Dressler, Matthew R.

Render, Todd

Strickland, Michael A.

Taylor, Mark

English

Southampton (e-Prints Soton)

  1   2 Holistic approaches to pre-clinical TKR analysis: computationally-enriched  3 experimental testing   4   5   6 A.M.Strickland1, M.R.Dressler2, T.Render2, M.Taylor1  7 1 Bioengineering Sciences Research Group, University of Southampton (UK)  8 2 DePuy Orthopaedics, Warsaw, IN (USA)  9   10   11   12 SYNOPSIS   13    14 The drive for better TKR designs necessitates better understanding of TKR mechanics through pre- 15 clinical analysis methods. Currently, corroboration between in-silico and in-vitro testing methods is  16 limited, and the opportunity for collaboration is underexploited. Here we demonstrate how in-silico  17 and in-vitro testing methods can be complementary and mutually supportive. The case study is a  18 corroboration of the AMTI knee simulator (displacement & force control) including control-plant  19 modelling,  in-silico  wear prediction and  probabilistics.  We demonstrate  that more rigorous  20 corroboration  between numerical &  experimental techniques can benefit both  approaches, and  21 ultimately provide much richer data for pre-clinical analysis; however, to be effective this requires  22 close and open collaboration between different research specialists. Only by working together to  23 share information and ideas more effectively can the next major advances in our understanding of  24 TKR be achieved.  25   26   27 1.  INTRODUCTION  28 Considerable work goes into pre-clinical analysis of TKR designs, to refine them as much as possible  29 before time-consuming costly clinical trials. Historically, individual research groups specialised either  30 in computational or experimental approaches. These have provided valuable insights into TKR  31 performance, but are limited in scope. Whilst many in-silico studies are based on experimental data  32 PRE-PRINT: Strickland, M. A., M. Dressler, et al. (2009). Holistic Approaches to Pre-clinical TKR Analysis: Computationally-Enriched Experimental Testing. Knee Arthroplasty 2009: From Early Intervention to Revision. London, UK, Institute of Mechanical Engineers. (e.g. [1, 2]), the degree of interaction is often limited. The  need exists to establish better  1 collaborative links between theoretical, experimental, and computational modelling methods. This  2 demonstrates not only that test results are repeatable and consistent, but also that the underlying  3 physics of the test conditions are correctly and fully understood.   4   5   6 2.  METHODS  7 This paper focuses on an exploratory review of the AMTI knee wear simulator, operating under both  8 displacement & force control, based on closer corroboration between experimental & computational  9 methods. Rigid-body models were created using MSC.ADAMS [3-5]. These models were modified to  10 reflect the configuration of the AMTI simulator assembly (including the full tibial platen and  11 associated bearings). Further, a full control-plant model was implemented in MATLAB/Simulink, and  12 finally the model was fully parameterised to facilitate  probabilistic modelling.  Tests were  13 corroborated for different gait profiles with fixed-bearing PCL-retaining implants.  14   15 For displacement-driven models kinematic-feedback data from individual tests was used directly, so  16 a control plant was not required. In-silico force & torque predictions were compared to experimental  17 load-cell feedback. For force-driven tests a model of both the plant mechanics and control system  18 was used, to more fully model the system. Simple ‘isolation profiles’ were used to explore dynamic  19 effects (inertia, friction & damping) on each of the different axes individually. This was followed by  20 corroboration of force-driven gait tests.   21   22 Wear was predicted in-silico using a number of standard algorithms, including Archard wear [6],  23 A/A+B ‘cross-shear’ wear [7] and crossing-intensity wear [8]. Wear models were considered with and  24 without contact-pressure terms.  The results were also decomposed to explore individual wear  25 influences (sliding distance, cross-shear maps & contact pressures), to reveal which factors seemed  26 to correlate best with experimental data.  27   28 Studies were not merely deterministic: probabilistic methods were also used to model experimental  29 variability (similar to [9]), and further to corroborate this with statistical data from multiple wear  30 tests. This is believed to be the first time probabilistic results for TKR have been corroborated against  31 experimental data.  32   33   34 3.  RESULTS AND DISCUSSION  1   2 The displacement-driven tests corroborated well, closely matching force-feedback once test-specific  3 variables were tuned (e.g. AP-dwell position, bearing friction). The results reveal the sensitivity of the  4 model to these variables (e.g. deviations of only 1mm in AP-dwell alter the AP axis force-feedback by  5 as much as ±100%). These tests also show the importance of accurately modelling friction not just at  6 the implant articulation, but also the other bearings in the mechanical rig. If experimental conditions  7 are correctly accounted for, the in-silico results lie well within experimental variation ranges [figure  8 1].  