Global sensitivity analysis of the joint kinematics during gait to the parameters of a lower limb multi-body model

Abstract

Sensitivity analysis is a typical part of biomechanical models evaluation. For lower limb multi-body models, sensitivity analyses have been mainly performed on musculoskeletal parameters, more rarely on the parameters of the joint models. This study deals with a global sensitivity analysis achieved on a lower limb multi-body model that introduces anatomical constraints at the ankle, tibiofemoral, and patellofemoral joints. The aim of the study was to take into account the uncertainty of parameters (e.g. 2.5 cm on the positions of the skin markers embedded in the segments, 5° on the orientation of hinge axis, 2.5 mm on the origin and insertion of ligaments) using statistical distributions and propagate it through a multi-body optimisation method used for the computation of joint kinematics from skin markers during gait. This will allow us to identify the most influential parameters on the minimum of the objective function of the multi-body optimisation (i.e. the sum of the squared distances between measured and model-determined skin marker positions) and on the joint angles and displacements. To quantify this influence, a Fourier-based algorithm of global sensitivity analysis coupled with a Latin hypercube sampling is used. This sensitivity analysis shows that some parameters of the motor constraints, that is to say the distances between measured and model-determined skin marker positions, and the kinematic constraints are highly influencing the joint kinematics obtained from the lower limb multi-body model, for example, positions of the skin markers embedded in the shank and pelvis, parameters of the patellofemoral hinge axis, and parameters of the ankle and tibiofemoral ligaments. The resulting standard deviations on the joint angles and displacements reach 36° and 12 mm. Therefore, personalisation, customisation or identification of these most sensitive parameters of the lower limb multi-body models may be considered as essential.

Multibody Kinematics Optimization for the Estimation of Upper and Lower Limb Human Joint Kinematics: A Systematized Methodological Review

“…In MKO based on quaternions or rotation matrices, the initial guess at each sampled instant of time is often defined as the kinematics resulting from SKO applied to the skin markers [44,58]. MKO based on natural coordinates reported an initial guess of the points and axes describing the segments similarly obtained from the skin marker positions at each sampled instant of time [52,56,72]. As these natural coordinates enclose additional information about the segment geometry, the definition of the model geometrical parameters is also commonly derived from this initial guess by averaging segment lengths, position and orientations of joint centers and axis over all the sampled instants of time.…”

“…resulting standard deviation in model-derived joint kinematics reached up to 36° and 12 mm [72]. Sensitivity analyses demonstrated that STA had the most deleterious effect on hip gait kinematics [28,77], while errors in bony landmark location resulted in moderate effects [69,72,77,85]. Moreover, sensitivity of MKO to reduced marker sets [15,64] Journal of Biomechanical Engineering 20 showed good performance with less than three markers per body segment.…”

“…A unique study modelled the knee joint as universal [26] while another considered six Dofs [31]. Parallel mechanisms or four-bar mechanisms were also proposed as more realistic models for the knee [52,55,70,72] and ankle joints [52,70,72], seldom with deformable ligaments [51,54,56]. Few studies modelled the knee joint with both tibiofemoral and patelloferomal mechanisms [60,66,72].…”

Prediction of In Vivo Knee Joint Loads Using a Global Probabilistic Analysis

“…When the possible amount of an uncertainty is not available, the sensitivity of a particular output (e.g., joint kinematics, muscle moment arms, muscle function) to the change of an uncertain input (e.g., musculoskeletal geometry, musculotendon properties, joint axis location) can be quantified and provide valuable insights into the possible effects of lack of knowledge [5,16,17]. The impact of the uncertainty in different input parameters on several outputs of interest has been analyzed for musculotendon parameters [18][19][20][21][22], musculotendon geometry [23][24][25], joint center location [26], degree of freedom classification [27], joint models [28][29][30], skin marker placement [30], and pose estimation algorithms [31]. On the other hand, when the amount of possible uncertainty is known, an accurate evaluation of the output variability can be quantified.…”

“…While many studies have used probabilistic tools to analyze the effect of uncertain parameters on the output of interest [18][19][20][21][22][23][24][25][26][27][28][29][30][31], few of them have performed probabilistic analyses that combine multiple uncertainties belonging to different categories of parameters (described hereafter simply as "global") [36,37]. These global analyses allow a more complete investigation of the overall reliability of a model.…”