Reaction-diffusion models in weighted and directed connectomes.

Connectomes represent comprehensive descriptions of neural connections in a nervous system to better understand and model central brain function and peripheral processing of afferent and efferent neural signals. Connectomes can be considered as a distinctive and necessary structural component alongside glial, vascular, neurochemical, and metabolic networks of the nervous systems of higher organisms that are required for the control of body functions and interaction with the environment. They are carriers of functional phenomena such as planning behavior and cognition, which are based on the processing of highly dynamic neural signaling patterns. In this study, we examine more detailed connectomes with edge weighting and orientation properties, in which reciprocal neuronal connections are also considered. Diffusion processes are a further necessary condition for generating dynamic bioelectric patterns in connectomes. Based on our precise connectome data, we investigate different diffusion-reaction models to study the propagation of dynamic concentration patterns in control and lesioned connectomes. Therefore, differential equations for modeling diffusion were combined with well-known reaction terms to allow the use of connection weights, connectivity orientation and spatial distances. Three reaction-diffusion systems Gray-Scott, Gierer-Meinhardt and Mimura-Murray were investigated. For this purpose, implicit solvers were implemented in a numerically stable reaction-diffusion system within the framework of neuroVIISAS. The implemented reaction-diffusion systems were applied to a subconnectome which shapes the mechanosensitive pathway that is strongly affected in the multiple sclerosis demyelination disease. It was found that demyelination modeling by connectivity weight modulation changes the oscillations of the target region, i.e. the primary somatosensory cortex, of the mechanosensitive pathway. In conclusion, a new application of reaction-diffusion systems to weighted and directed connectomes has been realized. Because the implementation was realized in the neuroVIISAS framework many possibilities for the study of dynamic reaction-diffusion processes in empirical connectomes as well as specific randomized network models are available now.

Modeling and simulation for prediction of multiple sclerosis progression.

In light of extensive work that has created a wide range of techniques for predicting the course of multiple sclerosis (MS) disease, this paper attempts to provide an overview of these approaches and put forth an alternative way to predict the disease progression. For this purpose, the existing methods for estimating and predicting the course of the disease have been categorized into clinical, radiological, biological, and computational or artificial intelligence-based markers. Weighing the weaknesses and strengths of these prognostic groups is a profound method that is yet in need and works directly at the level of diseased connectivity. Therefore, we propose using the computational models in combination with established connectomes as a predictive tool for MS disease trajectories. The fundamental conduction-based Hodgkin-Huxley model emerged as promising from examining these studies. The advantage of the Hodgkin-Huxley model is that certain properties of connectomes, such as neuronal connection weights, spatial distances, and adjustments of signal transmission rates, can be taken into account. It is precisely these properties that are particularly altered in MS and that have strong implications for processing, transmission, and interactions of neuronal signaling patterns. The Hodgkin-Huxley (HH) equations as a point-neuron model are used for signal propagation inside a small network. The objective is to change the conduction parameter of the neuron model, replicate the changes in myelin properties in MS and observe the dynamics of the signal propagation across the network. The model is initially validated for different lengths, conduction values, and connection weights through three nodal connections. Later, these individual factors are incorporated into a small network and simulated to mimic the condition of MS. The signal propagation pattern is observed after inducing changes in conduction parameters at certain nodes in the network and compared against a control model pattern obtained before the changes are applied to the network. The signal propagation pattern varies as expected by adapting to the input conditions. Similarly, when the model is applied to a connectome, the pattern changes could give an insight into disease progression. This approach has opened up a new path to explore the progression of the disease in MS. The work is in its preliminary state, but with a future vision to apply this method in a connectome, providing a better clinical tool.