₀ and J₁ are the Bessel functions of the first kind (of orders 0 and 1, respectively). This model accounts for both convection and heat conduction. The relationship between w and v in the model presented in this work is given by

where A_vessels is the effective, cross-sectional area of the microvascular blood vessels. Using these models, the authors find that the induced ischemia leads to a measured v = 0.3 mm/s, the congestive state causes v = 0.2 mm/s, for a baseline of v = 1 mm/s. Perfusion can also be computed using Eq. (45). Thermal anemometry, as demonstrated in this work, is promising for applications such as assessments of skin flap viability and in the future could be used for direct interfacing with large vessels of interest to determine macrovascular v. Development of wearable, noninvasive thermal anemometry devices is the subject of on-going work.

Calorimetric sensors use the constant q method. A thermal power density q induces a local temperature change (ΔT_heater) on the surface of the skin, above the flow channel. Two temperature sensors, placed away from the heater at lateral distances s₁ upstream of the flow and s₂ (distance between the edge of the heater to the center of the temperature sensor) downstream of the flow, record a differential temperature ΔT_ud = ΔT_s1 − ΔT_s2 [Figs. 13(d)–13(f)]. Typically, s₁ = s₂ = s. The magnitude of v influences ΔT_ud. When v = 0, the lateral heat distribution on the skin is isotropic, and hence, ΔT_ud = 0. When v is finite, ΔT_downstream > ΔT_upstream, and thus, ΔT_ud > 0 [Fig. 15(a)].

Apart from v, several thermophysical properties affect ΔT_ud, including k, heat capacity c, and density ρ of both blood and tissue, blood vessel depth, and radius R_vessel. Device geometry (i.e., heater radius r_heater and s) also influences ΔT_ud. For example, for the epidermal calorimetric sensing structure reported by Krishnan et al., ΔT_ud is maximum for v = 0.1 ml/min when s ≈ 3 mm.¹⁹⁶ The values for k, c, and ρ of blood are well known in literature and can be assumed as constants.¹⁵¹ The multi-parameter dependence of ΔT_ud on tissue thermal properties and vessel geometry complicates the extraction of v, but recent research demonstrates methods to reduce the number of unknowns. To determine the tissue thermal transport parameters, the authors in Ref. 151 used TPS at short measurement times (t = 2 s) to measure local tissue k, α with a radial array of 14 individual epidermal sensors, each with r = 0.5 mm.¹⁵¹ Experimentally measured ΔT_ud normalized by its steady state value (⁠$ΔTud¯$⁠) is independent of v and r_vessel, allowing for the extraction of blood vessel depth through fitting to computational results based on finite element analysis [Fig. 15(b)]. Finally, $ΔTud¯$/ΔT_heater yields a relationship with the remaining two unknown variables, r_vessel and v; r_vessel can be approximated by values found in the literature specific to body location, leaving v as the final unknown variable.

Calorimetric sensors exhibit a non-monotonic response to v [Figs. 15(c) and 15(d)]. As v increases from v = 0, thermal diffusion dominates the response and $ΔTud¯$ increases until v = v_to (turnover velocity), after which convective cooling of the heater causes a decrease in the measured $ΔTud¯$ (i.e., $dΔTud¯dv<0$⁠).²¹⁶ The response, then, can occur in either the low flow regime (v < v_to) or the high flow regime (v > v_to). Sensitivity to a particular range of v and v_to can be tuned by adjusting r_heater and S.²¹⁶ Venous blood flow velocities fall within the high-flow regime reported for the sensing geometry in Ref. 151 (r_heater = 1.5 mm, s = 1 or 3 mm). Epidermal thermal flow sensors can measure changes in v that have frequencies < 0.1 Hz, defined by the response time of the sensor for these measurement depths (∼10 s).¹⁵¹ 

