# Design Study on Customised Piezoelectric Elements for Energy Harvesting in Total Hip Replacements

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Finite Element Model

_{app}[25] was assumed with a maximum Young’s modulus of 20 GPa, please see [15] for more detail.

^{®}Xeon

^{®}Gold 6248 CPU processors (2.50 GHz) and 192 GB RAM per node. A sparse direct solver was used.

#### 2.2. Postprocessing

_{Imp}), where a local stress concentration is induced by integration of the EHS. This parameter was considered uncritical when not exceeding 290.9 MPa which was the global stress maximum for the unmodified geometry in the same loading situation, shown in [15]. For the piezoelectric element, the von Mises stress (σ

_{Piez}) was evaluated in the mid plane, since the contact situation leads to local stress singularities at the top and bottom end faces. The limit was defined as 30.0 MPa. This value was specified by the manufacturer as maximum preload for using the element with a constant force [32].

_{33}(t) by solving the differential equation for different load resistance R

_{layer}and the piezoelectric constants ${\mathsf{\epsilon}}_{33}^{\mathrm{T}}$ and d

_{33}. In the design study, the base area A of the element was variable, as well as the height h and the resulting number of layers n

_{layer}. The layer thickness was kept constant at h

_{layer}= 0.05 mm as for the off-the-shelf piezoelectric elements specified by the manufacturer. The used input parameters for the piezoelectric element are listed in Table 2. Since the off-the-shelf piezoelectric elements had passive top and bottom layers of around 0.175 mm thickness at a height of 2.5 mm for each single element (i.e., 2.15 mm of active height and 43 layers for a single element and 4.35 mm of active height and 86 layers for the stacked element, respectively) we assumed an according passive proportion for the customised geometries. If necessary, we reduced the active height to obtain an integer number of layers, thereby choosing for a conservative power approximation.

_{33}from the FEA [18]. The resulting load profile F

_{33}(t) approximated the force profile on the piezoelectric element, requiring only the simulation of a single load step (Figure 3a exemplary shows the scaled force profile for the final design). The generated power for different load resistance R was calculated by

#### 2.3. Geometry Variants

**Recalculation of previous data:**For the customised geometries the individual representation of the multilayer elements would exceed the computational capacity, as mentioned above. For comparison with our previous data and as reference basis for new simulations, we recalculated the off-the-shelf configurations (single and stacked multilayer piezoelectric element, see Figure 2) with the approach described above, neglecting the layers in the simulation, and considering them only for the power calculation.

**New geometries:**In addition to the off-the-shelf stacked piezoelectric element with a ring base area, we considered a full cylinder stacked multilayer element.

**Iterative design study**: On basis of the initial customised geometry, we conducted a design study to optimise the power output. Starting with the initial cavity design, we successively changed the piezoelectric element’s height to find the geometry providing the maximum power output, but ensuring compliance with the defined critical stress values (Table 3). The larger the piezoelectric element’s height, the shorter its extension towards the cavity needed to be defined to fit in the UHMW-PE housing (see Figure 2b, A to G). The best design point was then used as input for a new cavity geometry where we changed the cavity height or depth (see Figure 2a for the definition). Again, the piezoelectric element’s height was changed to comply with our specified stress values. After five new cavity geometries and over 20 simulated design points, we stopped the study. All design point geometries are presented and listed in Figure A1 and Table A1, Appendix A.

## 3. Results

_{33}was notably larger, and the stress in the piezoelectric element rose compared to the single element. The full cylinder also absorbed more load, however, the stress in the piezoelectric element was smaller and thereby less voltage and power were generated. All the three design variants fulfilled the stress criteria for the metallic implant component and for the piezoelectric element (see Table 5).

