Theory of energy harvesting from heartbeat including the effects of pleural cavity and respiration

1. Introduction

Implantable devices, aiming to solve problems such as heart failure, obesity, blood pressure control, wound healing, neural-stimulation and drug delivery, have made significant progress in clinical applications in recent years [1–5]. Pacemakers and implantable cardioverter defibrillators (ICDs) are most commonly used among these devices mentioned above. Both pacemakers and ICDs need a replacement every several years for various reasons, e.g. end of the battery life [6]. This needs additional surgeries which may bring a notable complication risk, especially in the case of involving lead additions [7]. On the other hand, these surgeries and device replacements are costly and apt to bring additional injuries to patients. However, the development of currently available battery technology is much slower than the electronic devices, which limits the pace of improvement in design and functionality of implantable electronic devices.

Self-powered implantable devices provide a potential way to address the shortcomings of battery replacement problem of implantable devices with the breakthrough technology of energy harvesting from ambient environments [8–13]. The main mechanical energy scavenging strategies are to harvest energy from biomechanical motions of human organs, such as heart-beating, blood flow and breathing etc. Lead zirconate titanate (PZT) is the mostly used material in mechanical energy harvesters (MEHs) for its high piezoelectric coefficients, and flexible/stretchable electronics with PZT material were studied intensively by Huang's group [14–18]. Based on these mechanical strategies, Dagdeviren et al. demonstrated a conformal device to collect electric power from motions of porcine heart, lung or diaphragm based on a flexible PZT MEH [19]. Ansari et al. [20] designed a fan-folded structure consisting of bimorph PZT beams for powering biomedical devices and sensors inside the body. Other piezoelectric materials, e.g. zinc oxide (ZnO), PMN-PT or PVDF, were also resorted to fabricate flexible MEHs [21–23]. For example, people may generate electric power using a flexible PVDF piezoelectric generator from the pulsation of ascending aorta of a swine or employing a ZnO breathing-driven implanted triboelectric nanogenerator powered by the rat's diaphragm [24–26].

Most recently, Lu et al. conducted a set of experiments to invest energy harvesting from the porcine heartbeat using flexible PZT MEH [27], in which the output voltage was measured under various conditions, i.e. chest open, chest closed and awake from anaesthesia. When the device is mounted on the heart surface in a matter of covering from the apex of the left ventricle (LV) to the right ventricle, the peak-to-valley amplitude of the output voltage reduces from 1.91 V with chest open to 1.09 V with chest closed, i.e. a reduction of 50%, while the average power is 0.02 µW with chest open to 0.005 µW with chest closed, i.e. a reduction of 75%. To demonstrate the underlying mechanism of the reduction in energy harvesting in chest closed environment relative to chest open, Zhang et al. [28] proposed a nonlinear compressive spring model to account for the impeding effects of surrounding tissues on the energy harvesting efficiency of the electromagnetic harvesting device. They treated the surrounding tissues, including the pericardium serosa, pleura and lung, approximately as a homogeneous medium that posed impeding effects on the deformation of the device. That is, once deformed, the device will be impeded by the spring. However, the anatomy shows that the cavum is enveloped by the visceral and parietal layer of the pericardium and that a gap of 5–10 mm exists between the parietal layer and the pleura [29]. As a result, the device may deform freely at its early stage and will be impeded only if the deformation amplitude exceeds this gap. In addition, the back-and-forth deformation of the device will also vary with respiration as the chest is closed.

In this paper, we propose a restricted deformation space model to demonstrate this mechanism of energy harvesting efficiency reduction in chest closed environment based on an electromechanical analysis. An analytical solution for the output voltage and power has been derived and will be validated by comparing with experimental measurements. A simple scaling law will be established which reveals the dependence of the normalized electric outputs on the normalized permitted space and the normalized electrical load. The output power can be tuned and optimized according to this scaling law by choosing properly the material, geometric and circuit parameters of the energy harvesting system. The results can also provide design guidelines for similar MEH devices that are applied in other biological environments.