The main sources of error in these measurements result from changes in ambient conditions (ambient temperature, skin temperature, and air convection) and from imperfect alignment of the sensors above the flow channel of interest.^87,151 Air convection can be minimized with the inclusion of small, sealed air gaps or thermally insulating polyurethane (PU) foams placed above the heating/sensing components.^79,87 Reference 87 reports an order-of-magnitude improvement in SNR with the PU foam approach. Changes in ambient/skin temperature can be accounted for using pulsed sensor operation or separate temperature sensors for measurements of environmental/skin temperature.^151,156

Calorimetric sensors can also be operated as thermal ToF sensors,²¹⁷ also using the constant q method. The simplest layout comprises a heater and single temperature sensor (separated by distance S) overlaying the flow channel [Figs. 13(g)–13(i)]. The heater delivers a thermal pulse to the skin (typically < 100 mW, < 2 s duration). A downstream sensor captures ΔT as a function of t (transit time of the thermal pulse) [Figs. 7(h)–7(i)].^218,219 Assuming a line heating source of length L (often used in ToF systems), heat transport through a fluid is given by the combined diffusion and forced convection equation as follows:²²⁰ 

where Q is the total the heat (in Joules) injected into the system by the heater. The analytical solution to this equation is²²¹ 

Differentiating Eq. (47) with respect to t at the location of the heater/sensor (y = 0) yields the “time of flight”(ToF) as follows:²²⁰ 

Equation (48) is valid at high v, for the condition 4αt ≪ S, corresponding to the case that forced convection from flow dominates the response and the influence from thermal diffusion is minimal.²²⁰ At low v, when diffusion must be considered, the following holds:²²⁰ 

The value of τ is experimentally derived from $dΔTdtt=ToF=0$⁠, which represents the maximum of the ΔT vs t curve measured by the downstream temperature sensor.²¹⁸ ToF sensors are most suited for measuring low flow rates²²² at small values of ΔT (∼1 °C).^219,τ can be detected for these small ∼1 °C thermal pulses even in the presence of baseline T drifts (as high as $±$ 5 °C): evaluation of $d2Tdt2t=ToF2=0$ yields τ₂ which has sensitivity only to the thermal pulse, and is a faster measure of pulse transit time.²¹⁹ 

Point measurements of temperature or temperature maps obtained by an infrared camera alone can be insufficient for characterizing complex health conditions, such as cardiovascular disease.¹⁴⁹ Instead, parameters of vascular blood flow velocity, viscosity, volume, and pressure are of much greater relevance.¹⁴⁹ Laser-induced dynamic thermography (LIDT) allows for the measurement of v in superficial veins/arteries by local heating of the skin using a laser source (810-nm, 1.2 W through an optical fiber of diameter 100 μm) and tracking skin temperature changes with infrared thermography. Jin et al. demonstrated the use of LIDT to measure superficial arterial v in rabbit auricle skin.¹⁴⁹ The optical fiber probe (placed 50 mm away from the rabbit ear) focused on a local area of the skin above the auricular artery and induced local heating (< 10 °C) for 30 s [Fig. 16(a)]. Infrared thermography (sampling rate of 3.75 frames/second) captured spatiotemporal characteristics of the heat before (10 s), during (30 s), and after (80 s) delivery of the heat to the skin. Similar to thermal ToF, v follows from measurements of the transit time τ across a given distance over the artery [Fig. 16(b)]. Post hoc image processing and analysis isolates the auricular artery from the rest of the image to ultimately determine v (36.94 and 38.74 mm/s for the left and right artery, respectively) [Fig. 9(a)]. Theoretical models that include the thermal properties of blood and tissue (k, mass m, and c_p), the heat transfer coefficient H and temperature T of blood and air result in values that are comparable to those obtained by Doppler ultrasound. Errors in measurements of the temperature of the blood lead to ∼5% error in extracted v, and error in H_blood, H_air leads to ∼6% and 22% error in v, respectively, illustrating that air convection can have a significant influence on the measurement. Uncertainty in the depth of the vessels beneath the skin surface represents an additional source of error in the computed v.

