Designing and analyzing multi-coil multi-layers for wireless power transmission in stent restenosis coronary artery

Alghrairi, Mokhalad; Sulaiman, Nasri; Mutashar, Saad; Wan Hasan, Wan Zuha; Jaafar, Haslina; Algriree, Waleed

doi:10.1063/5.0121532

Wireless power transfer technology features shorter power transmission distances in biomedical applications. This is a result of the small size of the implanted coils, biocompatible material conductivity, and the large distances between the receiving and transmitting coils. There have been numerous attempts to improve the power transfer efficiency across longer distances. Multiple coils, including 2-, 3-, 4-, and multi-layered coils, were previously considered. This study proposes a novel approach to achieve higher power transmission efficiency by integrating a single coil on the receiving side and three asymmetric coils on the transmitter side. As such, it delivers power to the sensor implanted within the coronary artery that monitors the blood pressure while introducing a uniquely shaped stent. The efficiency of power transmitted to the stent in its dual implanted forms, helical and zigzag helical, was examined as well, with the wireless power transmission system thereby analyzed at the 27 MHz Industrial Scientific Medical band operating frequency. For the four-coil technique, the power transmission efficiency at a distance of 25 mm between the receiver and transmitter sides by using biological human tissue as a medium between the transmission coils and the receiver stent can reach 56.42%, whereas other approaches show lower efficiencies: the three-coil method’s efficiency is 32.88%, the double-layer parallel method’s efficiency is 27.75%, the two-coil method’s efficiency is 24.76%, the triple-layer parallel method’s efficiency is 17.31%, the double-layer series method’s efficiency is 0.501%, and the triple-layer series method’s transmission efficiency is 0.092%. In addition, the suggested approach is demonstrated to be more efficient than prior designs with regard to the size of the implanted coils, which represent stents.

INTRODUCTION

Coronary Artery Disease (CAD) refers to the slow contraction of coronary arteries as plaque accumulates on arterial walls. The formation impedes and reduces arterial blood flow, which may lead to heart attacks or strokes.¹ Plaque forms as a waxy substance that accumulates on arterial walls and thereby constricts the flow of blood. The majority of plaque consists of macrophage cells, smooth muscle cells, and complex extracellular compounds including cholesterol, fibrin, collagen, and sulphated glycosaminoglycan.^2,3 Percutaneous Coronary Intervention (PCI) is an invasive medical method, which is in widespread use as a means to remedy such arterial plaque. A balloon expanded at high-pressure is used to remove plaque formation while expanding the diameter of the affected blood vessel.⁴ PCI has been successfully used to reduce arterial plaque and mitigate symptoms. In addition, the procedure is less invasive than coronary artery heart bypass graft surgery and thus provides a more comfortable patient experience. Percutaneous coronary intervention also costs less and enables faster recovery.⁵ A coronary stent is a type of metal scaffold that is designed to extend at the location of a blockage and thereby open up the impeded vessel. The interior of the typical stent re-narrows after deployment; a procedure termed in-stent restenosis (ISR).⁶ Neointimal proliferation (scar tissue development) within and surrounding the stent is the cause of the re-narrowing, a process that results from the immunological reaction of the body to implanted foreign substances.⁷ The probability of in-stent restenosis occurring among stented patients reaches 50%.^8,9 Consequently, it is vital to detect and properly treat in-stent restenosis well before the patient’s condition deteriorates. Continuous blood pressure monitoring using minimally invasive devices inserted in the coronary artery serves as a diagnostic as well as an early warning system for enhanced coronary health.¹⁰ In biomedical technology, wireless sensors are used in numerous applications. Studies have been performed on telemetric medical diagnostics that can function on Radio Frequency (RF).^11–13 Based on passive inductor–capacitor (LC) resonant circuits, these devices are able to function along with changeable resonant frequencies that rely on physiological or biological properties of interest. Due to this, necessary diagnostic information can be obtained via determination of the wireless resonant frequency. In order to meet the power transmission as well as resonance constraints linked with the receiving and transmitting coils, it is crucial to formulate efficient designs for such processes.¹⁴ Several factors can impact the transferring power efficiency from outside the body to inside the coronary artery, the determination of which can provide the required power to the sensor. These factors can be the coronary artery’s small diameter as well as the total distance for transmitting the power from inside the coronary artery to outside the body, which can be greater than 20 mm.¹⁵ Researchers have made several attempts to design wireless power transfer (WPT) systems, whose modeling can be performed using two magnetically coupled resonators, wherein an inductor, resistor, and capacitor are included in each resonator. The receiver side and the load are connected in parallel or series.^16,17 A considerably shorter transmission distance was found corresponding to the critical coupling. Moreover, the sensitivity of the two coils to the alignment between the coils was very high.¹⁸ Thus, instead of two coils, the WPT system utilized multi-coils. As a special case, the design of a three coil structure involved including an additional component to the WPT system.¹⁹ In the transmitter or the receiver, an additional resonator is included, and it can be placed within the same plane as that of the receiver/transmitter coil.^19–21 The addition of a coil to the transmitter allows the input impedance to become larger, thereby improving the system’s total power efficiency. It is obvious that higher transmission efficiency and lower sensitivity to the load change can be achieved with the three coil system vs two coils.²¹

In order to decrease the size, designing of multiple layers of coils was carried out on the transmitter side. Multi-layers can be designed based on two approaches. The first approach involves a series connection that puts forward geometric design solutions to reduce these parasitic losses.²² The Genetic Algorithm (GA) optimization technique is employed to construct double-, single-, and multiple-layer variable-width PSCs that have minimum losses.²³ The current research on multi-layer coils in a series link has reported the presence of a large inductance value in a limited area; however, there will also be an increase in the resistance value, generating heat as well as consuming excessive power with regard to the coil, thereby decreasing the efficiency of wireless power transfer. The second approach would be a link in parallel. A parallel connection can decrease the resistance and increase the coil’s Q value. This enhances the system’s transmission efficiency. Even though connecting the coils in parallel results in enhancing the transmission efficiency, the transmission power is still not adequate when it comes to far distances. The researchers designed four coils, two on the transmitter side characterized as the source and transmitter coils and two on the receiver side characterized as the receiver and load coils, for enabling high transmission efficiency.²⁴ This method offers achieving high efficiency along with extension of the transmission distance. Since the human body has limited available space inside, placing multiple coils inside the human body, such as coronary artery sensors, is challenging. Thus, the implanted coil’s size needs to be very small.

This paper includes design and analysis of a helical coil on the receiver side as well as multiple rectangular coils on the transmitter side. This paper will also try to compare the various methods, such as one, two, and three coils, with regard to the transmitter side. Furthermore, on the transmitter side, designing a double layer and three layers in parallel and series connection is carried out. Then, three asymmetric coils are applied on the transmitter side, wherein a stent is employed to open up the blockage artery by placing a zigzag helical coil prior to expansion and a helical coil after expansion in order to determine the power transmission via the air medium at a resonance frequency of 27 MHz.

METHODOLOGY

The common multi-coil and multi-layer coil structures for WPT systems are shown in Fig. 1. This paper designed a single layer coil on the receiver side because it is used inside the coronary artery and because a smaller size is required so as not to obstruct the flow of blood and designed one single layer coil, two single layer coils, and three single layer coils on the transmitter side, as shown in Fig. 1(a). In addition, double single layer and triple single layer coils connected in series and parallel are designed as shown in Fig. 1(b). In addition, the design of single double layer and single triple layer coils connected in series and parallel are shown in Fig. 1(b). These different methods designed at the transmitter side have been developed to find an effective design that can be used in monitoring intracoronary blood pressure. The transmitter coil’s outer and inner diameters are 80 and 30 mm, respectively. The turn’s width is 0.6 mm with a turn spacing of 0.4 mm, and a cork was employed as the substrate amongst the three transmitter coils with a permittivity of ε₀ = 1. In the design, the number of turns employed is 25, with a wire thickness of 0.3 mm employed in the coil.

FIG. 1.

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(a) Structure of WPT for different methods such as one, two, or three coils on the transmitter side and one coil on the receiver side. (b) The structure of WPT for different methods such as multi-layers of coils on the transmitter side and one coil on the receiver side.

The equivalent circuit theory pertaining to multi-layer coils and multi-single-layer coils in parallel and series is shown in Fig. 2. The first, second, third, and fourth coils (receiver) are signified with subscripts 1, 2, 3, and 4, respectively. C denotes the capacitance, L represents the coil’s inductance, R characterizes the resistance of the coil, M symbolizes the mutual inductance, RL signifies the load resistance, K represents the coupling factor, and I denotes the current.

FIG. 2.

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(a) Multi-single-layer coil [(a) the two single-layer coil method, (b) three single-layer coil method, and (c) four single-layer coil method]. (b) Multi-layer coil [(a) the double single layer coil method connected in series, (b) double single layer coil method connected in parallel, (c) triple single layer coil method connected in series, and (d) triple single layer coil method connected in parallel].

