A Python framework for the development of hybrid models of neuromodulation

Computational models provide mathematical abstractions of real-world problems and are typically used to understand the behavior of a physical system, formulate hypotheses, and make predictions, while reducing the economical and ethical cost of experiments. In the field of neuromodulation, modeling the effects of neural stimulation is a fundamental step in the design of neuroprosthetic devices. Currently, the so-called hybrid models (HMs), which encompass the problems of volume conduction and neural response computation, have been successfully employed in the context of spinal cord stimulation, deep brain stimulation and peripheral nerve stimulation. At the state of the art, the main weakness of HMs is their high computational cost and the consequent difficulty of parameter optimizations requiring many model evaluations. To partially overcome these limitations, we can resort to the use of surrogate models, which leverage machine learning techniques to predict simulation outcomes abstracting from biophysical details. Moreover, the modularity of the HM framework allows to reuse a handful of fundamental tools for very different neuroprosthetic applications. For these reasons, we propose to build a framework to build HMs of peripheral nerve and spinal cord stimulation using Python, an object-oriented programming language (OOP), widely used for machine learning. Our models range from simplified models to very complex models of spinal cord stimulation including vertebral geometries and elaborate fascicular morphologies in peripheral nerves. Starting with the translation in Python of HMs of nerves with a relatively simple morphology already present in the literature, we have defined a method that allows for the automatic and programmatic generation of nerves models with merging, splitting and rotating fascicles. We show how to train a surrogate model, based on 3D UNet, a convolutional neural network architecture mainly employed for biomedical image segmentation, in the cases of nerves whose fascicles follow straight or curved paths. We show that the building blocks used to create a model are the same, regardless of the geometry to be created. Furthermore, the extensive use of OOP language paves the way for the creation of a single software suite capable of generating any model with simple integrations, such as the addition of specific classes, to the existing codebase. Our framework has been thoroughly documented and use cases and tutorials have been provided, to maximize the usability and expandability of the framework, both through the inclusion of further modelling modules and machine learning surrogate models.