@article{pmid40771353,

title = {Sensitivity analysis of a mathematical model of Alzheimer's disease progression unveils important causal pathways},

author = {Seyedadel Moravveji and Halima Sadia and Nicolas Doyon and Simon Duchesne},

doi = {10.3389/fninf.2025.1590968},

issn = {1662-5196},

year  = {2025},

date = {2025-01-01},

journal = {Front Neuroinform},

volume = {19},

pages = {1590968},

abstract = {INTRODUCTION: Mathematical models serve as essential tools to investigate brain aging, the onset of Alzheimer's disease (AD) and its progression. By studying the representation of the complex dynamics of brain aging processes, such as amyloid beta (Aβ) deposition, tau tangles, neuro-inflammation, and neuronal death. Sensitivity analyses provide a powerful framework for identifying the underlying mechanisms that drive disease progression. In this study, we present the first local sensitivity analysis of a recent and comprehensive multiscale ODE-based model of Alzheimer's Disease (AD) that originates from our group. As such, it is one of the most complex model that captures the multifactorial nature of AD, incorporating neuronal, pathological, and inflammatory processes at the nano, micro and macro scales. This detailed framework enables realistic simulation of disease progression and identification of key biological parameters that influence system behavior. Our analysis identifies the key drivers of disease progression across patient profiles, providing insight into targeted therapeutic strategies.nnMETHODS: We investigated a recent ODE-based model composed of 19 variables and 75 parameters, developed by our group, to study Alzheimer's disease dynamics. We performed single- and paired-parameter sensitivity analyses, focusing on three key outcomes: neural density, amyloid beta plaques, and tau proteins.nnRESULTS: Our findings suggest that the parameters related to glucose and insulin regulation could play an important role in neurodegeneration and cognitive decline. Second, the parameters that have the most important impact on cognitive decline are not completely the same depending on sex and APOE status.nnDISCUSSION: These results underscore the importance of incorporating a multifactorial approach tailored to demographic characteristics when considering strategies for AD treatment. This approach is essential to identify the factors that contribute significantly to neural loss and AD progression.},

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pubstate = {published},

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}

@article{pmid39625537,

title = {Mathematical properties of pump-leak-cotransport models},

author = {Vincent Ouellet and Nicolas Doyon and Antoine G Godin and Pierre Marquet},

doi = {10.1007/s00285-024-02163-z},

issn = {1432-1416},

year  = {2024},

date = {2024-12-01},

journal = {J Math Biol},

volume = {90},

number = {1},

pages = {2},

abstract = {Models of ordinary differential equations are often used to describe the electrical, ionic and volumetric responses of cells to external stimuli. Although these cellular models are often solved numerically, rigorous evidence regarding their steady state solutions is scarce. In this work, we provide a formalism defining the conditions ensuring the existence and uniqueness of a steady-state solution in a large class of models including leak channels, a pump and cotransporters. Our work generalizes previous results and provides explicit conditions that a model must satisfy to guarantee the existence and uniqueness of a steady state.},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{pmid38657971,

title = {The Determining Role of Covariances in Large Networks of Stochastic Neurons},

author = {Vincent Painchaud and Patrick Desrosiers and Nicolas Doyon},

doi = {10.1162/neco_a_01656},

issn = {1530-888X},

year  = {2024},

date = {2024-05-01},

journal = {Neural Comput},

volume = {36},

number = {6},

pages = {1121--1162},

abstract = {Biological neural networks are notoriously hard to model due to their stochastic behavior and high dimensionality. We tackle this problem by constructing a dynamical model of both the expectations and covariances of the fractions of active and refractory neurons in the network's populations. We do so by describing the evolution of the states of individual neurons with a continuous-time Markov chain, from which we formally derive a low-dimensional dynamical system. This is done by solving a moment closure problem in a way that is compatible with the nonlinearity and boundedness of the activation function. Our dynamical system captures the behavior of the high-dimensional stochastic model even in cases where the mean-field approximation fails to do so. Taking into account the second-order moments modifies the solutions that would be obtained with the mean-field approximation and can lead to the appearance or disappearance of fixed points and limit cycles. We moreover perform numerical experiments where the mean-field approximation leads to periodically oscillating solutions, while the solutions of the second-order model can be interpreted as an average taken over many realizations of the stochastic model. Altogether, our results highlight the importance of including higher moments when studying stochastic networks and deepen our understanding of correlated neuronal activity.},