Recent research in noninvasive and wearable thermal flow sensors create means for continuous monitoring of patient health, of direct clinical relevance. Applications range from mapping of micro- and macro-vascular cutaneous blood flow during various physiological circumstances to measurements of ventricular shunt flow in hydrocephalous patients through the skin.

Techniques based on thermal anemometry can measure cutaneous, microvascular w of the skin with peripheral neuropathy and atherosclerosis in type 2 diabetes patients.^198,199 References 198 and 199 report an anemometer-based heat-washout method, performed using a probe consisting of a thermally coupled heater and temperature sensor attached to the skin using silk tape and contact fluid between the skin and probe.^198,199,223 After measurement of the initial temperature of the skin T₀, heating for 3–5 min with constant q yields a steady state increase in temperature $ΔT¯$ between 2 and 10 °C. After saturation at $ΔT¯$⁠, the heater was turned off and skin T was recorded at a sampling rate of 0.1 Hz until saturating at ∼T₀. The heat “washout” refers to the measured exponential temperature decay after the heater is turned off. Plotting ΔT as a function of t in logarithmic scale produces a straight line with a slope m (units min⁻¹) proportional to Q²²⁴ 

where Δw is the local volumetric rate of blood flow leaving a volume of tissue ΔV. K is the tissue partition coefficient, given by

The authors in Ref. 224 assume constant K ≈ 1 ml g⁻¹, based on literature values for the thermal properties of tissue and blood for all computations of w. The mean w for diabetic patients [47.6 ml (100 g min)⁻¹] and healthy patients [53 ml (100 g min)⁻¹], when lying in a recumbent position on the forefoot were comparable. However, differences arose during changes in posture. Lowering the leg 50 cm below heart level increased w of the right hallux by > 50% in 5/7 non-diabetic patients with intermittent claudication (a symptom of peripheral artery disease), where the remaining two experienced a slightly lower increase in w; this change was < 20% in 4/6 healthy patients, where the remaining two subjects exhibited no change in w. In diabetic patients, the increase in w was > 20% in 7/9 patients. Thermal flow sensing of this type, therefore, holds potential for identifying thermal signatures associated with atherosclerosis and peripheral neuropathy in the pathogenesis of diabetic foot ulcer formation.

Sim et al. report a miniaturized device (20 $×$ 23 $×$ 0.9 mm³) using a similar heat-washout technique for the measurement of peripheral blood perfusion with skin contact force compensation [Fig. 17(a)].²²⁵ The device in this case consists of a thin-film (300-nm Ni) metal RTD and four doped-Si piezo resistors as a contact force sensor. The authors compare the performance of the heat washout data to perfusion units measured by LDF with linear correlation (r = 0.94). Large differences in measured blood flow from reference sites with no contact force applied are observed (up to ∼75%) when appreciable contact force (∼3N) is applied to the skin (inducing vasoconstriction). Experimental studies on human subjects using both the heat-washout sensor and LDF reveal an approximately linear dependence of the measured blood flow on contact force (− 31.7% N⁻¹). Contact force compensation using this linear approximation reduces differences between measurement and reference sites to < 6.4%.