9   10   11   12   13   14 Force-controlled simulation proved more challenging; a simple ‘quasi-static’ mechanical model could  15 not adequately describe the system – the dynamics are highly influential. The influence of friction (of  16 the implant and other bearings) and damping in the system is considerable, and must be accounted  17 for. The role of inertia is relatively limited. Because the mechanical system sits within a control loop  18 the  demanded  and achieved waveforms will not perfectly  match.  Further, due to inertial and  19 damping elements between the actuator application point and the load cells, it is not adequate to  20 use force-feedback.  Rather, the demanded  inputs should be used with a control system (the  21 achieved feedback can be used to corroborate this control system). Corroboration of the ‘isolation  22 Figure 1: force-feedback comparison for computational model (black trace), compared to experimental variability (dashed lines)  tests’ has been successful in predicting output kinematics and load-cell feedback. However  1 discrepancies remain for the full gait test; these are believed to be related to further uncharacterised  2 system dynamics and the influence of pliancy in the fixed axes [10], on the tibial as well as the  3 femoral side.  4   5 Wear results demonstrate that (whilst not quantitatively precise) current in-silico algorithms provide  6 a useful qualitative ‘ranking’ tool for TKR wear. In-silico methods can provide a richer diagnostic data  7 set than in-vitro tests alone (e.g. surface maps and probability distribution functions for cross-shear,  8 sliding distance &  contact  pressure [figure  2]).  This is valuable for designers, clinicians &  9 theoreticians trying to better understand the causal influences of wear.   10   11   12   13   14   15   16   17   18   19 In addition  to  this,  corroborated  probabilistic studies provide  additional insight into wear  20 characteristics. By comparing the distributions for experimental and predicted wear, it is possible to  21 compare the performance of different theoretical wear algorithms against in-vitro data [figure 3].  22 Note that it is very clear from this probabilistic vantage-point that current wear algorithms are not  23 ideal. They are able to match the ‘mean’ deterministic value for wear rate (with appropriate tuning  24 of the wear constant). However, they are not accurately capturing the ‘spread’ of wear rates based  25 Figure 2: examples of in-silico visualisations: cross-shear maps (above) & intra-cycle wear rate plots (left) on variations in the experimental set-up. This clearly shows further  work is needed to better  1 understand the mechanics of wear, and also the factors influencing test variability.  2   3   4   5   6   7   8   9   10   11   12 Conventionally, numerical models are ‘validated’ using experimental results, and the AMTI simulator  13 has been a popular target for this  (e.g.  [10, 11]). The present work  advances this practice by  14 rigorously corroborating the system dynamics, controller behaviour & experimental variability- not  15 just the most basic mechanics. It is apparent that these test rigs are more complex than older models  16 have assumed, and artefacts of the rig construction and dynamics are influencing results. In the past,  17 a ‘first-approximation’ was adequate to lay the foundation for theories of knee mechanics and wear,  18 but we now require a more detailed appreciation of these tests if we are to further our theories of  19 wear.  Specifically, researchers testing with the AMTI simulator are advised to pay particular  20 attention to the AP-dwell position, and the degree of friction from the roller bearing assembly. An  21 advantage here of computational modelling is that it can be used post-hoc to further investigate  22 anomalous in-vitro test outcomes or sensitivity to experimental uncertainty.   23   24 Considering the wear algorithms, we know that these empirical models are imperfect [4]; however  25 they represent the state-of-the-art, and to advance further, more accurate corroboration is required.  26 Accounting for  discrepancies  between  in-silico  and  in-vitro  tests  (especially using probabilistic  27 methods) can provide valuable insights into the underlying factors involved in wear.  28 Figure 3: using probabilistics to compare wear rate PDFs; all existing models drastically under-predict the full range of experimental variability.   1 In conclusion, closer collaboration on these tests has lead to a better-understanding of the existing  2 experimental data, along with more accurate and powerful  computational models. As a result,  3 advances have been made in our fundamental understanding of wear simulator  mechanics.  4 Researchers in all fields of TKR testing are strongly encouraged to engage in closer collaboration  5 across disciplines, to more provide a better, richer and more rigorous toolset for pre-clinical analysis.  6   7 Acknowledgements: Research has been supported by the EPSRC and DePuy, A Johnson & Johnson  8 Company.  9   10 References: [1] Godest et al, 2002 J. Biomech 35(2). [2] Knight et al, 2007, J. Biomech 40(7).  [3]  11 Strickland et al, 2007, Trans 53rd ORS.  [4] Strickland et al, 2008 Trans 54th ORS.  [5] Arsene et al,  12 2008, Trans 8th Symp CMBBE.  [6] Archard, 1953, J.Appl Phys 24(8).  [7] Turell et al, 2003, Wear  13 255(7-12).  [8] Hamilton et al, 2005, J. Tribology 127(2).  [9] Laz et al, 2006, J. Biomech 39(12).  [10]  14 Lanovaz et al, 2008 Proc IMechE H 222(5).  [11] Zhao et al 2006, ASME SBC.  15   16 

Holistic approaches to pre-clinical TKR analysis: computationally-enriched experimental testing

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