Comparison of Optimization Strategies for Musculoskeletal Modeling of the Wrist for Therapy Planning in Case of Total Wrist Arthroplasty

Abstract

The human wrist joint is an elegant mechanism. The wrist allows the positioning and orienting of the hand to the forearm. The computational modeling of the human hand, especially of the wrist joint, can reveal important information about biomechanical mechanisms and provide the basis for its dysfunction and pathologies. For instance, this could be used for therapy planning in total wrist arthroplasty (TWA). In this study, different optimization methods and sensitivity analyses of anatomical parameters for musculoskeletal modeling were presented. Optimization includes finding the best available value of an objective function, including a variety of different types of objective functions. In the simplest case, optimization consists of maximizing or minimizing a function by systematically choosing input values from within an allowed set and computing the value of the function. Optimization techniques are used in many facets, such as the model building of joints or joint systems such as the wrist. The purpose of this study is to show the variability and influence of the included information for modeling, investigating the biomechanical function and load situation of the joint in representative scenarios. These possibilities to take them into account by an optimization and seem essential for the application of computational modeling to joint pathologies.

Keywords: TWA; biomechanics; modeling; total wrist arthroplasty.

Figure 1

Muscles direction and wrist joint moment arms: The force direction is parallel to the forearm so that the physiological cross-sectional area of the muscle is the leading parameter. (1): M. flexor carpi radialis, (2): M. palmaris longus, (3): M. flexor carpi ulnaris, (4): M. extensor carpi ulnaris, (5–6): Mm. extensors carpi radialis longus et brevis; U: Ulna; R: Radius; M: Metacarpal bone; C: Capitatum; L: Lunatum.

Figure 2

Free body diagram: (A): lever arm of ECRB; (B–C): lever arm of ECU and ECRL; (D): lever arm (10 cm = 0.1 m) of an applied load of 100 N.

Figure 3

Muscle moment arms: information taken from [11] are shown as black diamonds, the parameters shown as blue quadrat were taken from [28], the parameters shown as green quadrat were taken from [29], the parameters shown as red triangle were taken from [30], the parameters shown as red diamonds were taken from [31]. (M. flexor carpi radialis (FCR), M. palmaris longus (PL), M. flexor carpi ulnaris (FCU), M. extensor carpi ulnaris (ECU), Mm. extensors carpi radialis longus et brevis (ECRL and ECRB)).

Figure 4

Resulting wrist muscle force in case of varied different modeling parameters. (M. flexor carpi radialis (FCR), M. palmaris longus (PL), M. flexor carpi ulnaris (FCU), M. extensor carpi ulnaris (ECU), Mm. extensors carpi radialis longus et brevis (ECRL and ECRB); PCSA: physiological cross-sectional area; PFC: Peak force calculation).

Figure 5

The figure shows the resulting wrist moment during extension in case for different parameters (muscle forces and moment arm). (M. extensor carpi ulnaris (ECU), Mm. extensors carpi radialis longus et brevis (ECRL and ECRB)).

Figure 6

The figure shows the resulting wrist moment during flexion for varying different parameters (muscle forces and moment arms). (M. flexor carpi radialis (FCR), M. palmaris longus (PL), M. flexor carpi ulnaris (FCU)).

Figure 7

The figure shows the resulting wrist moment during radial deviation for different parameters. The adduction is produced by the ECU and FCU. The abduction is produced by the FCR, ECRL, and ECRB. (M. flexor carpi radialis (FCR), M. palmaris longus (PL), Mm. extensors carpi radialis longus et brevis (ECRL and ECRB)).

Figure 8

The figure shows the resulting wrist moment during ulnar deviation for different parameters. (M. flexor carpi ulnaris (FCU), M. extensor carpi ulnaris (ECU)).