13 papers · ranked by Valyu relevance
Kai Trepka
Building models of organismal growth enables predictions of natural variability and responses to perturbations. Complex systems such as animal pattern development and bacterial colonies can be modeled numerically using a reaction-diffusion system with relatively few factors and yield qualitatively accurate results…
Carlos Barajas, Domitilla Del Vecchio
Deterministic ordinary differential equation (ODE) models of genetic circuits, commonly assume a well-mixed ensemble of species inside the cell. However, intracellular spatial heterogeneity is frequently observed experimentally, with a circuit’s DNA location and volume occupied by the chromosome (excluded volume…
Stephen Coleman
This research examines the geographical distributions of several historical epidemics in the United States and investigates whether they reached a geographical equilibrium, however briefly. An equilibrium distribution over a geographical area, as the end state of a diffusion or spatial contagion process, has definitive…
Rafael Neto Henriques, Marta Correa, Maurizio Maralle, Elizabeth Huber + 5 more
Diffusion-weighted magnetic resonance imaging (dMRI) measurements and models provide information about brain connectivity and are sensitive to the physical properties of tissue microstructure. Diffusional Kurtosis Imaging (DKI) quantifies the degree of non-Gaussian diffusion in biological tissue from dMRI. These…
Anna M. Langmüller, Courtney C. Murdock, Philipp W. Messer
Ordinary differential equation models such as the classical SIR model are widely used in epidemiology to study and predict infectious disease dynamics. However, these models typically assume that populations are homogeneously mixed, disregarding possible variations in disease prevalence due to spatial heterogeneity. To…
Jose M. Guerrero, Nagesh Adluru, Barbara B. Bendlin, H. Hill Goldsmith + 5 more
NODDI is widely used in parameterizing microstructural brain properties. The model includes three signal compartments: intracellular, extracellular, and free water. The neurite compartment intrinsic parallel diffusivity (d_‖_) is set to 1.7 µm^2^⋅ms^−1^, though the effects of this assumption have not been extensively…
J. Hauth, J. Chodorski, A. Wirsen, R. Ulber
We expand the standard FRAP model introduced by Axelrod et al. in 1976. Our goal is to capture some common artifacts observed in the fluorescence measurements obtained with a confocal laser scanning microscope (CLSM) in biofilms: 1) linear drift, 2) exponential decrease (due to bleaching during the measurements), 3)…
Yin Hoon Chew, Fabian Spill
Metabolites have to diffuse within the sub-cellular compartments they occupy to specific locations where enzymes are, so reactions could occur. Conventional flux balance analysis (FBA), a method based on linear programming that is commonly used to model metabolism, implicitly assumes that all enzymatic reactions are…
Thomas Williams, James McCaw, James Osborne
There has been an increasing recognition of the utility of models of the spatial dynamics of viral spread within tissues. Multicellular models, where cells are represented as discrete regions of space coupled to a virus density surface, are a popular approach to capture these dynamics. Conventionally, such models are…
Andrew J. Loza, Marc S. Sherman
Biological systems frequently contain biochemical species present as small numbers of slowly diffusing molecules, leading to fluctuations that invalidate deterministic analyses of system dynamics. The development of mathematical tools that account for the spatial distribution and discrete number of reacting molecules…
Johannes G. Borgqvist, Philip Gerlee, Carl Lundholm
The formation of buds on the cell membrane of budding yeast cells is thought to be driven by reactions and diffusion involving the protein Cdc42. These processes can be described by a coupled system of partial differential equations known as the Schnakenberg system. The Schnakenberg system is known to exhibit…
Ramona Cirstian, Natalie J. Forde, Jesper L.R. Andersson, Stamatios N. Sotiropoulos + 2 more
Diffusion MRI is a neuroimaging modality used to evaluate brain structure at a microscopic level and can be exploited to map white matter fibre bundles and microstructure in the brain. One common issue is the presence of artefacts, such as acquisition artefacts, physiological artefacts, distortions or image…
Nathan H. Williamson, Rea Ravin, Dan Benjamini, Hellmut Merkle + 8 more
We develop magnetic resonance (MR) methods for measuring real-time changes of tissue microstructure and membrane permeability of live and fixed neural tissue. Diffusion and exchange MR measurements are performed using the large static gradient produced by a single-sided permanent magnet. Using tissue delipidation…