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

Study sample

The study sample comprised three third digits of fresh frozen cadaveric human hand specimens (age: 89.7 ± 4.0 years; gender: two female, one male; side: left) and one third digit of a fresh frozen bonobo hand specimen (taxon: Pan paniscus; age: 8 years; gender: female; side: left). Human samples were obtained via the Human Body Donation Programme of the University of Leuven, Belgium and the bonobo sample was made available by the Antwerp Zoo by Centre for Research and Conservation, Royal Zoological Society Antwerp (KMDA/RZSA) as part of the Bonobo Morphology Initiative 2016. The Bonobo Morphology Initiative made the cadavers of bonobos euthanized for medical reasons available for research.

Specimen preparation

The digits were disarticulated from the hands at the carpometacarpal joints and soft tissues were removed to identify the tendons of all intrinsic and extrinsic muscles as listed in Table 1. The soft tissues around the metacarpophalangeal (MCP) joint were kept intact to the maximum extent possible to maintain physiological conditions. Sutures were applied to each tendon using the Clove-Hitch technique (Abraham et al., 2012). In cases where intrinsic muscle tendons clearly split into two parts inserting either at the extensor mechanism (EM) or proximal phalanx (PP) base, sutures were applied to each part of the tendon (see Table 1).

Experimental design

Each specimen was mounted to the experimental setup and placed in four postures that vary in their degree of flexion/extension and simulate common postures used by both humans and African apes (see Fig. 2 and Table 2): (1) major flexion, (2) minor flexion, (3) hook grip, and (4) hyperextension. Respective joint angles were set using a goniometer. In each posture, the tendons were loaded in proportion to the maximum muscle force t_max, as estimated from the muscle specific PCSA and the maximum specific muscle tension of 45 N/cm² (Holzbaur, Murray & Delp, 2005). Human muscle PCSA data were taken from Chao et al. (1989) and the bonobo muscle PCSAs were obtained from a dissection study on the contralateral arm of the same bonobo cadaver (Article S1). The sutures were aligned in parallel to the long axis of the metacarpal bone (see Fig. 2) to best approximate physiological loading conditions.

For parameter identification, the load cell was mounted at the fingertip clamp and forces were recorded while each individual tendon was loaded to 5% of the maximum muscle force (see Table 1 for muscle-specific weights). In the combined tendon loading scenario, the fingertip forces and net metacarpal bone loads were recorded while the flexor digitorum profundus (FDP) and flexor digitorum superficialis (FDS) muscle were loaded simultaneously at two different force levels, namely 5% and 2% of the maximum muscle force (see Table 1). The tendons were loaded with only 2% to 5% of the maximum muscle force to prevent ruptures at the sutures.

Data acquisition and processing

A compact data acquisition system (NI cDAQ-9174, National Instruments, Austin, TX, USA) and a custom LabVIEW (National Instruments, Austin, TX, USA) program were used to measure forces both in the loaded and unloaded finger. The fingertip and net metacarpal bone forces were then computed as the difference of the measurements in the loaded and unloaded state to exclude gravitational forces and constraint forces resulting from specimen positioning.

After the experiments were conducted, the intended tendon load (governed by the attached weights) was compared to the true tendon loading computed based on static equilibrium equations using the fingertip force and net metacarpal bone loading available from the combined tendon loading scenarios. Deviations between intended and computed values were found and larger than expected. These deviations were attributed to friction at a pulley in the experimental setup which deflects the suture as required to apply the weights. In order to diminish the resulting error, a linear correction factor c was calculated: (1)${\displaystyle c=\frac{1}{n}\sum _{i=1}^n\left(\frac{\parallel {\mathit{F}}_{\mathrm{tip},i}+{\mathit{F}}_{\mathrm{bone},i}\parallel }{m_i\cdot g}\right)}$

In the above equation, m_i⋅g is the weight attached to the tendons during load case i computed from mass m_i and the gravitational constant g = 9.81 m∕s², F_tip,i is the respective fingertip force, F_bone,i is the net metacarpal bone loading, and ∥⋅ ∥ is the Euclidean norm. Including all four specimens, all four postures, and both load levels (i.e., n = 32) led to a correction factor of 0.835. This factor was used to correct all tendon tensions for both the combined and single tendon load cases.

Kinematics

Both the human and bonobo musculoskeletal models were generated based on the kinematic description and tendon via points provided by An et al. (1979) and implemented using custom Python scripts. The kinematics comprise of three movable (proximal, middle, and distal phalanx) and one fixed (metacarpal) bone segments interconnected by three joints, namely the MCP, the proximal interphalangeal (PIP) and the distal interphalangeal (DIP) joint (see Fig. 3). PIP and DIP joints were modelled as hinge joints with one degree of freedom (flexion/extension) and the MCP joint as a condylar joint with two rotational degrees of freedom (flexion-extension and radial/ulnar deviation). All flexion/extension joint axes were fixed and parallel to each other and the two MCP joint axes were intersecting and perpendicular.

Muscles and tendons

Six muscles actuate the finger models (see Fig. 3): the three extrinsic muscles FDP, FDS and extensor digitorum communis (EDC), and the three intrinsic muscles radial interosseus (RI), ulnar interosseus (UI) and lumbrical (LU). The extensor mechanism was included using the common Winslow’s rhombus simplification (Zancolli, 1979; Valero-Cuevas, Zajac & Burgar, 1998; Synek & Pahr, 2016). It consists of two slips and two bands, namely the central slip, terminal slip, ulnar band, and radial band (see Fig. 3). The tendon paths were approximated by straight line segments using via points proximal and distal to each joint as described by An et al. (1979) (see also Fig. 4). The coordinates of the proximal and distal via points were assumed to be constant in the coordinate systems of the proximal and distal bone of the articulation, respectively. Note that the joint posture still affects the line segment connecting the proximal and distal via point, leading to posture-specific moment arms (see also Fig. 1 of Article S2).