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pubstate = {published},

tppubtype = {article}

}

@article{pmid38586183,

title = {A computational model of Alzheimer's disease at the nano, micro, and macroscales},

author = {Éléonore Chamberland and Seyedadel Moravveji and Nicolas Doyon and Simon Duchesne},

doi = {10.3389/fninf.2024.1348113},

issn = {1662-5196},

year  = {2024},

date = {2024-01-01},

journal = {Front Neuroinform},

volume = {18},

pages = {1348113},

abstract = {INTRODUCTION: Mathematical models play a crucial role in investigating complex biological systems, enabling a comprehensive understanding of interactions among various components and facilitating  testing of intervention strategies. Alzheimer's disease (AD) is characterized by multifactorial causes and intricate interactions among biological entities, necessitating a personalized approach due to the lack of effective treatments. Therefore, mathematical models offer promise as indispensable tools in combating AD. However, existing models in this emerging field often suffer from limitations such as inadequate validation or a narrow focus on single proteins or pathways.nnMETHODS: In this paper, we present a multiscale mathematical model that describes the progression of AD through a system of 19 ordinary differential equations. The equations describe the evolution of proteins (nanoscale), cell populations (microscale), and organ-level structures (macroscale) over a 50-year lifespan, as they relate to amyloid and tau accumulation, inflammation, and neuronal death.nnRESULTS: Distinguishing our model is a robust foundation in biological principles, ensuring improved justification for the included equations, and rigorous parameter justification derived from published experimental literature.nnCONCLUSION: This model represents an essential initial step toward constructing a predictive framework, which holds significant potential for identifying effective therapeutic targets in the fight against AD.},

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pubstate = {published},

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}

@article{pmid38550514,

title = {A scoping review of mathematical models covering Alzheimer's disease progression},

author = {Seyedadel Moravveji and Nicolas Doyon and Javad Mashreghi and Simon Duchesne},

doi = {10.3389/fninf.2024.1281656},

issn = {1662-5196},

year  = {2024},

date = {2024-01-01},

journal = {Front Neuroinform},

volume = {18},

pages = {1281656},

abstract = {Alzheimer's disease is a complex, multi-factorial, and multi-parametric neurodegenerative etiology. Mathematical models can help understand such a complex problem by providing a way to explore and conceptualize principles, merging biological knowledge with experimental data into a model amenable to simulation and external validation, all without the need for extensive clinical trials. We performed a scoping review of mathematical models describing the onset and evolution of Alzheimer's disease as a result of biophysical factors following the PRISMA standard. Our search strategy applied to the PubMed database yielded 846 entries. After using our exclusion criteria, only 17 studies remained from which we extracted data, which focused on three aspects of mathematical modeling: how authors addressed continuous time (since even when the measurements are punctual, the biological processes underlying Alzheimer's disease evolve continuously), how models were solved, and how the high dimensionality and non-linearity of models were managed. Most articles modeled Alzheimer's disease at the cellular level, operating on a short time scale (e.g., minutes or hours), i.e., the micro view (12/17); the rest considered regional or brain-level processes with longer timescales (e.g., years or decades) (the macro view). Most papers were concerned primarily with amyloid beta ( = 8), few described both amyloid beta and tau proteins ( = 3), while some considered more than these two factors ( = 6). Models used partial differential equations ( = 3), ordinary differential equations ( = 7), and both partial differential equations and ordinary differential equations ( = 3). Some did not specify their mathematical formalism ( = 4). Sensitivity analyses were performed in only a small number of papers (4/17). Overall, we found that only two studies could be considered valid in terms of parameters and conclusions, and two more were partially valid. This puts the majority ( = 13) as being either invalid or with insufficient information to ascertain their status. This was the main finding of our paper, in that serious shortcomings make their results invalid or non-reproducible. These shortcomings come from insufficient methodological description, poor calibration, or the impossibility of experimentally validating or calibrating the model. Those shortcomings should be addressed by future authors to unlock the usefulness of mathematical models in Alzheimer's disease.},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{pmid37798311,

title = {Predicting cognitive decline in a low-dimensional representation of brain morphology},

author = {Rémi Lamontagne-Caron and Patrick Desrosiers and Olivier Potvin and Nicolas Doyon and Simon Duchesne},

