Musculoskeletal models of a human and bonobo finger: parameter identification and comparison to in vitro experiments

Introduction Knowledge of internal finger loading during human and non-human primate activities such as tool use or knuckle-walking has become increasingly important to reconstruct the behaviour of fossil hominins based on bone morphology. Musculoskeletal models have proven useful for predicting these internal loads during human activities, but load predictions for non-human primate activities are missing due to a lack of suitable finger models. The main goal of this study was to implement both a human and a representative non-human primate finger model to facilitate comparative studies on metacarpal bone loading. To ensure that the model predictions are sufficiently accurate, the specific goals were: (1) to identify species-specific model parameters based on in vitro measured fingertip forces resulting from single tendon loading and (2) to evaluate the model accuracy of predicted fingertip forces and net metacarpal bone loading in a different loading scenario. Materials & Methods Three human and one bonobo (Pan paniscus) fingers were tested in vitro using a previously developed experimental setup. The cadaveric fingers were positioned in four static postures and load was applied by attaching weights to the tendons of the finger muscles. For parameter identification, fingertip forces were measured by loading each tendon individually in each posture. For the evaluation of model accuracy, the extrinsic flexor muscles were loaded simultaneously and both the fingertip force and net metacarpal bone force were measured. The finger models were implemented using custom Python scripts. Initial parameters were taken from literature for the human model and own dissection data for the bonobo model. Optimized model parameters were identified by minimizing the error between predicted and experimentally measured fingertip forces. Fingertip forces and net metacarpal bone loading in the combined loading scenario were predicted using the optimized models and the remaining error with respect to the experimental data was evaluated. Results The parameter identification procedure led to minor model adjustments but considerably reduced the error in the predicted fingertip forces (root mean square error reduced from 0.53/0.69 N to 0.11/0.20 N for the human/bonobo model). Both models remained physiologically plausible after the parameter identification. In the combined loading scenario, fingertip and net metacarpal forces were predicted with average directional errors below 6° and magnitude errors below 12%. Conclusions This study presents the first attempt to implement both a human and non-human primate finger model for comparative palaeoanthropological studies. The good agreement between predicted and experimental forces involving the action of extrinsic flexors—which are most relevant for forceful grasping—shows that the models are likely sufficiently accurate for comparisons of internal loads occurring during human and non-human primate manual activities.


INTRODUCTION
In order to ensure that the musculoskeletal finger models as presented in the main manuscript were implemented correctly, their predictions were verified using the frequently used open source musculoskeletal modelling software OpenSim (Delp et al., 2007). In OpenSim, moment arm-based models can be easily implemented and computations of moment arms, muscle forces, and joint loads can be performed. However, tendon bifurcations, such as they occur in the extensor mechanism of the finger, cannot be accounted for. Given the functional significance of the extensor mechanism (Synek and Pahr, 2016), a custom model implementation in Python was preferred over an OpenSim model.
In this supplemental article, a simple finger model including six muscles but no extensor mechanism was implemented in both OpenSim 3.2 and Python (see Fig. 1). All model parameters (bone segment lengths, tendon via points, physiological cross sectional areas) were similar. In the OpenSim model, cylindrical wrapping geometries were added for all tendon segments except the intrinsic muscles (radial and ulnar interosseus, lumbricals) at the metacarpophalangeal (MCP) joint and the radial and ulnar band at the proximal interphalangeal (PIP) joint (see Fig. 1, left). The radii of the wrapping geometries were set to the moment arms of the respective tendon segments in neutral posture. In the Python implementation, wrapping geometries were not directly modelled. Instead, it was assumed that moment arms remain constant if the tendon would naturally wrap around the bone, e.g. an extensor tendon in flexion (see Fig. 1, right). Otherwise, bowstringing conditions were assumed, e.g. a flexor tendon in flexion (also shown in Fig. 1, right). All computations of the Python model followed the descriptions provided in the main manuscript.

MOMENT ARMS
Moment arms of each muscle/tendon at each degree of freedom (DoF) were compared within a predefined range of motion (interphalangeal and MCP joint flexion/extension: -20 to +80 • ; MCP joint radial/ulnar deviation: -20 to +20 • ). As shown in Fig. 2, the results of the Python implementation were in good agreement with the computations of OpenSim except for a slight mismatch of the extensor digitorum communis (EDC) moment arm for radial/ulnar deviation. The mean absolute error ranged from 0 to 0.03 mm for all but the EDC muscle moment arm in radial/ulnar deviation, which was 0.16 mm.

JOINT TORQUES, MUSCLE FORCES, AND JOINT LOADS
The computation of joint torques from external finger loading, muscle forces, and joint loads were verified with OpenSim using five different test cases (Fig. 3, left column). Test case one was a random posture with loads applied at each finger segment with random magnitude and random orientation. Test cases two to five represented the postures described in the main manuscript, with loads applied at the centre of the distal phalanx and oriented perpendicular to the long bone axis.
The results of the Python model were generally in line with OpenSim, although a slight mismatch of muscle force estimations could be observed (Fig. 3). The error is likely caused by the simplifying assumptions of the wrapping geometries. As expected, this error also propagated to the joint load predictions, where the error of individual force components ranged from 0 to 0.18 N (0.05 N on average). Relative to the joint load magnitude computed by OpenSim, this means that the error of the force components was within a range of 0 to 2.09 % (0.61 % on average). This relative error was considered acceptable to justify the simplified tendon wrapping assumptions of the Python implementation as a good trade off between accuracy and modelling effort.  . Joint torques resulting from external finger loading at all degrees of freedom (τ DIP , τ PIP , τ MCP,FE , τ MCP,RU ), muscle forces (t RI , t LU , t UI , t FDP , t FDS , t EDC ), and MCP joint load components (F x , F y , F z ) predicted by the OpenSim model and custom Python implementation in five test cases as shown in the leftmost column. FDS: flexor digitorum superficialis; FDP: flexor digitorum profundus; RI: radial interosseus; UI: ulnar interosseus; LU: lumbrical; EDC: extensor digitorum communis; DIP: distal interphalangeal; PIP: proximal interphalangeal; MCP: metacarpophalangeal