Soft, epidermal electronics for thermal calorimetry have also been used for measurements venous blood flow and tissue perfusion for applications in vascular diseases like atherosclerosis, sickle cell anemia, diabetes, and chronic kidney disease, and inflammation induced by external sources, such as sunburns [Fig. 17(b)].¹⁵¹ The device platform reported in this work allows for the detection of flow in vessels with a maximum depth of 2 mm and radius as small as 0.25 mm, and a flow rate range of v = 0.1–100 mm/s.¹⁵¹ The epidermal form factor allows for conformal contact, reducing error related to poor thermal contact and to relative motion between the device and skin. A radial array of ∼14 temperature sensors (r_sensor = 0.5 mm) surrounding a central heater (r_heater = 1.5 mm) at s = 3.5- or 5.5-mm heater-edge-to sensor-center spacing allows for spatial mapping of flow rate without the need for precise alignment over the superficial vein/artery of interest. Applying pressure to various locations around the perimeter of the device (laying over a near-surface vessel in the wrist) illustrates the ability to track both magnitude and direction of blood flow without exact placement. Pressure applied directly above the vessel reduces the measured blood flow, while application away from the vessel causes no appreciable change in the measurements. The same experiment performed over a region of the forearm with no visible large blood vessels illustrates no measurable change with applied pressure, indicating the ability to distinguish between regions of macrovascular and microvascular flow. Device measurements of venous blood flow overlying a vein in the wrist during occlusion/reperfusion of the upper arm by a blood pressure cuff (∼200 mm Hg) and comparison with an LCSI tool show good correlation. The epidermal calorimetry device captures additional pulsatory signals for a subject with deep veins (∼1.7 mm) where the LCSI tool does not, due to limited measurement depth of the latter. The detection of perfusion can be accomplished with measurements of ΔT_ud overlying regions, as described above, without the presence of large vessels, such as the fingertips. The authors demonstrate the ability to track perfusion changes, with good correlation to an LCSI tool, associated with induced urticaria and deep breathing.

Krishnan et al. followed up on the work of Ref. 151 for a different application: monitoring of ventricular shunt flow through the skin in hydrocephalous patients. Hydrocephalous is a neurological disorder characterized by overproduction or compromised reabsorption of cerebrospinal fluid (CSF) produced in the ventricular system of the brain.²²⁶ Treatment typically entails implantation of a thin silicone catheter (< 3 mm outer diameter) that drains CSF from the brain to a different part of the body, such as the peritoneum, pleural cavity, or right atrium. Malfunction of a valve (“shunt”) that regulates the flow rate of CSF or clogging of the catheter itself can lead to nonspecific clinical systems, thus typically requiring imaging (x-ray, CT, and MRI) for accurate diagnosis [Fig. 18(a)].^226–228 The catheters pass through superficial layers of the clavicular dermis (1 – 2 mm) and support relatively low rates of flow of CSF (< 1 ml/min), ideal for noninvasive thermal sensing from the surface of the skin.^87,196,229 Soft, epidermal devices designed for this purpose include (1) a square array of ∼100 temperature sensors surrounding a central heater (r_heater = 2.5 mm) [Fig. 18(b)] and (2) a linear array of 4 temperature sensors spaced equidistantly from the central heater (of same radius) [Fig. 18(c)]. The square array enables evaluation of catheter position and the presence of flow. The linear array represents a simplified form of the square array, for measurements of v when the catheter position is known. For a typical patient, the authors find that v_to = 0.05 ml/min, within the range of physiologically relevant CSF flow rates through the catheter [Fig. 18(d)]. In general, a measurement of ΔT_ud yields two solutions for v. To discern whether the measurement lies within the high- or low-flow regime, the authors propose use of the average of the upstream/downstream temperature sensors $Tud¯=12(Tus+TDS)$⁠. T_DS varies non-monotonically with v, while T_US decreases monotonically for all v; hence, $Tud¯$ is nearly constant for v < v_to and decreases for v > v_to [Fig. 18(e)].⁸⁷ Data on hydrocephalous patients indicate cases of occluded flow (v = 0.01–0.0027 ml/min) which are nearly one order of magnitude lower than those of un-occluded, healthy flow rates (v = 0.13–0.36 ml/min) with statistical significance (p = 0.012) [Fig. 18(f)]. Measurements of flow through the catheter before and after surgical revision and other treatments show trends that agree with clinical imaging (CT and MRI) and evaluations of patient health status. Demonstrations of wireless data transmission capability through BLE and a follow-up work (2020) allow for untethered/unrestricted patient movements and studies of flow rate with respect to patient posture [Figs. 18(g)–18(i)].⁸⁷ The systems described in Ref. 87 use commercial SMD resistors and NTC thermistors for the heater/sensor, respectively, for ease of fabrication and reduction of overall costs.