## 4. Discussion

_{33.}This has already been shown in our previous work and can be explained by the linear relationship between force and generated voltage which in contrast is contained as squared value in the calculation of the power (see Equation (2)) [15]. The difference for the stress in the piezoelectric element especially for the larger stacked configuration may result from the different height of the finite elements in the very area. The element height was notably smaller when the individual layers were modelled. With respect to the minor absolute deviation, the difference is acceptable and the approach still considered straightforward since the reduction of the model size is necessary to allow the simulation of larger piezoelectric elements of increased height or increased base area. To minimise the mesh density influence for a good comparability of the different design points in the iterative design study, the finite element height for the piezoelectric elements was kept constant for all design points.

_{33}can be withstood. This can be realised by increasing the height or base area to maximise the force transmission on the piezoelectric element. Therefore, the overall design aspect of the EHS with the mediating function of the UHWM-PE housing allows perfectly matching the piezoelectric elements geometry while maintaining the cavity geometry. This is demonstrated by the initial customised geometry; increasing the base area using the maximum available space for the same height largely raised the generated power but showed a tolerable stress level. The potential of a higher piezoelectric element, pushing the stress to the specified allowed limit, is not even exploited.

_{33}and the new configuration of the piezoelectric element, the generated voltage maximum was higher and the best matching resistance was slightly shifted to a lower value.

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Appendix A

**Figure A1.**Variants of the geometry study for the customised geometries showing the different cavity designs from left to right (the changed cavity parameters are underlined), all design points are ordered according to the height of the piezoelectric elements (top down). The arrows indicate the proceeded progress. The evaluated stresses (MPa) and power (mW) are shown in bars based on the maximum reached values. Green bars indicate a value below the critical value, and red above. For quantitative date, see Table A1.