2. Mechanical analyses of the mechanical energy harvester device

The PZT MEH is a layered structure (figure 1a), where PI (thickness ∼ 1.2 µm, E = 8.55 GPa) serves as the adhesive layer, Pt (thickness ∼ 0.3 µm, E = 196 GPa) serves as the bottom electrode, then PZT ribbons (length ∼ 2.2 mm, width ∼ 100 µm, thickness ∼ 500 nm, E = 128 GPa) serve as the functional layer which can generate electric power under deformation, Au (thickness ∼ 0.2 µm, E = 97 GPa) and Cr (thickness ∼ 10 nm, E = 292 GPa) serve as the top electrode and PI (thickness ∼ 1.2 µm, E = 8.55 GPa) serves as the top protective layer. Lithography and wet etching methods were employed to form the stack pattern (10 PZT nano ribbons connected in parallel in one module and 3 × 4 moduli connected in series) [27]. Then the functional part was transfer-printed to polyimide thin film (thickness ∼ 50 µm, E = 2.83 GPa), which serves as the soft bottom substrate layer. At last, the device is connected to a flexible anisotropic conductive film cable (figure 1b). To investigate the in vivo biomechanical energy harvesting efficiency, we integrated the device on the heart surface of experimental swine (figure 1c). The swine in the experiment was handled with the permission from the Ethics Committee. When the porcine heart was beating, the flexible PZT MEH was forced to deform, and the output voltage of the device was measured by an AD/DA card and transmitted to a computer for further analyses.

• Download figure
• Open in new tab
• Download PowerPoint

As the outer LV is a curved surface, the device, when sewed at the LV surface by its two ends, is subjected to bending deformation with large deflections (figure 1d) during the heart motion in experiment [27]. The PZT nano ribbons are much more compliant than the substrate, and, therefore, the contribution of the PZT nano ribbons to the bending and stretching rigidity of the device is neglected. During the cardiac systole and diastole process, the device is forced to deform periodically. Neglecting the initial curvature of the device due to the LV surface, the deformation of the device is governed by

among which $N_0=E_{\mathrm{s}}{A}_{\mathrm{s}}[(\mathrm{d}{u}_0/\mathrm{d}x)+1/2{(\mathrm{d}w/\mathrm{d}x)}^2]$ is the constant membrane force due to large deflection of the device, w is the deflection and u₀ is the in-plane displacement at the neutral axis, while E_s, A_s and I_s are, respectively, the elastic modulus, area and moment of inertia of the substrate.

According to anatomy, there exists a small space (A_c = 5–10 mm [29]) between the left lung and the heart, this may accommodate free deformation of the device when the deformation amplitude A < A_c. However, the lung will pose an impedance effect on the device as A ≥ A_c, and thus, the output voltage is reduced. Therefore, the boundary conditions for the governing equation (2.1) will depend on the relationship between the deformation amplitude A and the permitted space A_c.

(a) Free deformation (A < A_c)

At the free deformation stage (A ≤ A_c), the MEH device is only constrained at its sewed ends with an end-to-end displacement of ΔL. The sewed ends are regarded as in clamped condition (figure 1d) to satisfy

The general solutions for the governing differential equation (2.1) are

where ${\alpha }_1=\sqrt{N_0/(E_{\mathrm{s}}{I}_{\mathrm{s}})}$ is the eigenvalue of equation (2.1) and c_i are unknown constants.

Upon incorporating the boundary conditions in equation (2.2), the non-zero parameters in (2.3) and (2.4) are obtained as $c_1=c_4=(L_0/\pi )\sqrt{(\mathrm{\Delta }L/L_0)-(4{\pi }^2/L_0^2)(I_{\mathrm{s}}/A_{\mathrm{s}})}$, ${\alpha }_1=2\pi /L_0$ and $N_0=(4{\pi }^2/L_0^2)E_{\mathrm{s}}{I}_{\mathrm{s}}$. During the systole of the heart, the relative end-to-end displacement of the device ΔL/L₀ (approx. 10⁻¹) is much larger than the membrane strain $(4{\pi }^2/L_0^2)(I_{\mathrm{s}}/A_{\mathrm{s}})$ (approx. 10⁻⁵); therefore, the displacements are derived as