Thermoelectric ToF has also been used to find CSF flow rates through hydrocephalous shunts.^222,230 Instead of heating, local cooling of the skin (∼4° C) using a semiconductor thermoelectric cooling (TEC) device produces the required temperature gradient for the measurement [Fig. 18(j)]. Other work uses ice instead of a TEC for local cooling of the skin.^231,232 The time-difference τ between the minimum temperature (resulting from the cooling) measured by the two temperature sensors (located at distances 20 and 30 mm downstream of the TEC, respectively) is the time of flight. The value of v is computed as the distance between the two temperature sensors (Δy) divided by τ. The authors in Ref. 230 derive v through a thermal equivalent circuit (lumped element model) for the skin, CSF, and modified catheter tube including sections of titanium to enhance thermal coupling to the skin. The relevant parameters are R_l, the lateral thermal resistance along the skin, R_sh, that along the catheter tube, R_sk, between the skin and titanium, and R_cv, between the titanium and CSF. Replacing three sections, directly underlying the TEC and temperature sensors, of the silicone catheter tube with a biocompatible, high-thermal k metal (titanium, 21.9 W/m K) reduces R_sk and R_cv. The authors illustrate benchtop sensing capabilities for physiologically relevant CSF flow velocities (v = 0.5–1 mm/s) and ∼1.2 mm thick skin [Fig. 18(k)].

In another measurement strategy, a commercial device called the “ShuntCheck” (similar to an anemometer) measures ΔT = $Tcenter$ - $T¯ref$ (induced by an ice cube applied to the skin for ∼60 s) from a central temperature sensor directly along the flow channel (T_center) compared to the average of two reference temperature sensors (⁠$T¯ref$⁠) lying perpendicular to the direction of flow [Fig. 18(l)].²³¹ In the presence of flow, the central temperature sensor experiences net cooler T than the reference temperature sensors; conversely, when there is no flow, all three temperature sensors record nearly the same T. Measurements on hydrocephalous patients with malfunctioning shunts pre-and post-operatively illustrate visible ΔT minima associated with the presence of flow and with good statistical sensitivity (80%) and specificity (100%) [Fig. 18(m)].

Emerging methods in thermal sensing provide the basis for versatile measurements of skin health. The ability to capture spatiotemporal variations of temperature across the surface of the skin has widespread potential for monitoring skin disorders. Measurements of skin temperature can also serve direct or indirect indications of core body temperature as a core vital sign. Integration with, or operation as heat sources, allows temperature sensors to be used to assess local thermal transport characteristics, as indicators of hydration status or microvascular perfusion, with applications in diagnosis and monitoring of cutaneous diseases and wound healing. Arrays of heaters and sensors can also be used to quantitatively measure flow rates of blood through large, near-surface blood vessels, and cerebrospinal fluid through ventriculoperitoneal shunts. In all cases, physics-based models define optimal layouts and modes of operation. Multimodal methods that exploit multiple different measurement techniques allow a single device to output various different parameters simultaneously (e.g., T, k, v, and w). Wireless data transfer capabilities permit free, untethered use in non-clinical environments, as alternatives to traditional optical and imaging techniques used for the analysis of vascular and tissue health. The various thermal sensing technologies outlined here allow for precision, low-cost measurements. Development of soft, epidermal devices greatly enhance applicability and use of such devices for both clinical and non-clinical environments.

Distilling the individual contributions of perfusion and macrovascular flow to the measured thermal responses, especially within physiological regions where both venous and capillary flow are significant, remains a challenge. Convective flow from v or w both influence ΔT or Δq. Spatiotemporal mapping offers the greatest potential in capturing both the magnitude and direction of flow. Techniques like those found in Ref. 151 offer the ability to compute v and w using wearable device form factors, while optical mechanisms, such as LCSI offer alternate, non-wearable approaches to accomplish similar goals.

