8 research outputs found
Multiple sclerosis disease: A computational approach for investigating its drug interactions
Multiple Sclerosis (MS) is a chronic and potentially highly disabling disease that can cause permanent damage and deterioration of the central nervous system. In Europe it is the leading cause of non-traumatic disabilities in young adults, since more than 700,000 EU people suffer from MS. Although recent studies on MS pathophysiology have been performed, providing interesting results, MS remains a challenging disease. In this context, thanks to recent advances in software and hardware technologies, computational models and computer simulations are becoming appealing research tools to support scientists in the study of such disease. Motivated by this consideration, we propose in this paper a new model to study the evolution of MS in silico, and the effects of the administration of the daclizumab drug, taking into account also spatiality and temporality of the involved phenomena. Moreover, we show how the intrinsic symmetries of the model we have developed can be exploited to drastically reduce the complexity of its analysis
Analysis of Petri Net Models through Stochastic Differential Equations
It is well known, mainly because of the work of Kurtz, that density dependent
Markov chains can be approximated by sets of ordinary differential equations
(ODEs) when their indexing parameter grows very large. This approximation
cannot capture the stochastic nature of the process and, consequently, it can
provide an erroneous view of the behavior of the Markov chain if the indexing
parameter is not sufficiently high. Important phenomena that cannot be revealed
include non-negligible variance and bi-modal population distributions. A
less-known approximation proposed by Kurtz applies stochastic differential
equations (SDEs) and provides information about the stochastic nature of the
process. In this paper we apply and extend this diffusion approximation to
study stochastic Petri nets. We identify a class of nets whose underlying
stochastic process is a density dependent Markov chain whose indexing parameter
is a multiplicative constant which identifies the population level expressed by
the initial marking and we provide means to automatically construct the
associated set of SDEs. Since the diffusion approximation of Kurtz considers
the process only up to the time when it first exits an open interval, we extend
the approximation by a machinery that mimics the behavior of the Markov chain
at the boundary and allows thus to apply the approach to a wider set of
problems. The resulting process is of the jump-diffusion type. We illustrate by
examples that the jump-diffusion approximation which extends to bounded domains
can be much more informative than that based on ODEs as it can provide accurate
quantity distributions even when they are multi-modal and even for relatively
small population levels. Moreover, we show that the method is faster than
simulating the original Markov chain
Multiple Sclerosis disease: a computational approach for investigating its drug interactions
Multiple Sclerosis (MS) is a chronic and potentially highly disabling disease
that can cause permanent damage and deterioration of the central nervous
system. In Europe it is the leading cause of non-traumatic disabilities in
young adults, since more than 700,000 EU people suffer from MS. Although recent
studies on MS pathophysiology have been provided, MS remains a challenging
disease. In this context, thanks to recent advances in software and hardware
technologies, computational models and computer simulations are becoming
appealing research tools to support scientists in the study of such disease.
Thus, motivated by this consideration we propose in this paper a new model to
study the evolution of MS in silico, and the effects of the administration of
Daclizumab drug, taking into account also spatiality and temporality of the
involved phenomena. Moreover, we show how the intrinsic symmetries of the
system can be exploited to drastically reduce the complexity of its analysis.Comment: Submitted to CIBB 2019 post proceedings - LNC
A computational approach based on the colored Petri net formalism for studying multiple sclerosis
Multiple Sclerosis (MS) is an immune-mediated inflammatory disease of the Central Nervous System (CNS) which damages the myelin sheath enveloping nerve cells thus causing severe physical disability in patients. Relapsing Remitting Multiple Sclerosis (RRMS) is one of the most common form of MS in adults and is characterized by a series of neurologic symptoms, followed by periods of remission. Recently, many treatments were proposed and studied to contrast the RRMS progression. Among these drugs, daclizumab (commercial name Zinbryta), an antibody tailored against the Interleukin-2 receptor of T cells, exhibited promising results, but its efficacy was accompanied by an increased frequency of serious adverse events. Manifested side effects consisted of infections, encephalitis, and liver damages. Therefore daclizumab has been withdrawn from the market worldwide. Another interesting case of RRMS regards its progression in pregnant women where a smaller incidence of relapses until the delivery has been observed
From Epidemic to Pandemic Modelling
We present a methodology for systematically extending epidemic models to
multilevel and multiscale spatio-temporal pandemic ones. Our approach builds on
the use of coloured stochastic and continuous Petri nets facilitating the sound
component-based extension of basic SIR models to include population
stratification and also spatio-geographic information and travel connections,
represented as graphs, resulting in robust stratified pandemic metapopulation
models. This method is inherently easy to use, producing scalable and reusable
models with a high degree of clarity and accessibility which can be read either
in a deterministic or stochastic paradigm. Our method is supported by a
publicly available platform PetriNuts; it enables the visual construction and
editing of models; deterministic, stochastic and hybrid simulation as well as
structural and behavioural analysis. All the models are available as
supplementary material, ensuring reproducibility.Comment: 79 pages (with Appendix), 23 figures, 7 table
From Symmetric Nets to Differential Equations exploiting Model Symmetries
Stochastic Symmetric Nets (SSNs) are a High-Level Stochastic Petri Net formalism which provides a parametric system description and an efficient analysis technique that exploit system symmetries to automatically aggregate its states. Even if significant reductions can be achieved in highly symmetric models, the reduced state space can still be too large to derive and/or solve the underlying stochastic process, so that Monte Carlo simulation and fluid approximation remain the only viable ways that need to be explored. In this paper, we contribute to this line of research by proposing a new approach based on fluid approximation to automatically derive from an SSN model a set of ordinary differential equations (ODEs) which mimic the system behavior, and by showing how the SSN formalism allows us to define an efficient translation method which reduces the size of the corresponding ODE system with an automatic exploitation of system symmetries. Additionally, some case studies are presented to show the effectiveness of the method and the relevance of its application in practical cases