The current equation pertaining to the two coil structure at resonance frequency, when the Kirchhoff’s current law is applied, is

R_{1} I_{1} - J w M_{12} I_{2} = V_{s},

(1)

\frac{R_{2} R_{L}}{R_{2} + R_{L}} I_{2} - J w M_{12} I_{1} = 0,

(2)

P_{i n} = V_{s} I_{1},

(3)

P_{out} = I_{2}^{2} R_{L},

(4)

\begin{align} η = \frac{P_{out}}{P_{i n}} = \frac{I_{2}^{2} R_{L}}{V_{s} I_{1}} \\ = \frac{K_{12}^{2} Q_{1} Q_{2}^{3} R_{2} R_{load}}{(K_{12}^{2} Q_{1} Q_{2}^{3} R_{2} R_{load} + K_{12}^{2} Q_{1} Q_{2} R_{load}^{2} + Q_{2}^{4} R_{2}^{2} + 2 Q_{2}^{2} R_{2} R_{load} + R_{load}^{2})}, \end{align}

(5)

where K_mn defines the coupling factor between the two coils and $Q_{n} = \frac{ω L_{n}}{R_{n}}$ ⁠. The calculation of inductance L can be performed using the following equation:

L = \frac{1.27 μ N_{square}^{2} d_{avg}}{2} [\ln (\frac{2.07}{\emptyset} + 0.18 \emptyset + 0.1 {3 \emptyset}^{2})],

(6)

where N_square denotes the number of turns pertaining to a square coil, μ signifies the permeability, and d_avg = (d_out + d_in)/2, where d_out and d_in represent the coil’s outer and inner side lengths, respectively. ∅ = (d_out − d_in)/(d_out + d_in) can be defined as a fill factor parameter that transforms from zero to one. At a value of ≈0.45, this is regarded as an efficient design.²⁵

At the resonance frequency, for the three coil design, the circuit equation can be represented as

R_{1} I_{1} - J w M_{12} I_{2} - J w M_{23} I_{3} = V_{s},

(7)

R_{2} I_{2} - J w M_{12} I_{1} - J w M_{21} I_{3} = 0,

(8)

\frac{R_{3} R_{L}}{R_{3} + R_{L}} I_{3} - J w M_{12} I_{1} - J w M_{23} I_{2} = 0 .

(9)

By overlooking K₁₃ due to the distance being far, the efficiency will then be

\begin{align} η = \frac{P_{out}}{P_{i n}} = \frac{I_{3}^{2} R_{L}}{V_{s} I_{1}} \\ = \frac{K_{12}^{2} K_{23}^{2} Q_{1} Q_{2}^{2} Q_{3} R_{3} R_{load}}{(\frac{R_{load}}{R_{load} + R_{3}} + K_{23}^{2} Q_{2} Q_{3}) (\frac{R_{load}}{R_{load} + R_{3}} + K_{23}^{2} Q_{2} Q_{3} + \frac{K_{12}^{2} Q_{1} Q_{2} R_{load}}{R_{3} + R_{load}})} . \end{align}

(10)

The circuit equation pertaining to the four coils that have been designed at resonance frequency is

R_{1} I_{1} - J w M_{12} I_{2} - J w M_{23} I_{3} - J w M_{34} I_{4} = V_{s},

(11)

R_{2} I_{2} - J w M_{12} I_{1} - J w M_{23} I_{3} - J w M_{34} I_{4} = 0,

(12)

R_{3} I_{3} - J w M_{12} I_{1} - J w M_{23} I_{2} - J w M_{34} I_{4} = 0,

(13)

\frac{R_{4} R_{L}}{R_{4} + R_{L}} I_{4} - J w M_{12} I_{1} - J w M_{23} I_{2} - J w M_{34} I_{3} = 0 .

(14)

By overlooking K₁₄, K₁₃, and K₂₄ due to their distance being far, the efficiency can be represented as

η = \frac{P_{out}}{P_{i n}} = \frac{I_{4}^{2} R_{L}}{V_{s} I_{1}} = \frac{K_{12}^{2} K_{23}^{2} K_{34}^{2} Q_{1} Q_{2}^{2} Q_{3}^{2} Q_{p}}{(1 + K_{34}^{2} Q_{3} Q_{p} + K_{23}^{2} Q_{2} Q_{3}) (1 + K_{34}^{2} Q_{3} Q_{p} + K_{23}^{2} Q_{2} Q_{3} + K_{12}^{2} Q_{1} Q_{2} + K_{12}^{2} K_{34}^{2} Q_{1} Q_{2} Q_{3} Q_{p})} \times \frac{R_{load}}{R_{load} + R_{4}} .

(15)

The efficiency of the WPT is maximum when L₁, L₂, L₃, and L₄ are tuned to the resonant frequency at 27 MHz, as shown in the following equation:

ω_{0} = \sqrt{\frac{1}{L_{1} C_{1}}} = \sqrt{\frac{1.3924}{L_{2} C_{2}}} = \sqrt{\frac{1.8225}{L_{3} C_{3}}} = \sqrt{\frac{1}{L_{4} C_{4}}},

(16)

where L₁, L₂, L₃, and L₄ are self-inductances and C₁, C₂, C₃, and C₄ are tuning capacitances.

The circuit equation pertaining to the two layer coil structure on the transmitter side that is connected in series at resonance frequency can be represented as

R_{e q} I_{1} - J w M_{eq3} I_{3} = V_{s},

(17)

\frac{R_{3} R_{L}}{R_{3} + R_{L}} I_{3} - J w M_{eq3} I_{1} = 0,

(18)

\begin{align} η = \frac{P_{out}}{P_{i n}} = \frac{I_{3}^{2} R_{L}}{V_{s} I_{1}} \\ = \frac{K_{eq3}^{2} Q_{e q} Q_{3}^{3} R_{3} R_{load}}{(K_{eq3}^{2} Q_{e q} Q_{3}^{3} R_{3} R_{load} + K_{eq3}^{2} Q_{e q} Q_{3} R_{load}^{2} + Q_{3}^{4} R_{3}^{2} + 2 Q_{3}^{2} R_{3} R_{load} + R_{load}^{2})} . \end{align}

(19)

When an identical inductance value of the asymmetric coil exists, then the following equation can be employed to calculate the inductance of multi-layers connected in series:

L_{e q} = 2 L \pm 2 M_{12},

(20)

where M₁₂ denotes the mutual inductance that exists between the two layers. Calculation of the equivalent resistance can be performed using R_eq = R₁ + R₂.

The same circuit equations apply for the two layer coil structure connected in parallel on the transmitter side at resonance frequency for the two layers connected in series; however, the equal inductance $(L_{e q})$ with regard to the transmitter side was seen to be different, as shown in the following equation:

L_{e q} = \frac{L_{1} L_{2} - K^{2} L_{1} L_{2}}{L_{1} + L_{2} - 2 K \sqrt{L_{1} L_{2}}} = \frac{(L - M)}{2} .

(21)

On the transmitter side, the circuit equation pertaining to the three layer coil structure that is connected in series at resonance frequency is

R_{e q} I_{1} - J w M_{eq4} I_{4} = V_{s},

(22)

\frac{R_{4} R_{L}}{R_{4} + R_{L}} I_{4} - J w M_{eq4} I_{1} = 0,

(23)

η = \frac{P_{out}}{P_{i n}} = \frac{I_{4}^{2} R_{L}}{V_{s} I_{1}} = \frac{K_{eq4}^{2} Q_{e q} Q_{4}^{3} R_{4} R_{load}}{(K_{eq4}^{2} Q_{e q} Q_{4}^{3} R_{4} R_{load} + K_{eq4}^{2} Q_{e q} Q_{4} R_{load}^{2} + Q_{4}^{4} R_{4}^{2} + 2 Q_{4}^{2} R_{4} R_{load} + R_{load}^{2})} .

(24)

For the same inductance value of the asymmetric coil, the inductance pertaining to multi-layers connected in series can be determined using the following equation:

L_{e q} = 3 L \pm 3 M .

(25)

In addition, the equivalent resistance is R_eq = R₁ + R₂ + R₃.

The same circuit equations apply for the three-layer coil structure on the transmitter side connected in parallel at resonance frequency and the three layers connected in series; however, the equal inductance pertaining to the transmitter side differs as presented in the following equations:

u_{1} = L_{1} \frac{d I_{1}}{d t} + M_{12} \frac{d I_{2}}{d t} + M_{23} \frac{d I_{3}}{d t},

(26)

u_{2} = L_{2} \frac{d I_{2}}{d t} + M_{12} \frac{d I_{1}}{d t} + M_{23} \frac{d I_{3}}{d t},

(27)

u_{3} = L_{3} \frac{d I_{3}}{d t} + M_{12} \frac{d I_{1}}{d t} + M_{23} \frac{d I_{2}}{d t},

(28)

u = u_{1} = u_{2} = u_{3} = L \frac{d I}{d t} = L \frac{d I_{1}}{d t} + L \frac{d I_{2}}{d t} + L \frac{d I_{3}}{d t},

(29)

(L - L_{1}) \frac{d I_{1}}{d t} + (L - M_{12}) \frac{d I_{2}}{d t} + (L - M_{23}) \frac{d I_{3}}{d t} = 0,

(30)

(L - M_{12}) \frac{d I_{1}}{d t} + (L - L_{2}) \frac{d I_{2}}{d t} + (L - M_{23}) \frac{d I_{3}}{d t} = 0,

(31)

(L - M_{12}) \frac{d I_{1}}{d t} + (L - M_{23}) \frac{d I_{2}}{d t} + (L - L_{3}) \frac{d I_{3}}{d t} = 0 .

(32)

Here, the triple layer coils are asymmetric; then M₁₂ = M₂₃ = M, and

L = \sqrt[3]{3 L^{2} M - 3 L M^{2} + M^{3}} .

(33)

In addition, the equivalent resistance is

R_{e q} = \frac{R_{1} R_{2} R_{3}}{R_{1} R_{3} + R_{2} R_{3} + R_{1} R_{2}} .

(34)

The parameter value used in the design for all methods is shown in Table I.

TABLE I.

The parameter of coils for the different methods used.

Parameter	coils	side	transmitter side	side	side	side	side
		Three coils			Four coils
				Double layers		Triple layers	Triple layers
		Two single	Double layers	connected in	Three single	connected in	connected in
		layers in the	connected in	parallel in	layers in the	series in	parallel in
	Two	transmitter	series in the	the transmitter	transmitter	the transmitter	the transmitter
L_t (μH)	44.80	44.80	26.1	31.1	44.80	24.4	27.7
L_r (μH)	0.325	0.325	0.325	0.325	0.325	0.325	0.325
R_in (Ω)	14.98	14.98	28.38	7.49	14.98	44.94	5
R_out (Ω)	8	8	8	8	8	8	8
R_Load (Ω)	115	115	115	115	115	115	115
Q_t	507.09	598.36	155.9	704.04	807.79	92.06	939.36
Q_r	6.99	6.99	6.99	6.99	6.99	6.99	6.99
K at	0.026	0.0269	0.0011	0.0212	0.0286	0.0089	0.0193
(25) mm

Parameter	coils	side	transmitter side	side	side	side	side
		Three coils			Four coils
				Double layers		Triple layers	Triple layers
		Two single	Double layers	connected in	Three single	connected in	connected in
		layers in the	connected in	parallel in	layers in the	series in	parallel in
	Two	transmitter	series in the	the transmitter	transmitter	the transmitter	the transmitter
L_t (μH)	44.80	44.80	26.1	31.1	44.80	24.4	27.7
L_r (μH)	0.325	0.325	0.325	0.325	0.325	0.325	0.325
R_in (Ω)	14.98	14.98	28.38	7.49	14.98	44.94	5
R_out (Ω)	8	8	8	8	8	8	8
R_Load (Ω)	115	115	115	115	115	115	115
Q_t	507.09	598.36	155.9	704.04	807.79	92.06	939.36
Q_r	6.99	6.99	6.99	6.99	6.99	6.99	6.99
K at	0.026	0.0269	0.0011	0.0212	0.0286	0.0089	0.0193
(25) mm

The coil that is utilized on the receiver part is of a helical shape and set within the coronary artery. After expansion, it assumes a diameter of 5 mm and length of 30 mm; before expanding, it is a zigzag helical coil of a diameter of 2 mm, as shown in Fig. 3.

FIG. 3.

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Smart stent before and after expansion.

Since the coronary artery’s diameter is limited to 5 mm, the spiral coil that is used cannot be rectangular or circular in shape because it affects the flow of blood in the artery. Thus, the most effective solution is to implant a helical shaped coil inside the coronary artery. Mathematically, the self-inductance and helical coil can be computed using the following equation:²⁶

L_{helical coil} = \frac{μ π r^{2} N_{stent}^{2} T}{l_{stent}},

(35)

where μ is the free-space permeability, the radius of stent r = diameter of stent (d_stent)/2, N_stent is the number of stent turns, l_stent is the length of the wire in the stent, and T is Nagaoka’s coefficient,²⁶ estimated as

T = Y_{z} (\ln (1 + \frac{1}{Y_{z}}) U),

(36)

where $U = \frac{1}{(X_{0} + X_{1} (\frac{d_{stent wire}}{d_{stent}})) + X_{2} {(\frac{d_{stent wire}}{d_{stent}})}^{2} + \frac{a_{1}}{{(a_{2} + \frac{d_{stent}}{d_{stent wire}})}^{v}}}$ ⁠.

Here, $Y_{z} = \frac{d_{stent wire}}{π r}$ ⁠, d_stent wire is the diameter of the wire used in the coil, d_stent is the diameter of the helical coil, X₀ = 2.300 38, X₁ = 3.437, X₂ = 1.763 56, a₁ = −0.47, a₂ = 0.755, v = 1.44, and l_stent is the length of the wire used in the helical coil.

A stent of size 2 mm is inserted by PCI operation, which is then expanded by a balloon to a size of 5 mm. Gold is used as a material here since it is biocompatible and possesses the excellent electrical conductivity required for better wireless power transmission. The stent parameters after expansion are computed by using Eq. (37) and before expansion are computed using (38)–(40), as illustrated in Fig. 4,

l_{one revolution} = \sqrt{H^{2} + C^{2}},

(37)

where H = 2πr, C depicts the rise of the helix in one revolution (pitch), l_{one revolution} is the length of the wire in one revolution, and r is the radius of the helical coil,

l_{one revolution} = N_{strut} [2 l_{strut} + 2 l_{arc}],

(38)

l_{strut} = \frac{p i t c h}{2} - 2 [\frac{s}{2} + t h],

(39)

l_{arc} = [\frac{s}{2} + t h] π,

(40)

where N_strut is the number of struts in a single revolution. l_strut is the length of the strut, l_arc is the length of the arc connecting the struts, th is the thickness of the strut, and s is the space between the struts.

FIG. 4.

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Zigzag helical coil (stent) before expansion with a diameter of 2 mm.

The parameters of the stent before expansion when the shape is zigzag helical are shown in Table II.

TABLE II.

The parameters of the stent.

Parameter	Value (mm)
l_{one revolution}	15.82
N_strut	3
l_strut	0.36
Pitch	2
S	0.2
th	0.6
l_arc	2.198

With regard to these designs, the external coil placed on the surface of the human body was made of copper, while the internal coil implanted within the coronary artery was made of gold (at a 25 mm depth). This depth has been determined by considering the combined thickness of the human body tissue in the chest zone (skin, fat, muscle, and cortical bone), as shown in Fig. 5. In addition, the dielectric properties of biological human tissue are determined based on the 27 MHz ISM (Industrial Scientific Medical) frequency band,²⁷ as illustrated in Table III.

FIG. 5.

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Structure of WPT for different methods such as multi-layers of coils on the transmitter side and one coil on the receiver side with a tissue depth of 25 mm.

TABLE III.

The constitutive characteristics of human biological tissue at 27 MHz.

Freq. at	Conductivity	Relative	Wavelength	Penetration	Thickness at
27 MHz	(S/m)	permittivity	(m)	depth (m)	25 mm (mm)
Skin	0.328 3	165.59	0.748 76	0.239 79	5
Fat	0.032 909	8.4678	2.777 7	0.644 83	9
Muscle	0.654	95.947	0.674 61	0.133 6	10
Bone cortical	0.051 538	21.824	1.986 4	0.575 76	1

Freq. at	Conductivity	Relative	Wavelength	Penetration	Thickness at
27 MHz	(S/m)	permittivity	(m)	depth (m)	25 mm (mm)
Skin	0.328 3	165.59	0.748 76	0.239 79	5
Fat	0.032 909	8.4678	2.777 7	0.644 83	9
Muscle	0.654	95.947	0.674 61	0.133 6	10
Bone cortical	0.051 538	21.824	1.986 4	0.575 76	1

Table III shows the constitutive characteristics of human biological tissue at 27 MHz.

RESULT AND DISCUSSION

The different multi-layers and multi-single coil techniques are compared and tested in the air medium through simulation by using the Maxwell Ansys software for FEA (Finite Element Analysis), which have the permittivity ɛ₀ of 1.0006, as illustrated in Fig. 6, which displays the magnetic flux density between the receiver and the transmitter side for all techniques used in WPT.

FIG. 6.

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Magnetic flux density for each system: the (a) four coil method, (b) three coil method, (c) two coil method, (d) double layer in series connection method, (e) double layer in parallel connection method, (f) triple layer in series connection method, and (g) triple layer in parallel connection method. All methods were simulated using FEA software (Maxwell Ansys).

The coupling coefficient (K) for coupling among the receiver and transmitter coils provides the mutual coupling measurement. The value of the coupling factor is used to determine which technique is more efficient for WPT. Figure 7 displays the coupling coefficient for all techniques testing in the air medium. The X-axis denotes the distance between the receiver and the transmitter coil, while the Y-axis denotes the coupling factor (coupling coefficient). The result implies better coupling in the case of a triple single layer that is connected in series compared to a double single layer that is connected in series, while the method of double single-layer coils connected in parallel is more effective than the triple single layer that is connected in parallel. In addition, the two single layers show a better coupling coefficient than the single layer on the transmitter side. Finally, the technique of four coils with three single layers on the transmitter side is found to have the best coupling with a coupling coefficient of 0.028 and a distance of 25 mm.

FIG. 7.

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Coupling coefficient with a variable distance for all methods.

The efficiency is substantiated with the variation in the coupling coefficient testing within the tissue medium, which is denoted as the distance variation by using MATLAB simulation software, as displayed in Fig. 8. The variation of 0–1 in the coupling is represented by the X-axis, while the Y-axis stands for the efficiency at a fixed load resistance of 115 Ω based on R_load ≥ 2ωs L₄.²⁸ The outcome shows that the efficacy of the four-coil method with three single layers in the transmitter side is greater than that of other techniques and the technique of double single layers where connections are made in series has lower efficacy than other techniques.

FIG. 8.

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Variation between the coupling factor and power transfer efficiency for different methods.