## References

- Ledet, E.H.; Liddle, B.; Kradinova, K.; Harper, S. Smart implants in orthopedic surgery, improving patient outcomes: A review. Innov. Entrep. Health
**2018**, 5, 41–51. [Google Scholar] [CrossRef] [Green Version] - Schmidt, C.; Zimmermann, U.; Van Rienen, U. Modeling of an Optimized Electrostimulative Hip Revision System under Consideration of Uncertainty in the Conductivity of Bone Tissue. IEEE J. Biomed. Health Inform.
**2015**, 19, 1321–1330. [Google Scholar] [CrossRef] - Raben, H.; Kämmerer, P.W.; Bader, R.; Van Rienen, U. Establishment of a Numerical Model to Design an Electro-Stimulating System for a Porcine Mandibular Critical Size Defect. Appl. Sci.
**2019**, 9, 2160. [Google Scholar] [CrossRef] [Green Version] - Dos Santos, M.P.S.; Marote, A.; Santos, T.; Torrão, J.; Ramos, A.; Simões, J.A.O.; da Cruz e Silva, O.A.B.; Furlani, E.P.; Vieira, S.I.; Ferreira, J.A.F. New cosurface capacitive stimulators for the development of active osseointegrative implantable devices. Sci. Rep.
**2016**, 6, 30231. [Google Scholar] [CrossRef] - Platt, S.R.; Farritor, S.; Garvin, K.; Haider, H. The Use of Piezoelectric Ceramics for Electric Power Generation within Orthopedic Implants. IEEE/ASME Trans. Mechatron.
**2005**, 10, 455–461. [Google Scholar] [CrossRef] - Platt, S.R.; Farritor, S.; Haider, H. On Low-Frequency Electric Power Generation with PZT Ceramics. IEEE/ASME Trans. Mechatron.
**2005**, 10, 240–252. [Google Scholar] [CrossRef] - Almouahed, S.; Gouriou, M.; Hamitouche, C.; Stindel, E.; Roux, C. Self-powered instrumented knee implant for early detection of postoperative complications. In Proceedings of the 2010 Annual International Conference of the IEEE Engineering in Medicine and Biology, Buenos Aires, Argentina, 31 August–4 September 2010; pp. 5121–5124. [Google Scholar] [CrossRef]
- Almouahed, S.; Hamitouche, C.; Stindel, E. Optimized Prototype of Instrumented Knee Implant: Experimental Validation. IRBM
**2017**, 38, 250–255. [Google Scholar] [CrossRef] - Wilson, B.E. Modeling and Experimentation for Evaluation of Piezoelectric Sensors for In-Vivo Monitoring. Master’s Thesis, Tennessee Technological University, Cookeville, TN, USA, 2015. [Google Scholar]
- Safaei, M. A Piezoelectric Instrumented Total Knee Replacement for Sensing and Energy Harvesting. Ph.D. Thesis, Tennessee Technological University, Cookeville, TN, USA, 2019. [Google Scholar]
- Luciano, V.; Sardini, E.; Serpelloni, M.; Baronio, G. An energy harvesting converter to power sensorized total human knee prosthesis. Meas. Sci. Technol.
**2014**, 25, 25702. [Google Scholar] [CrossRef] [Green Version] - Ibrahim, A.; Jain, M.; Salman, E.; Willing, R.; Towfighian, S. A smart knee implant using triboelectric energy harvesters. Smart Mater. Struct.
**2019**, 28, 025040. [Google Scholar] [CrossRef] - Morais, R.; Silva, N.; Santos, P.; Frias, C.; Ferreira, J.; Ramos, A.; Simõesd, J.; Baptista, J.; Reis, M. Permanent magnet vibration power generator as an embedded mechanism for smart hip prosthesis. Procedia Eng.
**2010**, 5, 766–769. [Google Scholar] [CrossRef] - Santos, M.; Ferreira, J.; Ramos, A.; Pascoal, R.; Morais, R.; Silva, N.; Simoes, J.; Reis, M.J.C.S.; Boeri, C.N.; Festas, A.; et al. Multi-Source Energy Harvesting Power Generators for Instrumented Implants—Towards the Development of a Smart Hip Prosthesis. In Biodevices 2012, Proceedings of the International Conference on Biomedical Electronics and Devices, Vilamoura, Algarve, Portugal, 1–4 February 2012; [integrated in BIOSTEC (International Joint Conference on Biomedical Engineering Systems and Technologies)]. International Conference on Biomedical Electronics and Devices; Gabriel, J., Ed.; SciTePress: Setubal, Portugal, 2012; pp. 71–81. ISBN 978-989-8425-91-1. [Google Scholar]
- Lange, H.-E.; Hohlfeld, D.; Bader, R.; Kluess, D. A piezoelectric energy harvesting concept for an energy-autonomous instrumented total hip replacement. Smart Mater. Struct.
**2020**, 29, 115051. [Google Scholar] [CrossRef] - Soodmand, E.; Kluess, D.; Varady, P.A.; Cichon, R.; Schwarze, M.; Gehweiler, D.; Niemeyer, F.; Pahr, D.; Woiczinski, M. Interlaboratory comparison of femur surface reconstruction from CT data compared to reference optical 3D scan. Biomed. Eng. Online
**2018**, 17, 29. [Google Scholar] [CrossRef] [Green Version] - Kluess, D.; Soodmand, E.; Lorenz, A.; Pahr, D.; Schwarze, M.; Cichon, R.; Varady, P.A.; Herrmann, S.; Buchmeier, B.; Schröder, C.; et al. A round-robin finite element analysis of human femur mechanics between seven participating laboratories with experimental validation. Comput. Methods Biomech. Biomed. Eng.
**2019**, 22, 1020–1031. [Google Scholar] [CrossRef] [PubMed] - Bergmann, G.; Deuretzbacher, G.; Heller, M.; Graichen, F.; Rohlmann, A.; Strauss, J.; Duda, G. Hip contact forces and gait patterns from routine activities. J. Biomech.
**2001**, 34, 859–871. [Google Scholar] [CrossRef] - Heller, M.; Bergmann, G.; Deuretzbacher, G.; Dürselen, L.; Pohl, M.; Claes, L.; Haas, N.; Duda, G. Musculo-skeletal loading conditions at the hip during walking and stair climbing. J. Biomech.
**2001**, 34, 883–893. [Google Scholar] [CrossRef] - Heller, M.; Bergmann, G.; Kassi, J.-P.; Claes, L.; Haas, N.; Duda, G. Determination of muscle loading at the hip joint for use in pre-clinical testing. J. Biomech.