from which the deflection amplitude is $A=(2/\pi )\sqrt{L_0\mathrm{\Delta }L}$. This solution is identical to the traditional empirical results based on the post-buckling analyses [30,31]. The axial strain in the PZT ribbon is ${\epsilon }_{\mathrm{PZT}}=-(E_{\mathrm{s}}{I}_{\mathrm{s}}/\overline{EI})z_{\mathrm{p}}({\mathrm{d}}^{2}w/\mathrm{d}{x}^2)$, where $\overline{EI}$ and z_p are, respectively, the effective bending stiffness and the distance from the centre of the PZT ribbons to the neutral axis of the composite part of the device. As the PZT ribbons are integrated near the substrate centre, and their lengths (approx. 2 mm) are much shorter than the substrate (approx. 50 mm), the average strain of the PZT ribbons may be approximated as

(b) Constrained deformation (A ≥ A_c)

When undergoing a large deformation (A > A_c) during the systole of the heart, the MEH device will contact with the surrounding tissues at the centre part. Here, the adhesion effect between the MEH device and the surrounding tissues is neglected, then the contact length will be zero [32,33], that is, the device will have only the centre point contacting with the surround tissues. For simplicity, the deformation of the surrounding tissues is further ignored or the surrounding tissues are assumed rigid when compared with the MEH device, then the displacement and the slope at the device centre will keep at $w{|}_{x=0}=A_{\mathrm{c}}$ and $w^{\mathrm{\prime }}{|}_{x=0}=0$. Combining these constraint conditions and the symmetric nature of the device ($u_0{|}_{x=0}=0$) with the boundary conditions in equation (2.2), the non-zero unknown constants c_i are determined by

and the membrane force is $N_0=4E_{\mathrm{s}}{I}_{\mathrm{s}}({\lambda }^2/L_0^2)$, where $\lambda ={\alpha }_1{L}_0/2$ is the root of the following characteristic equation,

The average strain of the PZT ribbons may be approximated as

Noted that we have λ = π when A_c = A, then the solution in equation (2.9) may be reduced to equation (2.6) for the case of A < A_c.

3. Electric outputs of the mechanical energy harvester device

According to the electromechanical coupling behaviour of piezoelectric materials and following the previous analyses [28], the governing equation for total output voltage V_total of the MEH device with an electrical resistance R is

where n_p and n_s are the number of PZT ribbons connected in parallel and the number of moduli connected in series, h_p and A_p are the thickness and area of each individual PZT ribbon, while ${\overline{e}}_{31}$ and ${\overline{\mu }}_{33}$ are, respectively, the effective piezoelectric and dielectric constants of the PZT ribbons. The total output voltage from equation (3.1) with the initial condition V_total(0) = 0 is

Equations (3.2) and (2.9) or (2.6) indicate that the output voltage of the MEH device may be calculated once the real-time end-to-end displacement of the device ΔL(t) is known.

For the current energy harvesting from heartbeat by sewing the MEH device at the LV surface, the end-to-end displacement ΔL(t), according to the assumption of bullet-shape or ellipsoid-shape [34], may be determined by $\mathrm{\Delta }L(t)/L_0=[D_{\mathrm{diastolic}}-D(t)]/[D_{\mathrm{diastolic}}+2t_{\mathrm{wall}}]$, where t_wall, D_diastolic and D(t) are, respectively, the wall thickness, diastolic and the real-time minor axis diameter of the LV. The real-time minor axis diameter D(t) is related to the volume of the LV by $V_{\mathrm{LV}}=7.0D^3(t)/[2.4+D(t)]$ [35]. As the real-time LV volume V_LV of swine is not available, we will use the corresponding in vivo data of human heart [36] to approximate the porcine LV due to their similar cardiac physiology [37–39]. The main difference between the real-time LV volume V_LV of human and swine is the cardiac period, which makes it necessary to scale the cardiac period of human heart to the porcine heart in experiment.

The current PZT MEH device in the experiment contains 12 moduli connected in series with each module containing 10 PZT nano ribbons (h_p = 0.5 µm, A_p = 0.22 mm²) connected in parallel. The effective piezoelectric ${\overline{e}}_{31}$ and dielectric constants ${\overline{\mu }}_{33}$ of the PZT nano ribbon are −6.2 C m⁻² and 2 × 10⁻⁸ C/(Vm) [40], respectively. Using the loading condition generated by the above analogy, the predicted real-time output voltages with chest open and closed (A_C = 6.5 mm, figure 2b) exhibit a reduction of about 40% in the peak-to-valley voltage, which is generally consistent with experiments (figure 2a). This demonstrates the capability of the current theoretical model to reveal the underlying mechanism of reduction in voltage output by the MEH device in chest closed environment.

• Download figure
• Open in new tab
• Download PowerPoint

The energy harvesting efficiency is the foremost concern that determines the feasibility of the MEH device for practical applications to power biointegrated or implanted microdevices. Normally, the effective output power $P_{\mathrm{eff}}=V_{\mathrm{eff}}^2/R$ is used to evaluate the efficiency of the MEH device, where $V_{\mathrm{eff}}=\sqrt{\left({\int }_0^T{V}_{\mathrm{total}}^2\mathrm{d}t\right)/T}$ is the root of mean squares of the output voltage, or termed as the effective voltage. Theoretical predictions exhibit that the effective output power P_eff increases monotonically with the permitted space A_c until it exceeds a certain value that will not pose impeding effects on the device (figure 3). Correspondingly, the effective output power will have a larger reduction $(P_{\mathrm{eff}}^{\mathrm{free}}-P_{\mathrm{eff}})/P_{\mathrm{eff}}^{\mathrm{free}}$ for smaller permitted space. The predicted output power is 0.021 µW for chest open and 0.005 µW for chest closed with a permitted space A_C = 6.5 mm (with a reduction of 76%), which are identical to the experimental measurements, 0.02 and 0.005 µW with chest open and closed (with a reduction of 75%) [27].

• Download figure
• Open in new tab
• Download PowerPoint

In the chest closed environment, respiration may induce elastic deformation or volume change of the lung [41], and, hence, the timely variation of the pleural cavity or permitted space A_C. The porcine cardiac rate is about 120–140 beats min⁻¹ [41], while the respiratory rate is about 20 times min⁻¹ [42]. Sinusoidal expiratory flow is usually used for studying lung mechanical properties [43], then we assume $A_{\mathrm{C}}=A_{\mathrm{C}0}+A_{\mathrm{C}1}\sin ({\omega }_{\mathrm{r}}t)$, where A_C0 = 6.5 mm is the average permitted space [29], while A_C1 and ω_r are, respectively, the amplitude and frequency of the resonant space. According to the typical statistics of normal adult lung during respiration, these two parameters may be obtained approximately as A_C1 = 3.0 mm and ω_r = 2.1 rad s⁻¹ [43]. Theoretical results of the real-time output voltage again agree very well with experiments (figure 4), indicating that the current theoretical model is robust for predicting energy harvesting from heartbeat in practical living environment. The result is also inspiring for potential applications in respiratory monitoring, for example, to retrieve real-time respiratory rate and respiratory intensity.

• Download figure
• Open in new tab
• Download PowerPoint

4. Scaling laws for energy harvesting

Multiple parameters, including material parameters (e.g. piezoelectric constant ${\overline{e}}_{31}$, dielectric constant ${\overline{\mu }}_{33}$, Young's modulus of the substrate E_s and the effective modulus of the whole device $\overline{E}$), geometrical parameters (e.g. length of the device L₀, thickness and effective area of the PZT ribbon h_p and A_p, thickness of the substrate h_s, moment of inertia of the substrate I_s, effective moment of inertia of the whole device $\overline{I}$, the distance from the centre of the PZT layer to the centre of the PZT MEH z_p, and the permitted space A_C), circuit parameters (e.g. number of PZT ribbons n_p connected in parallel in one module, number of energy harvesting moduli n_s connected in series and electrical load of the circuit R) and loading parameters (e.g. the real-time end-to-end displacement ΔL, the period of heartbeat T and the respiration rate ω_r), are contained in the output voltage V_total given in equation (3.2). This makes the investigation of the effects of each individual parameter on the energy harvesting efficiency intricate and complex. To investigate the intrinsic effects of these parameters on the energy harvesting efficiency from heartbeat, we will establish simple scaling laws to reveal the underlying physics and links between the electric outputs and various parameters.