The efficacy of all the proposed techniques is verified with variations in the load resistance by using MATLAB simulation software, as displayed in Fig. 9. The variation in the load resistance from 100–400 Ω is represented by the X-axis while the Y-axis represents the efficiency at a 25 mm fixed distance between the receiver and the transmitter coil. The outcome shows that the efficiency of the technique of four coils with three single layers on the transmitter side is not affected by variations in the load but rather by other techniques. It gives stability to the system in the case of different loads.

FIG. 9.

View large Download slide

Efficiency variation with load resistance at a 25 mm distance for all proposed methods.

The above-mentioned outcome with the best coupling, higher efficiency, and good stability to the system in the case of different loads confirmed that the four-coil technique with three single layer coils in the transmitter side is the most efficient to use in wireless power transmission, particularly in applications with bio-implants. Thus, it is applied to determine the efficiency of power transmission for smart stents before as well as after expansion by using the simulation in the Maxwell Ansys software for FEA (finite element analysis), as illustrated in Fig. 10.

FIG. 10.

View large Download slide

Magnetic flux density simulated by Maxwell Ansys software for each system (a) Three coils with stents, i.e., the four coil method before expansion and (b) three coils with stents, i.e., the four coil method after expansion.

Figure 11 illustrates the coupling factor as well as the distance between the stent and transmitter coil before and after expansion. The variation of 5–25 mm in the distance between the stent and transmitter coil is represented by the X-axis while the coupling factor at a fixed load resistance of 115 Ω is represented by the Y-axis. The outcome proves that the coupling factor before expansion of the stent is greater than that after its expansion because it depends on the value of the stent inductance, which is in the form of a zigzag helix, that is, the coupling factor before the expansion is greater than the that of the stent after the expansion, and thus, we notice an increase in the coupling.

FIG. 11.

View large Download slide

Relation between the coupling factor and distance between the transmitter coil and the stent before and after expansion.

The efficacy is substantiated through the variation in the coupling coefficient, which is denoted as the distance variation to confirm the efficiency of power transmission between the two cases. The efficiency of power transmission is greater for stents prior to expansion than stents after expansion. The value of inductance before expansion is 320 nH; the inductance value after expansion is 200 nH. Moreover, before expansion, the coupling factor is greater than that after expansion (Fig. 12).

FIG. 12.

View large Download slide

Efficiency between the transmitter coil and the stent before and after expansion.

To validate the proposed design, it was compared with other studies, as shown in Table IV. The results indicated that their proposed design exhibited better PTE (Power Transmission Efficiency) and high transfer distance between the transmitter and receiver coils.

TABLE IV.

Validation of the proposed design compared with designs of other researchers.

References	Receiver coil	Transmitter coil	(dBm)	transmission	(mm)	Efficiency %
			Input		Distance of
			power	Medium of	transmission
29	Stent (38 mm in length)	One helical coil	70	Subdermal tissue	0	≥0.03
30	Stent (15 mm in length)	One helical coil	70	Water and bioartificial vessel	0	0.52
31	Stent (30 mm in length)	One planar coil	25	Air	5	0.09
32	Stent (20 mm in length)	Seven circular coils in an array shape	33	Meat tissue	15	6.8
Proposed design	Stent (30 mm in length)	Double single layer coils in a series connection	23.979	Skin, fat, muscle, and cortical bone	25	0.092
Proposed design	Stent (30 mm in length)	Triple single layer coils in a series connection	23.979	Skin, fat, muscle, and cortical bone	25	0.501
Proposed design	Stent (30 mm in length)	Triple single layer coils in a parallel connection	23.979	Skin, fat, muscle, and cortical bone	25	17.31
Proposed design	Stent (30 mm in length)	One single layer coil	23.979	Skin, fat, muscle, and cortical bone	25	24.76
Proposed design	Stent (30 mm in length)	Double single layer coils in a parallel connection	23.979	Skin, fat, muscle, and cortical bone	25	27.75
Proposed design	Stent (30 mm in length)	Two single layer coils	23.979	Skin, fat, muscle, and cortical bone	25	32.88
Proposed design	Stent (30 mm in length)	Three single layer coils	23.979	Skin, fat, muscle, and cortical bone	25	56.42

