An investigation of tendon strains in jersey finger injury load cases using a finite element neuromuscular human body model

Introduction: A common hand injury in American football, rugby and basketball is the so-called jersey finger injury (JFI), in which an eccentric overextension of the distal interphalangeal joint leads to an avulsion of the connected musculus flexor digitorum profundus (FDP) tendon. In the field of automotive safety assessment, finite element (FE) neuromuscular human body models (NHBMs) have been validated and are employed to evaluate different injury types related to car crash scenarios. The goal of this study is to show, how such a model can be modified to assess JFIs by adapting the hand of an FE-NHBM for the computational analysis of tendon strains during a generalized JFI load case. Methods: A jersey finger injury criterion (JFIC) covering the injury mechanisms of tendon straining and avulsion was defined based on biomechanical experiments found in the literature. The hand of the Total Human Model for Safety (THUMS) version 3.0 was combined with the musculature of THUMS version 5.03 to create a model with appropriate finger mobility. Muscle routing paths of FDP and musculus flexor digitorum superficialis (FDS) as well as tendon material parameters were optimized using literature data. A simplified JFI load case was simulated as the gripping of a cylindrical rod with finger flexor activation levels between 0% and 100%, which was then retracted with the velocity of a sprinting college football player to forcefully open the closed hand. Results: The optimization of the muscle routing node positions and tendon material parameters yielded good results with minimum normalized mean absolute error values of 0.79% and 7.16% respectively. Tendon avulsion injuries were detected in the middle and little finger for muscle activation levels of 80% and above, while no tendon or muscle strain injuries of any kind occurred. Discussion: The presented work outlines the steps necessary to adapt the hand model of a FE-NHBM for the assessment of JFIs using a newly defined injury criterion called the JFIC. The injury assessment results are in good agreement with documented JFI symptoms. At the same time, the need to rethink commonly asserted paradigms concerning the choice of muscle material parameters is highlighted.


Supplementary Table 2.
Specific muscle parameters of all implemented hand muscles.

Muscle Name Finger
No. 1

Muscle Routing Optimization Guide
The following guide will provide a detailed description of the optimization method used for placing the FDP and FDS routing nodes.To minimize the runtime, the optimization was not performed in the software environment of the FE solver LS-DYNA (Ansys, Canonsburg, PA, USA) but was instead done in MATLAB R2022a (Mathworks, Natick, MA, USA) using the least-squares optimization functionality "lsqcurvefit" provided in the Optimization Toolbox.Each muscle and each joint were tackled separately as to reduce the problem complexity.The optimization procedure will be explained for the example of the little finger FDP spanning the MCP joint.As such, "Body 1" refers to the little finger metacarpal, "Body 2" to the little finger proximal phalanx and the "Joint Axis" to the revolute axis of the little finger MCP joint (see Supplementary Figure 7).
3) Calculate point necessary for routing node directional vectors.First, find the general form of plane  that intersects   and has   as its normal vector (Eq.7).
4) Construct node placement vector  1 between  2, and   whose length is determined by the proximal phalanx geometry (Eq.10).
Through these steps, two vectors  1 and  2 were defined, which guarantee that the routing nodes are placed on a plane which is normal to the revolute joint axes and intersects with the joint center.This ensures that the force generated by the muscle elements can fully contribute to the resulting joint torque.The limits defined for  1, ,  2, and   were set such that: a) The nodes keep a minimum distance to the Joint Axis.
b) The nodes are placed on the medial palm side of the hand to avoid an overlap of the muscle trusses and the finger bones.
7) Rotate Body 2 and the routing nodes which are set as constrained to Body 2 around the Joint Axis while Body 1 is kept fixed.The joint angle is calculated as the angle between  1 and  2 using Eq.14.
8) Calculate the moment arm as the shortest distance between the muscle beam defined through the nodes  , .(seeSupplementary Figure 8).9) Plot the moment arm over  and calculate the deviation from the reference moment arm using the NMAE (see Eq 1 and Eq 2 in the main manuscript).

Supplementary Figure 2 . 3 .
Model moment arm curves of FDS spanning the PIP and MCP joints compared to moment arm curves reported in the literature 7-9 .Notes: Fingers are denoted according to the following numbering scheme: 1 = Thumb; 2 = Index Finger; 3 = Middle Finger; 4 = Ring Finger; 5 = Little Finger Supplementary Figure Simplified Jersey Finger injury load case.A: FDP and FDS driven flexion to grip the rod (light blue) from 0 ms to   = 100 ms, finger flexion direction marked with a green arrow; B: Fully flexed hand position at   = 100 ms, rod retraction direction marked with a red arrow; C: Rod retraction from   = 100 ms to the simulation end time of 200 ms, rod retraction direction marked with a red arrow.

Options 2 :Supplementary Figure 8 .
options = optimoptions('lsqcurvefit', 'MaxFunctionEvaluations', 1e3, 'FunctionTolerance', 1e-6, 'FiniteDifferenceType', 'forward', 'MaxIterations', 1e6, 'OptimalityTolerance', 1e-24, 'StepTolerance', 1e-9); Considering all possible nodal combinations and the two sets of optimizer settings, 40 routing node configurations were optimized and evaluated for each muscle spanning each joint.From these 40 results, the one with the lowest NMAE was chosen to be included in the FE model.Schematic representation of the little finger MCP joint in MATLAB.A: extended state of the MCP joint; B: flexed state of the MCP joint.The metacarpal (Body 1) is marked in magenta, the proximal phalanx (Body 2) is marked in blue.The three routing nodes are in the same color as the body which they are constrained to.The muscle routing path is marked in red, the resulting moment arm is marked in green.

Table 3 .
Generic muscle parameters of all implemented hand muscles.
( ̇ = 0) between eccentric and concentric force-velocity relations   [-] 1.5 Coordinate of pole in   (  ) normalised to     (  ) for *Parameters determined in the presented work.