doi = {10.1038/s41598-023-43063-4},

issn = {2045-2322},

year  = {2023},

date = {2023-10-01},

journal = {Sci Rep},

volume = {13},

number = {1},

pages = {16793},

abstract = {Identifying early signs of neurodegeneration due to Alzheimer's disease (AD) is a necessary first step towards preventing cognitive decline. Individual cortical thickness measures, available after processing anatomical magnetic resonance imaging (MRI), are sensitive markers of neurodegeneration. However, normal aging cortical decline and high inter-individual variability complicate the comparison and statistical determination of the impact of AD-related neurodegeneration on trajectories. In this paper, we computed trajectories in a 2D representation of a 62-dimensional manifold of individual cortical thickness measures. To compute this representation, we used a novel, nonlinear dimension reduction algorithm called Uniform Manifold Approximation and Projection (UMAP). We trained two embeddings, one on cortical thickness measurements of 6237 cognitively healthy participants aged 18-100 years old and the other on 233 mild cognitively impaired (MCI) and AD participants from the longitudinal database, the Alzheimer's Disease Neuroimaging Initiative database (ADNI). Each participant had multiple visits ([Formula: see text]), one year apart. The first embedding's principal axis was shown to be positively associated ([Formula: see text]) with participants' age. Data from ADNI is projected into these 2D spaces. After clustering the data, average trajectories between clusters were shown to be significantly different between MCI and AD subjects. Moreover, some clusters and trajectories between clusters were more prone to host AD subjects. This study was able to differentiate AD and MCI subjects based on their trajectory in a 2D space with an AUC of 0.80 with 10-fold cross-validation.},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{pmid36534161,

title = {Sensitivity of the electrical response of a node of Ranvier model to alterations of the myelin sheath geometry},

author = {Frank Boahen and Nicolas Doyon and Jean Deteix},

doi = {10.1007/s00285-022-01841-0},

issn = {1432-1416},

year  = {2022},

date = {2022-12-01},

journal = {J Math Biol},

volume = {86},

number = {1},

pages = {17},

abstract = {Nodes of Ranvier play critical roles in the generation and transmission of action potentials. Alterations in node properties during pathology and/or development are known to affect the speed and quality of electrical transmission. From a modelling standpoint, nodes of Ranvier are often described by systems of ordinary differential equations neglecting or greatly simplifying their geometric structure. These approaches fail to accurately describe how fine scale alteration in the node geometry or in myelin thickness in the paranode region will impact action potential generation and transmission. Here, we rely on a finite element approximation to describe the three dimensional geometry of a node of Ranvier. With this, we are able to investigate how sensitive is the electrical response to alterations in the myelin sheath and paranode geometry. We could in particular investigate irregular loss of myelin, which might be more physiologically relevant than the uniform loss often described through simpler modelling approaches.},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{pmid36063212,

title = {Beyond Wilson-Cowan dynamics: oscillations and chaos without inhibition},

author = {Vincent Painchaud and Nicolas Doyon and Patrick Desrosiers},

doi = {10.1007/s00422-022-00941-w},

issn = {1432-0770},

year  = {2022},

date = {2022-12-01},

journal = {Biol Cybern},

volume = {116},

number = {5-6},

pages = {527--543},

abstract = {Fifty years ago, Wilson and Cowan developed a mathematical model to describe the activity of neural populations. In this seminal work, they divided the cells in three groups: active, sensitive and refractory, and obtained a dynamical system to describe the evolution of the average firing rates of the populations. In the present work, we investigate the impact of the often neglected refractory state and show that taking it into account can introduce new dynamics. Starting from a continuous-time Markov chain, we perform a rigorous derivation of a mean-field model that includes the refractory fractions of populations as dynamical variables. Then, we perform bifurcation analysis to explain the occurrence of periodic solutions in cases where the classical Wilson-Cowan does not predict oscillations. We also show that our mean-field model is able to predict chaotic behavior in the dynamics of networks with as little as two populations.},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{pmid36249484,

title = {Computational modeling of trans-synaptic nanocolumns, a modulator of synaptic transmission},

author = {Xiaoting Li and Gabriel Hémond and Antoine G Godin and Nicolas Doyon},

doi = {10.3389/fncom.2022.969119},

issn = {1662-5188},

year  = {2022},

date = {2022-01-01},

journal = {Front Comput Neurosci},

volume = {16},

pages = {969119},

abstract = {Understanding synaptic transmission is of crucial importance in neuroscience. The spatial organization of receptors, vesicle release properties and neurotransmitter molecule diffusion can strongly influence features of synaptic currents. Newly discovered structures coined trans-synaptic nanocolumns were shown to align presynaptic vesicles release sites and postsynaptic receptors. However, how these structures, spanning a few tens of nanometers, shape synaptic signaling remains little understood. Given the difficulty to probe submicroscopic structures experimentally, computer modeling is a useful approach to investigate the possible functional impacts and role of nanocolumns. In our  model, as has been experimentally observed, a nanocolumn is characterized by a tight distribution of postsynaptic receptors aligned with the presynaptic vesicle release site and by the presence of trans-synaptic molecules which can modulate neurotransmitter molecule diffusion. In this work, we found that nanocolumns can play an important role in reinforcing synaptic current mostly when the presynaptic vesicle contains a small number of neurotransmitter molecules. Our work proposes a new methodology to investigate  how the existence of trans-synaptic nanocolumns, the nanometric organization of the synapse and the lateral diffusion of receptors shape the features of the synaptic current such as its amplitude and kinetics.},

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pubstate = {published},

tppubtype = {article}

}