Strategies for Efficient Numerical Implementation of Hybrid Multi-scale Agent-Based Models to Describe Biological Systems

Abstract

Biologically related processes operate across multiple spatiotemporal scales. For computational modeling methodologies to mimic this biological complexity, individual scale models must be linked in ways that allow for dynamic exchange of information across scales. A powerful methodology is to combine a discrete modeling approach, agent-based models (ABMs), with continuum models to form hybrid models. Hybrid multi-scale ABMs have been used to simulate emergent responses of biological systems. Here, we review two aspects of hybrid multi-scale ABMs: linking individual scale models and efficiently solving the resulting model. We discuss the computational choices associated with aspects of linking individual scale models while simultaneously maintaining model tractability. We demonstrate implementations of existing numerical methods in the context of hybrid multi-scale ABMs. Using an example model describing Mycobacterium tuberculosis infection, we show relative computational speeds of various combinations of numerical methods. Efficient linking and solution of hybrid multi-scale ABMs is key to model portability, modularity, and their use in understanding biological phenomena at a systems level.

A computational tool integrating host immunity with antibiotic dynamics to study tuberculosis treatment

“…In addition, to reduce computational times ~5-fold, we implemented spectral methods for solving the partial differential equations describing diffusion [42, 43]. The use of spectral methods in this model context, including comparison with other methods, is discussed in detail in [44]. This change made the hundreds of runs necessary for sensitivity analysis computationally feasible.…”

Multiscale Model of Mycobacterium tuberculosis Infection Maps Metabolite and Gene Perturbations to Granuloma Sterilization Predictions

“…Model that captures and integrates real-world dynamics at multiple spatial or temporal scales (55,56,58).…”

Computational immuno-biology for organ transplantation and regenerative medicine

“…They predicted that chemotaxis increased total number of TC-DC contacts but decreased unique contacts between antigen-specific TCs and antigen-presenting DCs, producing less activated T-cells [83]. Subsequent refinements were developed to study T-cell and DC behavior, mediated by multiple cytokine signals and chemoattractants, after infection by Mycobacterium tuberculosis [49,[94][95][96][97]. Using these models, mechanisms that strongly correlate with better host-level outcomes have been identified, including elimination of uncontained lung granulomas by inducing low levels of lung tissue damage and inhibition of bacteria dissemination within the lung [96].…”

“…The implementation of hierarchical structures is useful to transfer the output of lower and finer spatial-temporal scales to higher and coarser scales. However, the need for feedback between scales demands multiscale approaches, where hybrid schemes need to be implemented [46,53,95]. Fig.…”

“…There are models that include genomics and systems biological networks, particularly signaling networks, that integrate stochastic simulations and differential equations [43,48,49,125]. Finally, there are hybrid multi-scale hierarchies that are implemented to integrate ordinary or partial differential equations with ABMs [46,95,97]. Currently, no multi-scale model covering the full range of scales has been successfully accomplished, from molecular/atomistic to organ/individual interactions, covering femtoseconds to hours.…”