**2005**, 38, 1155–1163. [Google Scholar] [CrossRef] - Speirs, A.; Heller, M.; Duda, G.N.; Taylor, W.R. Physiologically based boundary conditions in finite element modelling. J. Biomech.
**2007**, 40, 2318–2323. [Google Scholar] [CrossRef] - Nuño, N.; Groppetti, R.; Senin, N. Static coefficient of friction between stainless steel and PMMA used in cemented hip and knee implants. Clin. Biomech.
**2006**, 21, 956–962. [Google Scholar] [CrossRef] - Wang, Y.; Yin, Z.; Li, H.; Gao, G.; Zhang, X. Friction and wear characteristics of ultrahigh molecular weight polyethylene (UHMWPE) composites containing glass fibers and carbon fibers under dry and water-lubricated conditions. Wear
**2017**, 380–381, 42–51. [Google Scholar] [CrossRef] - Taddei, F.; Schileo, E.; Helgason, B.; Cristofolini, L.; Viceconti, M. The material mapping strategy influences the accuracy of CT-based finite element models of bones: An evaluation against experimental measurements. Med. Eng. Phys.
**2007**, 29, 973–979. [Google Scholar] [CrossRef] - Morgan, E.F.; Bayraktar, H.H.; Keaveny, T.M. Trabecular bone modulus–density relationships depend on anatomic site. J. Biomech.
**2003**, 36, 897–904. [Google Scholar] [CrossRef] - Kempf, I.; Leung, K.S.; Grosse, A.; Haarman, H.J.T.M.; Seidel, H.; Taglang, G. Practice of Intramedullary Locked Nails: Scientific Basis and Standard Techniques Recommended by AIOD; Springer: Berlin/Heidelberg, Germany, 2002; ISBN 3642563309. [Google Scholar]
- Saha, S.; Pal, S. Mechanical properties of bone cement: A review. J. Biomed. Mater. Res.
**1984**, 18, 435–462. [Google Scholar] [CrossRef] - Kurtz, S.M. UHMWPE biomaterials handbook. In Ultra High Molecular Weight Polyethylene in Total Joint Replacement and Medical Devices, 2nd ed.; Academic: London, UK, 2009; ISBN 9780123747211. [Google Scholar]
- PI Ceramic GmbH. Material Coefficients PIC255: V4.3; PI Ceramic GmbH: Lederhose, Germany, 2017. [Google Scholar]
- Zysset, P.K.; Guo, X.E.; Hoffler, C.E.; Moore, K.E.; Goldstein, S.A. Elastic modulus and hardness of cortical and trabecular bone lamellae measured by nanoindentation in the human femur. J. Biomech.
**1999**, 32, 1005–1012. [Google Scholar] [CrossRef] - Ashman, R.; Cowin, S.; Van Buskirk, W.; Rice, J. A continuous wave technique for the measurement of the elastic properties of cortical bone. J. Biomech.
**1984**, 17, 349–361. [Google Scholar] [CrossRef] - PI Ceramic GmbH. Data Sheet Round PICMA
^{®}Chip Actuators: Miniature Multilayer Piezo Actuators with and without Inner Hole. Available online: https://static.piceramic.com/fileadmin/user_upload/physik_instrumente/files/datasheets/PD0xx-Datasheet.pdf (accessed on 15 January 2019). - Safaei, M.; Meneghini, R.M.; Anton, S.R. Force detection, center of pressure tracking, and energy harvesting from a piezoelectric knee implant. Smart Mater. Struct.
**2018**, 27, 114007. [Google Scholar] [CrossRef] [PubMed] - Safaei, M.; Meneghini, R.M.; Anton, S.R. Parametric analysis of electromechanical and fatigue performance of total knee replacement bearing with embedded piezoelectric transducers. Smart Mater. Struct.
**2017**, 26, 094002. [Google Scholar] [CrossRef] - Safaei, M.; Meneghini, R.M.; Anton, S.R. Energy Harvesting and Sensing With Embedded Piezoelectric Ceramics in Knee Implants. IEEE/ASME Trans. Mechatron.
**2018**, 23, 864–874. [Google Scholar] [CrossRef] - Chen, H.; Liu, M.; Jia, C.; Wang, Z. Power harvesting using PZT ceramics embedded in orthopedic implants. IEEE Trans. Ultrason. Ferroelectr. Freq. Control
**2009**, 56, 2010–2014. [Google Scholar] [CrossRef] - Li, H.; Tian, C.; Deng, Z.D. Energy harvesting from low frequency applications using piezoelectric materials. Appl. Phys. Rev.
**2014**, 1, 041301. [Google Scholar] [CrossRef] [Green Version] - Safaei, M.; Sodano, H.A.; Anton, S.R. A review of energy harvesting using piezoelectric materials: State-of-the-art a decade later (2008–2018). Smart Mater. Struct.
**2019**, 28, 113001. [Google Scholar] [CrossRef] - Almouahed, S.; Hamitouche, C.; Poignet, P.; Stindel, E. Battery-free force sensor for instrumented knee implant. In Proceedings of the 2017 IEEE Healthcare Innovations and Point of Care Technologies (HI-POCT), Bethesda, MD, USA, 6–8 November 2017; ISBN 978-1-5386-1392-4. [Google Scholar]
- Anton, S.R.; Sodano, H.A. A review of power harvesting using piezoelectric materials (2003–2006). Smart Mater. Struct.
**2007**, 16, R1–R21. [Google Scholar] [CrossRef] - Okazaki, Y. Comparison of Fatigue Properties and Fatigue Crack Growth Rates of Various Implantable Metals. Materials
**2012**, 5, 2981–3005. [Google Scholar] [CrossRef] [Green Version] - Lange, H.-E.; Bader, R.; Kluess, D. Endurance testing and finite element simulation of a modified hip stem for integration of an energy harvesting system. Proc. Inst. Mech. Eng. Part H
**2021**. [Google Scholar] [CrossRef] - Wang, H.; Cooper, T.A.; Lin, H.-T.; Wereszczak, A.A. Fatigue responses of lead zirconate titanate stacks under semibipolar electric cycling with mechanical preload. J. Appl. Phys.
**2010**, 108, 084107. [Google Scholar] [CrossRef] - CTS Company. Actuators for Dynamic Applications: Tutorial. Version 1501. 2021. Available online: http://www.noliac.com/fileadmin/user_upload/documents/Tutorials/Tutorials_Actuator_2.pdf (accessed on 31 March 2021).

**Figure 1.**(

**a**) Femoral bone segment with modified hip stem implanted; in the detail view (cross section) the components of the EHS are visible including a cylindrical piezoelectric element. (

**b**) Loading of an arbitrary cylindrical piezoelectric element with the force F

_{33}transmitted through the implant and the UHMW-PE housing. The piezoelectric element in this picture is formed by stacking two single multilayer elements with passive top and bottom layers.

**Figure 2.**(

**a**) Modified hip stem with EHS (UHWM-PE housing in transparent view and exemplary customised piezoelectric element) with detail view. Arrows indicate the cavity depth (blue) and height (black). (

**b**) Different piezoelectric element geometries; (

**A**) off-the-shelf single element, (

**B**) off-the-shelf stacked element, (

**C**) full cylinder stacked element, (

**D**) initial customised geometry, (

**E**) to (

**G**) further customised geometries of different heights and depth for first cavity geometry.

**Figure 3.**(

**a**) Force profile of F

_{33}(t) acting on the piezoelectric element for the final design, scaled on the basis of Bergmann et al. [18] and our approach described in [15] (red) and the according calculated generated voltage for the best matching resistance R = 0.08 MΩ (blue). (

**b**) Calculated power output according to Equation (2) for different load resistance R for the final design with a maximum of 729.9 µW at R = 0.08 MΩ.