Combining thermal sensors with other complementary methods, such as sweat analytics, skin pH, transepidermal water loss, strain, and modulus is another important future direction for applications in cutaneous and systemic disease diagnosis and monitoring. For example, Lee et al. (2016) developed a graphene-based electrochemical device with thermo-responsive microneedles for monitoring and therapy of diabetes.²³³ The device contains a heater, and temperature, humidity, tremor (strain), glucose, and pH sensors, along with polymer microneedles that can deliver drugs transcutaneous upon thermal activation. This suite of sensors is essential for monitoring the pathogenesis of diabetes and for enabling closed-loop feedback control.

Programmable thermal therapy, which refers to the controlled delivery of heat to the surface of the skin at a desired temperature and duration, is another area of interest, where heat induces local vasodilation and thermal expansion of collagen tissue that can reduce swelling, muscle pain, and alleviate numbness.²³⁴ Wearable embodiments entail Joule heating of metal nanoparticles or other conductive nanomaterials embedded in elastomers. Stretchable, thin films of metal patterned into filamentary mesh/fractal geometries represent an additional option for wearable heaters.²³⁵ A recent work in flexible, stretchable, wearable thermotherapy bands and patches illustrates the ability to provide controlled heat to the skin for such purposes.^234,236 Such heating can also be used to study hemodynamic properties and tissue condition, including responsiveness to applied thermal stimuli as an indicator of vascular health.²³⁷ Thermally induced changes in biological properties of the skin and individual cell types also merit further study.

While this review focuses on noninvasive thermal measurements of the properties of the skin from its surface, injectable and implantable thermal sensors are also important, not only for skin but for underlying organs as well. A recent work (2022) demonstrates, for example, the use of wireless, implantable thermal probes for measuring changes in perfusion of skin flaps.²¹⁵ Injectable thermal sensors and “smart” balloon catheters can assist in cardiac ablation procedures.^238,239 This emerging field of implantable sensors for measurements of the thermophysical properties of internal organs holds great promise not only in monitoring disease progression but also in understanding disease mechanisms. Ultimately, measurements of the thermal properties of the skin and other tissues have great potential to impact our understanding of biology and medicine. This area of research combines fundamental aspects of measurement physics with practical opportunities in translation medicine, in a manner that suggests a vibrant future.

The authors would like to thank S. Coughlin for useful discussions. S.R.M. acknowledges support from the NSF Graduate Research Fellowship (No. NSF DGE-1842165). H.M.A acknowledges support from the National Institute of Neurological Disorders and Stroke of the National Institutes of Health under Award No. F31NS115422. The content is solely the responsibility of the authors and does not necessarily represent the official views of the National Institutes of Health.

The authors have no conflicts to disclose.

S.R.M., H.M.A., J.W., J.K., and J.Z. performed the relevant literature search. S.R.M., H.M.A., M.P., J.K. created figures. S.R.M., H.M.A., and J.A.R. wrote the manuscript. All authors read and provided comments on the manuscript.

Surabhi R. Madhvapathy: Conceptualization (lead); Resources (lead); Visualization (lead); Writing – original draft (lead). Hany M. Arafa: Resources (supporting); Visualization (supporting); Writing – original draft (supporting). Manish Patel: Resources (supporting); Visualization (supporting). Joshua Winograd: Resources (supporting). Jessy Kong: Visualization (supporting). Jason Zhu: Resources (supporting); Writing – review & editing (supporting). Shuai Xu: Writing – review & editing (supporting). John A. Rogers: Conceptualization (lead); Supervision (lead); Writing – review & editing (lead).

Data sharing is not applicable to this article as no new data were created or analyzed in this study.