To this end, we introduce the intrinsic scales of voltage $V_0=(E_{\mathrm{s}}{I}_{\mathrm{s}}/\overline{EI})(n_{\mathrm{s}}{\overline{e}}_{31}{h}_{\mathrm{p}}{z}_{\mathrm{p}}/{\overline{\mu }}_{33}{L}_0)$, time $t_0=n_{\mathrm{p}}{\overline{\mu }}_{33}{A}_{\mathrm{p}}R/n_{\mathrm{s}}{h}_{\mathrm{p}}$ or electrical load $R_0=n_{\mathrm{s}}{h}_{\mathrm{p}}T/n_{\mathrm{p}}{\overline{\mu }}_{33}{A}_{\mathrm{p}}$, and then the normalized real-time output voltage including the effects of limited space may be expressed as

when $\mathrm{\Delta }{L}_{max}/L_0$ is the normalized maximal end-to-end displacement of the device, and, for a healthy adult heart, this parameter is statistically constant of $\mathrm{\Delta }{L}_{max}/L_0\approx 0.25$ [36]. Accordingly, the scaling laws for the normalized electric outputs are obtained as where φ can either be the output voltage V, output current I or output power P, while V₀, $I_0=(E_{\mathrm{s}}{I}_{\mathrm{s}}/\overline{EI})(n_{\mathrm{p}}{\overline{e}}_{31}{z}_{\mathrm{p}}{A}_{\mathrm{p}}/L_{0}T)$ and $P_0=((E_{\mathrm{s}}{I}_{\mathrm{s}}/\overline{EI}){({\overline{e}}_{31}{z}_{\mathrm{P}}/L_0))}^2(n_{\mathrm{s}}{n}_{\mathrm{p}}{A}_{\mathrm{p}}{h}_{\mathrm{p}}/{\overline{\mu }}_{33}T)$ are, respectively, the intrinsic scales of current and power. The scaling law in equation (4.2) indicates that the normalized electric outputs (voltage, current, power or power density) only depend on two combined parameters, i.e. the normalized electrical load R/R₀ and the normalized permitted space A_c/L₀.

Figures 5 and 6 present the dependence of the normalized effective voltage V_eff/V₀, the normalized effective current I_eff/I₀ and the normalized effective power P_eff/P₀ on the normalized electrical load R/R₀ in the energy harvesting circuit for various normalized permitted space A_C/L₀. The normalized output voltage V_eff/V₀ increases monotonically with R/R₀ and tends to saturate for large electrical load with the limit corresponding to the case of open circuit voltage (figure 5). In comparison, the normalized output current I_eff/I₀ decreases monotonically with R/R₀ and approaches zero for large electrical load, corresponding to the case of open circuit current. When the electrical load is zero, the energy harvesting circuit is short connected, resulting in a zero voltage and large current. For both the two extreme cases, the effective output power is zero which indicates that the MEH device does not harvest any electrical energy. For a practical energy harvesting circuit, the output power P_eff/P₀ attains the maximum as R/R₀ = 0.130 (figure 6), nearly identical to 1/2π for the energy harvesting from harmonic motions [44]. The scaling law presented in the form of figure 6 is helpful to optimize the efficiency of energy harvester by selecting properly the electric load for the circuit or other system parameters. For example, for an MEH device with a fixed total number of PZT ribbons and moduli (n_sn_p is fixed), there exists an optimal ratio of n_p/n_s to deliver a maximal output power. The optimal output power may also be realized by designing the geometry of the PZT ribbon (a proper A_p/h_p) once the volume A_ph_p of the ribbon is given (figure 6).