Component | Young’s Modulus (GPa) | Poisson’s Ratio ^{1} (-) |
---|---|---|

Metallic implant | 195 [26] | 0.3 |

Bone cement mantle | 2.3 [27] | 0.3 |

UHMW-PE housing | 0.83 [28] | 0.46 [28] |

PZT piezoelectric element | 52.4 [29] | 0.35 [29] |

Femoral bone | 6850 × ρ_{app}^{1.49} [25],max. value 20 GPa [30,31] | 0.3 |

^{1}a Poisson’s ratio of 0.3 was assumed, if no other data was available.

Parameter | Value |
---|---|

A | Variable |

h | Variable, minus passive layers |

h_{layer} | 0.05 mm |

n_{layer} | Variable, defined by h and h_{layer} |

${\mathsf{\epsilon}}_{33}^{\mathrm{T}}/{\epsilon}_{0}$ | 1751 [29] |

d_{33} | 3.996E − 10 m/V [29] |

Symbol | Output Parameter | Limit |
---|---|---|

σ_{Imp} | Stress maximum at cavity base (metallic implant component) | 290.9 MPa |

σ_{Piez} | Stress maximum in the piezoelectric element’s mid plane | 30.0 MPa |

F_{33} | Contact force acting on the piezoelectric element’s end face | n/a |

P | Approximated power output | To be maximised |

**Table 4.**Comparison of output data when considering or neglecting the individual layers of the piezoelectric element during FEA.

Variant | σ_{Imp} (MPa) | σ_{Piez} (MPa) | F_{33} (N) | P (µW) | |
---|---|---|---|---|---|

Single | Layers | 269.4 | 14.0 | 141.6 | 8.1 |

No layers | 269.6 | 14.1 | 140.6 | 8.0 | |

Difference (%) | 0.08% | 0.64% | −0.67% | −1.33% | |

Stack | Layers | 267.2 | 16.9 | 196.3 | 31.1 |

No layers | 267.6 | 15.1 | 192.0 | 29.8 | |

Difference (%) | 0.14% | −10.71% | −2.20% | −4.36% |

**Table 5.**Output results of the different geometry variants and the initial and final geometry variants for the iterative design study.

Variant | |||||
---|---|---|---|---|---|

Single | Stacked | Stacked | Initial Final | ||

Off-The-Shelf | Full Cylinder | Customised Geometry | |||

σ_{Imp} (MPa) | 269.6 | 267.6 | 266.6 | 256.6 | 273.4 |

σ_{Piez} (MPa) | 14.1 | 15.1 | 11.9 | 16.9 | 29.7 |

F_{33} (N) | 140.6 | 192.0 | 207.7 | 536.0 | 1218.7 |

P (µW) | 8.0 | 29.8 | 26.1 | 77.8 | 729.9 |

Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. |

© 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Lange, H.-E.; Bader, R.; Kluess, D.
Design Study on Customised Piezoelectric Elements for Energy Harvesting in Total Hip Replacements. *Energies* **2021**, *14*, 3480.
https://doi.org/10.3390/en14123480

**AMA Style**

Lange H-E, Bader R, Kluess D.
Design Study on Customised Piezoelectric Elements for Energy Harvesting in Total Hip Replacements. *Energies*. 2021; 14(12):3480.
https://doi.org/10.3390/en14123480

**Chicago/Turabian Style**

Lange, Hans-E., Rainer Bader, and Daniel Kluess.
2021. "Design Study on Customised Piezoelectric Elements for Energy Harvesting in Total Hip Replacements" *Energies* 14, no. 12: 3480.
https://doi.org/10.3390/en14123480