Source Localization Using Spinal Cord Surface Potentials and Model-based Optimization

Intraspinal microstimulation is being investigated to elicit coordinated motor responses for restoration of function. However, detailed maps of the neuroanatomy of the human spinal cord are lacking. We are developing a method to map motor nuclei in the spinal cord using potentials recorded from the surface of the spinal cord and model-based optimization. A volume conductor model of the spinal cord consisting of two concentric cylinders and an internal monopolar source was developed. Experimental data was simulated by choosing a source location, using the model to generate surface potential data, and adding Gaussian white noise. Constrained optimization was able to identify the source location used to generate the simulated experimental data to within 100 m when noise was = 5%, and to within 250 m when noise was = 10%. Introduction/Background Electrical activation of neurons by intraspinal microstimulation is a promising technique to restore function in persons with neurological disorders or injury. One challenge to the clinical application of spinal cord stimulation is determining where to implant the microelectrodes. While organized motor columns have been identified in the human spinal cord [4], detailed maps do not exist, and variation among individuals will have to be accounted for at the time of electrode implantation. Therefore, it is necessary to develop an intraoperative mapping method before intraspinal stimulation techniques can be used clinically. In this study, we are exploring the feasibility of a mapping method based on recording evoked potentials on the surface of the spinal cord. The long-term project goal is to map antidromically activated motor nuclei of the spinal cord using potential recordings on the dorsal surface of the cord. Inverse problem solutions are generally challenging because multiple solutions exist. However, knowledge of the source [6] can be used to constrain the solution set, and intraspinal potentials produced by motor nuclei upon activation have been characterized [5] [7]. We propose to solve this inverse problem using a forward model in conjunction with an optimization algorithm. The forward model of the spinal cord allows us to prescribe the location of the source and solves for the resulting potentials on the model surface. The optimization algorithm compares the forward model surface potentials with the actual surface potential data and iteratively adjusts the location of the source in the forward model, attempting to minimize the difference between the actual data and the forward model output. When that minimum is found, the location of the source in the forward model is compared to the actual source location to evaluate the degree of success. This approach was evaluated in simulations using an analytical volume conductor model of the spinal cord. In this paper, the forward model and the optimization algorithm are presented, and the feasibility of the approach is demonstrated by simulation results. Methods The forward model is composed of two concentric cylinders of infinite length (Figure 1). The inner cylinder represents the gray matter and has isotropic resistivity, and the outer cylinder represents the white matter and has anisotropic resistivity [3]. FIGURE 1: The analytic volume conductor model. The conductivities of the gray matter region ( i) and the bath ( e) are isotropic, while the conductivity of the white matter region ( o) is anisotropic. A monopolar current source (I) is located within the gray matter. The input to the optimization routine was a set of spinal cord surface potential recordings. Surface potentials generated by a single point current source were calculated. Experimental data was simulated by choosing an arbitrary source location, using the forward model to generate surface potential data, and then adding Gaussian white noise (Figure 2). FIGURE 2: Surface potential data generated with the forward model (top) and additive Gaussian white noise (middle) comprised the simulated experimental data (bottom). The cartoon in the lower right illustrates how the potential maps show the voltage on the cylinder surface. An optimization routine was used to locate the source that generated the simulated experimental data. The objective of the optimizer was to minimize the difference between the simulated experimental data (SD) and the surface potential data generated by the forward model (MD) by iteratively moving the source location in the forward model. The function describing this objective is: