Computationally efficient modeling of proprioceptive signals in the upper limb for prostheses: a simulation study

Abstract

Accurate models of proprioceptive neural patterns could 1 day play an important role in the creation of an intuitive proprioceptive neural prosthesis for amputees. This paper looks at combining efficient implementations of biomechanical and proprioceptor models in order to generate signals that mimic human muscular proprioceptive patterns for future experimental work in prosthesis feedback. A neuro-musculoskeletal model of the upper limb with 7 degrees of freedom and 17 muscles is presented and generates real time estimates of muscle spindle and Golgi Tendon Organ neural firing patterns. Unlike previous neuro-musculoskeletal models, muscle activation and excitation levels are unknowns in this application and an inverse dynamics tool (static optimization) is integrated to estimate these variables. A proprioceptive prosthesis will need to be portable and this is incompatible with the computationally demanding nature of standard biomechanical and proprioceptor modeling. This paper uses and proposes a number of approximations and optimizations to make real time operation on portable hardware feasible. Finally technical obstacles to mimicking natural feedback for an intuitive proprioceptive prosthesis, as well as issues and limitations with existing models, are identified and discussed.

Keywords: biomechanics; golgi tendon organ; muscle spindles; neuromusculoskeletal model; neuroprosthesis; proprioceptive feedback; static optimization; upper limb.

Figure 1

Proprioceptive prosthesis concept. Crosshatched area indicates the part of the system presented here.

Figure 2

The models presented here: (A) overall system model; (B) static optimization model—(^*) indicate state variable values from previous iteration. Variable labels are explained in section 2.1.3.

Figure 3

The musculoskeletal model, showing the paths of the 17 muscles modeled here.

Figure 4

Predicted muscle activations for an actor brushing his teeth. Coefficient of determination (R²) and Root Mean Square Error (RMSE) are shown for each. (A) Standard OpenSim output. (B) Proposed system output.

Figure 5

Proposed spindle model compared to original results from paper Mileusnic et al. (2006a) for two triangular stretches with different levels of fusimotor activity. Results are from Figure 3: A–L showing primary and secondary afferent firing in the presence or absence of static or dynamic fusimotor activation at 70 pps. Labels are as in original paper.

Figure 6

Proposed spindle model compared to original results (Figure 4) from paper Mileusnic et al. (2006a) for triangular stretches with different levels of fusimotor activity. Results are from Figure 4: A–F showing primary afferent firing in the presence of static or dynamic fusimotor activation at 35 or 200 pps. Labels are as in original paper.

Figure 7

Comparison of Mileusnic modeled data and proposed approximation against recorded data from a cat (Figure 4A of Prochazka et al., 1979). Fusimotor activity was assumed to be absent.

Figure 8

Human muscle spindle firing patterns for imposed motions. Mean values and one standard deviation error bars are shown for recorded data from Edin and Vallbo (1990) and contrasted with modeled primary and secondary spindle firing patterns for the EDCI and EIP muscles. Firing patterns for EDCI and EIP muscles are almost identical. Fusimotor input was assumed to be absent.

Figure 9

Predicted proprioceptor firing patterns for the actor brushing his teeth. (A) Predicted primary afferent firing patterns. (B) Predicted GTO firing patterns.