Anatomically based lower limb nerve model for electrical stimulation

Abstract

Background: Functional Electrical Stimulation (FES) is a technique that aims to rehabilitate or restore functionality of skeletal muscles using external electrical stimulation. Despite the success achieved within the field of FES, there are still a number of questions that remain unanswered. One way of providing input to the answers is through the use of computational models.

Methods: This paper describes the development of an anatomically based computer model of the motor neurons in the lower limb of the human leg and shows how it can be used to simulate electrical signal propagation from the beginning of the sciatic nerve to a skeletal muscle. One-dimensional cubic Hermite finite elements were used to represent the major portions of the lower limb nerves. These elements were fit to data that had been digitised using images from the Visible Man project. Nerves smaller than approximately 1 mm could not be seen in the images, and thus a tree-branching algorithm was used to connect the ends of the fitted nerve model to the respective skeletal muscle. To simulate electrical propagation, a previously published mammalian nerve model was implemented and solved on the anatomically based nerve mesh using a finite difference method. The grid points for the finite difference method were derived from the fitted finite element mesh. By adjusting the tree-branching algorithm, it is possible to represent different levels of motor-unit recruitment.

Results: To illustrate the process of a propagating nerve stimulus to a muscle in detail, the above method was applied to the nerve tree that connects to the human semitendinosus muscle. A conduction velocity of 89.8 m/s was obtained for a 15 mum diameter nerve fibre. This signal was successfully propagated down the motor neurons to a selected group of motor units in the muscle.

Conclusion: An anatomically and physiologically based model of the posterior motor neurons in the human lower limb was developed. This model can be used to examine the effect of external stimulation on nerve and muscle activity, as may occur, for example, in the field of FES.

Figure 1

Digitising and fitting. An illustration of the nerve digitisation and fitting process. (a) Slice VM1195 from the Visible Man project with the sciatic nerve identified with a single point and arrow. (b) A fitted representation of part of sciatic nerve from the VM dataset and two of its branches- the tibial and common fibular nerves.

Figure 2

Connection to nerve entry points. Illustration of the process of connecting the fitted nerve trunk to the nerve entry points. (a) Nerve entry points were positioned at the appropriate locations on the VM images. (b) An automatic nerve tree was generated and connected to the main nerve trunk. (c) An enlarged picture of the generated nerve tree.

Figure 3

Motor unit recruitment. Generating nerve trees on the semimembranosus muscle from (a) 20 out of 20 motor entry points (100% recruitment). (b) 10 out of 20 motor entry points (50% recruitment) (c) 2 out of 20 motor entry points (10 % recruitment). A maximum of 20 motor units was used for illustrative purposes.

Figure 4

Completed nerve tree. Completed nerve tree in left lower leg, together with two of the images from the Visible Man dataset. The circled bits are the endplates for muscles.

Figure 5

Myelinated nerve and cable model. (a) A myelinated nerve (b) A simplified representation of the axon of a myelinated nerve by considering the axon as a cylinder with nodes of Ranvier at regular intervals along the cylinder and with myelinated sheaths between the nodes of Ranvier. The parameter l_m represents the length of the myelinated sheath and l_n represents the length of the node of Ranvier.

Figure 6

Action potential propagation. The entire nerve tree model. The coloured field between positions 1 and 2 represent an action potential that has been generated from an extracellular stimulus at the top of the tree. Action potentials at positions labelled 1 through 4 are given in Figure 6.

Figure 7

Action potentials. Action potential (AP) along the nerve tree. Positions are shown in Figure 5(a) AP at position 1. (b) AP at position 2. (c) AP at position 3 and 4.

Figure 8

Semitendinosus muscle fibres connected to nerve tree. Semitendinosus muscle fibres connected to the two branches of the nerve tree.

Figure 9

AP propagation to the semitendinosus muscle. Action potential (AP) along the nerve tree activating several motor units of the semitendinosus muscle. The timing reference given in each picture is the time since the stimulation at the beginning of the sciatic nerve and the direction of action potential propagation in both the nerve and the muscle is indicated by corresponding arrows. (a) AP has reached the proximal endplate of the muscle and begins depolarising fibres. (b) AP has reached the distal endplate of the muscle and continues down the nerve. APs continue to propagate along fibres at the proximal endplate. (c) AP depolarisation of muscle fibres spreads from both endplates.