References	Receiver coil	Transmitter coil	(dBm)	transmission	(mm)	Efficiency %
			Input		Distance of
			power	Medium of	transmission
29	Stent (38 mm in length)	One helical coil	70	Subdermal tissue	0	≥0.03
30	Stent (15 mm in length)	One helical coil	70	Water and bioartificial vessel	0	0.52
31	Stent (30 mm in length)	One planar coil	25	Air	5	0.09
32	Stent (20 mm in length)	Seven circular coils in an array shape	33	Meat tissue	15	6.8
Proposed design	Stent (30 mm in length)	Double single layer coils in a series connection	23.979	Skin, fat, muscle, and cortical bone	25	0.092
Proposed design	Stent (30 mm in length)	Triple single layer coils in a series connection	23.979	Skin, fat, muscle, and cortical bone	25	0.501
Proposed design	Stent (30 mm in length)	Triple single layer coils in a parallel connection	23.979	Skin, fat, muscle, and cortical bone	25	17.31
Proposed design	Stent (30 mm in length)	One single layer coil	23.979	Skin, fat, muscle, and cortical bone	25	24.76
Proposed design	Stent (30 mm in length)	Double single layer coils in a parallel connection	23.979	Skin, fat, muscle, and cortical bone	25	27.75
Proposed design	Stent (30 mm in length)	Two single layer coils	23.979	Skin, fat, muscle, and cortical bone	25	32.88
Proposed design	Stent (30 mm in length)	Three single layer coils	23.979	Skin, fat, muscle, and cortical bone	25	56.42

CONCLUSION

The multi-layer coils and multiple coils of WPT systems are examined theoretically, and a comparison is made based on circuit theory. The simplified models of the multi-layer coil and multi-coil systems are presented to determine the benefits of the four-coil technique. In the case of the simplified models, the configurations become intuitive of the differences among the two single layers, three single layers, four single layers, and double single layers connected in parallel and series and among the triple single layers connected in parallel and series. The major advantages of the four-coil method that include greater efficiency of power transfer and stiffness against load variations and distance variations are evaluated, and it is proven that the efficiency is greater than other techniques, which is tested within the biological human tissue. The outcomes of the simulation are presented to substantiate the analytical outcomes. The comparison of the efficiency of power transfer is performed on the basis of the soundness of the seventh structure, and it ascertains that the new four-coil technique is better than other techniques. Furthermore, a unique stent was proposed and verified before and after expansion. The presented stent may be suitable for coronary and vascular arteries, esophageal ducts, prostatic ducts, and ureteral ducts.

ACKNOWLEDGMENTS

This work was supported by the University of Putra Malaysia through a project under the title “A high efficient RLC inductive transmission coupling to monitor in-stent restenosis coronary artery,” under Geran Inisiatif Putra Siswazah (GP-IPS) Grant No. 9712900.

AUTHOR DECLARATIONS

Conflict of Interest

The authors have no conflicts to disclose.

Author Contributions

Mokhalad Alghrairi: Conceptualization (equal); Data curation (equal); Formal analysis (equal); Funding acquisition (equal); Investigation (equal); Methodology (equal); Resources (equal); Software (equal); Validation (equal); Visualization (equal); Writing – original draft (equal); Writing – review & editing (equal). Nasri Sulaiman: Conceptualization (equal); Data curation (equal); Formal analysis (equal); Funding acquisition (equal); Investigation (equal); Methodology (equal); Project administration (equal); Resources (equal); Software (equal); Supervision (equal); Validation (equal); Visualization (equal); Writing – original draft (equal); Writing – review & editing (equal). Saad Mutashar: Conceptualization (equal); Data curation (equal); Formal analysis (equal); Funding acquisition (equal); Investigation (equal); Methodology (equal); Resources (equal); Supervision (equal); Validation (equal); Visualization (equal); Writing – review & editing (equal). Wan Zuha Wan Hasan: Conceptualization (equal); Data curation (equal); Formal analysis (equal); Funding acquisition (equal); Investigation (equal); Methodology (equal); Resources (equal); Supervision (equal); Validation (equal); Visualization (equal); Writing – review & editing (equal). Haslina Jaafar: Conceptualization (equal); Data curation (equal); Formal analysis (equal); Funding acquisition (equal); Investigation (equal); Methodology (equal); Resources (equal); Supervision (equal); Validation (equal); Visualization (equal); Writing – review & editing (equal). Waleed Algriree: Conceptualization (equal); Data curation (equal); Formal analysis (equal); Funding acquisition (equal); Investigation (equal); Methodology (equal); Resources (equal); Validation (equal); Visualization (equal); Writing – review & editing (equal).

DATA AVAILABILITY

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

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Author(s)

Designing and analyzing multi-coil multi-layers for wireless power transmission in stent restenosis coronary artery

INTRODUCTION

METHODOLOGY

RESULT AND DISCUSSION

CONCLUSION

ACKNOWLEDGMENTS

AUTHOR DECLARATIONS

Conflict of Interest

Author Contributions

DATA AVAILABILITY

REFERENCES

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Designing and analyzing multi-coil multi-layers for wireless power transmission in stent restenosis coronary artery

INTRODUCTION

METHODOLOGY

RESULT AND DISCUSSION

CONCLUSION

ACKNOWLEDGMENTS

AUTHOR DECLARATIONS

Conflict of Interest

Author Contributions

DATA AVAILABILITY

REFERENCES

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