On the estimation of hip joint loads through musculoskeletal modeling

Abstract

Noninvasive estimation of joint loads is still an open challenge in biomechanics. Although musculoskeletal modeling represents a solid resource, multiple improvements are still necessary to obtain accurate predictions of joint loads and to translate such potential into practical utility. The present study, focused on the hip joint, is aimed at reviewing the state-of-the-art literature on the estimation of hip joint reaction forces through musculoskeletal modeling. Our literature inspection, based on well-defined selection criteria, returned seventeen works, which were compared in terms of methods and results. Deviations between predicted and in vivo measured hip joint loads, taken from the OrthoLoad database, were assessed through quantitative deviation indices. Despite the numerous modeling and computational improvements made over the last two decades, predicted hip joint loads still deviate from their experimental counterparts and typically overestimate them. Several critical aspects have emerged that affect muscle force estimation, hence joint loads. Among them, the physical fidelity of the musculoskeletal model, with its parameters and geometry, plays a crucial role. Also, predicted joint loads are markedly affected by the selected muscle recruitment strategy, which reflects the underlying motor control policy. Practical guidelines for researchers interested in noninvasive estimation of hip joint loads are also provided.

Appendix

The present Appendix details the process to obtain the hip joint reaction forces (HJRFs). At first, Fig. 

Fig. 9

A System of forces acting at the hip joint exerted by ligaments (green arrows) and by articular contact with the acetabular cup (orange arrows: normal contact forces, red arrows: tangential contact forces). B Corresponding equivalent system about H

9A graphically clarifies the contributors to hip joint reaction forces, i.e., the contact actions at the articular surfaces and the ligament actions, which are equivalent to system in Fig. 9B represented by the resultant force ${\varvec{F}}_{h}$ applied at the hip joint center H, and a torque ${\varvec{T}}_{h}$ equal to the resultant moment about H. As mentioned in Sect. 2, it is commonly assumed that ${\varvec{T}}_{h} \approx 0$.

The equivalent system is considered in the following equilibrium of the limb, where the symbols ${\varvec{F}}$ and ${\varvec{T}}$ denote forces and torques, respectively. Figure 

Fig. 10

A System made of thigh, shank, and foot. Representative muscles are shown in red through their lines of action. B Free-body diagram of the system (G is its center of mass). Muscles actuating the hip joint have been replaced by their corresponding forces ${\varvec{F}}_{{m_{i} }}$

10 shows the system made of thigh, shank and foot and its corresponding free-body diagram. External GRFs (${\varvec{F}}_{g}$ and ${\varvec{T}}_{g}$) are measured experimentally through a force plate; the total weight ${\varvec{P}}$ and the inertial actions ${\varvec{F}}_{i}$ and ${\varvec{T}}_{i}$ (reduced to the center of mass G) are known given system’s inertial properties (mass, center of mass position, inertia matrix), geometry, and kinematics of each body segment; the forces ${\varvec{F}}_{{m_{i} }}$ exerted by the N muscles crossing the hip joint are to be estimated. The interest is in obtaining the HJRFs ${\varvec{F}}_{h}$ and ${\varvec{T}}_{h}$; hence, a method to obtain the unknown ${\varvec{F}}_{{m_{i} }}$ is necessary.

The typical approach to estimate ${\varvec{F}}_{{m_{i} }}$ is based on a recursive process starting from the most distal body (i.e., the foot, for which ${\varvec{F}}_{g}$ and ${\varvec{T}}_{g}$ are known) and proceeding proximally toward the body of interest (i.e., the femur). It includes two stages: (i) inverse dynamics, which requires the model kinematics, inertial properties and applied external actions, and (ii) an optimization-based strategy to solve for muscle forces. This two-phase process is schematically shown in Fig. 

Fig. 11

Free-body diagrams of the femur ($G_{f} { }$ is its center of mass) for inverse dynamics (A) and optimization (B)

11 for the femur body. At the inverse dynamics level (Fig. 11A), muscles are replaced by ideal joint torque actuators, and net joint forces and torques (denoted by a tilde) are obtained: these include contributions from the muscles crossing the joint and from all other unmodeled elements such as articular contact and ligaments. In the optimization phase (Fig. 11B), muscles are introduced, and their actions are estimated by optimizing a certain performance criterion (e.g., through static optimization) that redistributes $\widetilde{{\bf T}}_{h}$ across the muscles spanning the joint and acting on the femur body. It is worth highlighting that the two systems in Fig. 11A and B are dynamically equivalent. Once muscle forces are known, ${\varvec{F}}_{h}$ and ${\varvec{T}}_{h}$ can be obtained by solving the Newton–Euler equations

$${\varvec{F}}_{h} + \mathop \sum \limits_{{{\varvec{i}} = 1}}^{{\varvec{N}}} {\varvec{F}}_{{m_{i} }} + \mathbf{ F}_{{i_{f} }} + {\varvec{P}}_{f} + \widetilde{{\bf F}}_{k} = 0$$

(3)

$${\varvec{T}}_{h} + \mathop \sum \limits_{i = 1}^{N} HP_{i} \times {\varvec{F}}_{{m_{i} }} + HG_{f} \times {\varvec{F}}_{{i_{f} }} + \mathbf{ T}_{{i_{f} }} + HG_{f} \times {\varvec{P}}_{f} + HK \times \tilde{\mathbf{F}}_{k} + \widetilde{{\bf T}}_{k} = 0$$

(4)

where moments are calculated with respect to the center of the femoral head H: $HP_{i}$, $HG_{f}$, $HK$ are the position vectors pointing from H to the points of application of muscle forces ($P_{i}$), to the center of mass ($G_{f}$), and to the knee joint center (K), respectively.

It is worth noting that inverse approaches on which estimation of joint reaction forces is based are intrinsically affected by cumulative errors that increase toward proximal joints. Thus, estimation of joint loads at the hip is affected by a larger error than the estimation of joint loads at the ankle.