Computation of fingertip forces

Following Valero-Cuevas, Zajac & Burgar (1998), static fingertip forces and moments ${\mathit{F}}_{\mathrm{tip}}^{\ast }={\left[{\mathit{F}}_{\mathrm{tip}}^{\mathrm{T}},M_z\right]}^{\mathrm{T}}$ (see Fig. 4) were computed from the tendon tensions $\mathit{t}={\left[t_{\mathrm{RI}},t_{\mathrm{LU}},t_{\mathrm{UI}},t_{\mathrm{FDP}},t_{\mathrm{FDS}},t_{\mathrm{EDC}}\right]}^{\mathrm{T}}$ using the following linear relation: (2)${\displaystyle {\mathit{F}}_{\mathrm{tip}}^{\ast }=-{\mathit{J}}^{-\mathrm{T}}\mathit{T}\mathit{t}}$

where J^−T is the 4 × 4 inverse transpose Jacobian matrix which converts joint torques into fingertip forces and torques and T is the 4 × 6 force transmission matrix which contains the effective moment arms of each muscle at each degree of freedom (Lee et al., 2008). Effective moment arms are corrected for the fraction of force transmitted to a certain part of the extensor mechanism. For instance, if only 50% of the muscle force is transmitted to a specific part of the extensor mechanism (e.g., the radial band) due to a tendon bifurcation, the respective moment arm is lowered by 50% accordingly. The moment arms of each tendon segment were computed using the generalized force method (Sherman, Seth & Delp, 2013) and the assumption of bowstringing between via point coordinates. Moment arms of tendon segment that would naturally wrap around the bone in a specific posture (e.g., the terminal slip in flexion, or flexor tendons in hyperextension) were computed using Landsmeer’s model 1 (Chao et al., 1989), i.e., the moment arms were assumed to be constant for this tendon segment. This assumption leads to similar results as using wrapping geometries (Article S2). All moment arm computations were verified using the musculoskeletal modelling software OpenSim (Delp et al., 2007) (Article S2).

Computation of metacarpal bone forces and MCP joint forces

Using the fingertip forces F_tip computed using Eq. (2), the MCP joint loads F_joint can be calculated from the static equilibrium equation: (3)${\displaystyle {\mathit{F}}_{\mathrm{joint}}=-\left({\mathit{F}}_{\mathrm{tip}}+\sum _i{t}_i{\mathit{u}}_i\right)}$

where t_i is the tension of muscle i and u_i is the unit vector pointing from the distal to the proximal via point of muscle i (see Fig. 4A). In case tendon segments would naturally wrap around the bone in a specific posture as described in the previous paragraph, direction u_i was considered constant with respect to the distal bone. Joint load computations were also verified by comparison to OpenSim (see Article S2).

Assuming that the extrinsic flexor tendons run in parallel to the long axis of the metacarpal bone as in the experiment, the net load acting on the metacarpal bone F_bone can be computed as: (4)${\displaystyle {\mathit{F}}_{\mathrm{bone}}={\mathit{F}}_{\mathrm{joint}}-\sum _i\left(t_i{\mathit{v}}_i-t_i{\mathit{u}}_i\right)}$

where v_i is the unit vector parallel to the long axis of the metacarpal bone, pointing in the proximal direction (see Fig. 4B). Note that compared to F_joint, F_bone takes into account anatomical pulley forces and forces from the tendon wrapping around the head of the metacarpal bone.

Initial model parameters

Initial parameters of the human model were taken from literature. Normalized bone segment lengths and tendon via points were taken directly from An et al. (1979). Force distributions due to tendon bifurcations were initally set as follows: the fraction of force transmitted to the proximal phalanx and extensor mechanism was defined by the ratio of PCSA values of the muscles (e.g., 50:50 ratio for the RI muscle, see Table 1). The remaining transmission fractions were initially set to 50% at each tendon bifurcation, e.g., 50% of the RI muscle force transmitted to the extensor mechanism is transferred to the radial band, and the remaining 50% is transferred to the central slip.

The initial bonobo model parameters were obtained from a dissection study on the contralateral arm of the same bonobo cadaver used in this study (see Article S1). In brief, bone segment lengths were measured from a computed tomography (CT) scan using Blender (v2.64; Blender Foundation, Amsterdam, Netherlands) and custom Python scripts. Two via points for each tendon and each joint were then determined to obtain a description of the tendon paths consistent with that of An et al. (1979) for the human finger model using the following method: First, tendon paths were digitized at regular intervals relative to the closest bone using an electromagnetic motion tracking system (Patriot, Polhemus, Vt, USA) and radio-opaque markers attached to each bone. Second, tendon path points were transformed into the CT coordinate system by registering the digitized bone marker locations to those identified in the CT scan. Third, one proximal and one distal point of each tendon relative to each joint that best represented an anatomical constraint (e.g., pulley of a flexor tendon) were chosen as the final via points. Initial force transmission fractions of the extensor mechanism of the bonobo were set in analogy to the human model.