• Download figure
• Open in new tab
• Download PowerPoint

• Download figure
• Open in new tab
• Download PowerPoint

The scaling laws (figures 5 and 6) also reveal the adverse effects of the limited permitted space A_C/L₀ on the efficiency of the MEH device. The smaller the permitted space is, the lower output power is achieved (figure 6). According to the physiology of heart motion, the resulted maximal end-to-end displacement of the device is $\mathrm{\Delta }{L}_{max}/L_0\approx 0.25$ [36], which can be substituted into the deflection amplitude in equation (2.5) leading to the maximal amplitude as A_max/L₀ = 0.32. This indicates that the device will behave like the case of free deformation as the permitted space A_C/L₀ > 0.32. Thus, the normalized output power P_eff/P₀ keeps increasing until A_C/L₀ exceeds 0.32 where the power remains constant and is equal to the case of chest open (figure 7). The effective power produced by the energy harvesting system in the experiment (R/R₀ = 0.192) is a little bit lower than the optimal case R/R₀ = 0.130. The scaling law presented in the form of figure 7 may also provide guidelines for designing the MEH device to achieve as higher output power as possible. Combining the investigations on equation (2.9) and the $P_{\mathrm{eff}}/P_0\sim A_{\mathrm{C}}/L_0$ curve in figure 7, the output power is inversely proportional to at least the fourth order of the device length L₀, that is, shorter devices (smaller L₀) may produce higher output power. Taking the device in experiment (R/R₀ = 0.192, L₀ = 5.0 cm), for example, the effective output power P_eff may increase up to 2.5 times if the device length decreases by 20% (L₀ = 4.0 cm). Even if the device is so short that the relative permitted space satisfies A_C/L₀ > 0.32, the output power will keep inversely proportional to the square of the device length L₀. The scaling law also implies that the output power is proportional to the square of the bending rigidity ratio $E_{\mathrm{s}}{I}_{\mathrm{s}}/\overline{EI}$, effective piezoelectric constant ${\overline{e}}_{31}$ and the distance z_p of the PZT ribbons away from the neutral axis of the device.

• Download figure
• Open in new tab
• Download PowerPoint

5. Conclusion

We have developed a restricted-space deformation model to predict the efficiency of energy harvesting from the heartbeat using flexible PZT devices. The model was validated by comparing analytical results to experimental measurements, which demonstrated its capability of revealing the underlying mechanism of reduction in the efficiency of energy harvesting in chest closed environment compared to the case of chest open. A simple scaling law for the energy harvesting from heartbeat is established in terms of material, geometric, circuit and heartbeat parameters. The normalized power output by the energy harvesting system only depends on two combined parameters, i.e. the normalized pleural cavity and the normalized electrical load of the circuit. With prescribed PZT ribbons and energy harvesting moduli, the most efficient means of increasing the energy harvesting efficiency is to select proper electrical load and decrease the device length. The results may serve as guidelines for optimization of energy harvesting from heartbeat or the motion of other biological organs.

Ethics

All in vivo experiments performed were approved by the Ethics Committee (Ethics Committee of Beijing Anzhen Hospital, Capital University of Medical Sciences) and in accordance with relevant guidelines and regulations. Experimental swine raised especially for cardiovascular research are selected for in vivo testing.

Data accessibility

The datasets supporting the conclusions are accessible in the article.

Authors' contributions

Y.Z. carried out the analytic modelling, analysed the data and drafted the manuscript; C.L. designed the analytic model, analysed the data, revised and finalized the manuscript. B.L. and X.F. provided the experimental data and photos.

Competing interests

We declare we have no competing interests.

Funding

C.L. acknowledges the financial supports by the National Natural Science Foundation of China at grant nos 11322216 and 11621062. X.F. acknowledges the supports by the National Natural Science Foundation of China at grant no. 11320101001. B.L. acknowledges the support of the National Natural Science Foundation of China at grant no. 11502126.

Footnotes