233 research outputs found
Modeling the Effects of Multiple Myeloma on Kidney Function
Multiple myeloma (MM), a plasma cell cancer, is associated with many health
challenges, including damage to the kidney by tubulointerstitial fibrosis. We
develop a mathematical model which captures the qualitative behavior of the
cell and protein populations involved. Specifically, we model the interaction
between cells in the proximal tubule of the kidney, free light chains, renal
fibroblasts, and myeloma cells. We analyze the model for steady-state solutions
to find a mathematically and biologically relevant stable steady-state
solution. This foundational model provides a representation of dynamics between
key populations in tubulointerstitial fibrosis that demonstrates how these
populations interact to affect patient prognosis in patients with MM and renal
impairment.Comment: Included version of model without tumor with steady-state analysis,
corrected equations for free light chains and renal fibroblasts in model with
tumor to reflect steady-state analysis, updated abstract, updated and added
reference
Computational Methods and Results for Structured Multiscale Models of Tumor Invasion
We present multiscale models of cancer tumor invasion with components at the
molecular, cellular, and tissue levels. We provide biological justifications
for the model components, present computational results from the model, and
discuss the scientific-computing methodology used to solve the model equations.
The models and methodology presented in this paper form the basis for
developing and treating increasingly complex, mechanistic models of tumor
invasion that will be more predictive and less phenomenological. Because many
of the features of the cancer models, such as taxis, aging and growth, are seen
in other biological systems, the models and methods discussed here also provide
a template for handling a broader range of biological problems
The Role of Osteocytes in Targeted Bone Remodeling: A Mathematical Model
Until recently many studies of bone remodeling at the cellular level have
focused on the behavior of mature osteoblasts and osteoclasts, and their
respective precursor cells, with the role of osteocytes and bone lining cells
left largely unexplored. This is particularly true with respect to the
mathematical modeling of bone remodeling. However, there is increasing evidence
that osteocytes play important roles in the cycle of targeted bone remodeling,
in serving as a significant source of RANKL to support osteoclastogenesis, and
in secreting the bone formation inhibitor sclerostin. Moreover, there is also
increasing interest in sclerostin, an osteocyte-secreted bone formation
inhibitor, and its role in regulating local response to changes in the bone
microenvironment. Here we develop a cell population model of bone remodeling
that includes the role of osteocytes, sclerostin, and allows for the
possibility of RANKL expression by osteocyte cell populations. This model
extends and complements many of the existing mathematical models for bone
remodeling but can be used to explore aspects of the process of bone remodeling
that were previously beyond the scope of prior modeling work. Through numerical
simulations we demonstrate that our model can be used to theoretically explore
many of the most recent experimental results for bone remodeling, and can be
utilized to assess the effects of novel bone-targeting agents on the bone
remodeling process
Mechanical and hygrothermal properties of hemp-silica bio-composites
This research investigated the development of a fast-drying silica-based binder for hemp concrete products with enhanced mechanical and thermal properties. Hemp-silica bio-composites were prepared by mixing hemp shivs with a two-component binder system composed of liquid sodium silicate and tributyl citrate (TBC). Compressive strength, thermal conductivity, moisture buffering value, cyclic moisture resistance and microstructure of hemp-silica composites were analysed, and the results were compared with those of hemp-lime concrete. Hemp-silica blocks with shiv-liquid sodium silicate mass ratio of 1:3.75 and TBC content of 37.5 wt% of sodium silicate dry matter produced a compressive strength of 0.56 MPa only after 3 days of drying and 1.92 MPa after 28 days. These were higher than hemp-lime blocks at the same density range. Hemp-silica panels showed a thermal conductivity of 0.101 W/mK and an excellent moisture buffering value of 3.49. Hemp silica formed an open porosity with large air gaps between the particles and a water-resistance silica-based layer on the shiv surface producing a higher moisture resistance compared to hemp-lime systems. This paper focuses on the development of a novel fast-drying binder system with a potential for use in conjunction with other lingnocellular plant aggregates to form low-carbon and efficient multifunctional building materials
Towards a New Spatial Representation of Bone Remodeling
Irregular bone remodeling is associated with a number of bone diseases such
as osteoporosis and multiple myeloma.
Computational and mathematical modeling can aid in therapy and treatment as
well as understanding fundamental biology. Different approaches to modeling
give insight into different aspects of a phenomena so it is useful to have an
arsenal of various computational and mathematical models.
Here we develop a mathematical representation of bone remodeling that can
effectively describe many aspects of the complicated geometries and spatial
behavior observed.
There is a sharp interface between bone and marrow regions. Also the surface
of bone moves in and out, i.e. in the normal direction, due to remodeling.
Based on these observations we employ the use of a level-set function to
represent the spatial behavior of remodeling. We elaborate on a temporal model
for osteoclast and osteoblast population dynamics to determine the change in
bone mass which influences how the interface between bone and marrow changes.
We exhibit simulations based on our computational model that show the motion
of the interface between bone and marrow as a consequence of bone remodeling.
The simulations show that it is possible to capture spatial behavior of bone
remodeling in complicated geometries as they occur \emph{in vitro} and \emph{in
vivo}.
By employing the level set approach it is possible to develop computational
and mathematical representations of the spatial behavior of bone remodeling. By
including in this formalism further details, such as more complex cytokine
interactions and accurate parameter values, it is possible to obtain
simulations of phenomena related to bone remodeling with spatial behavior much
as \emph{in vitro} and \emph{in vivo}. This makes it possible to perform
\emph{in silica} experiments more closely resembling experimental observations.Comment: Math. Biosci. Eng., 9(2), 201
Linking Cellular and Mechanical Processes in Articular Cartilage Lesion Formation: A Mathematical Model
A severe application of stress on articular cartilage can initiate a cascade
of biochemical reactions that can lead to the development of osteoarthritis. We
constructed a multiscale mathematical model of the process with three
components: cellular, chemical, and mechanical. The cellular component
describes the different chondrocyte states according to the chemicals these
cells release. The chemical component models the change in concentrations of
those chemicals. The mechanical component contains a simulation of pressure
application onto a cartilage explant and the resulting strains that initiate
the biochemical processes. The model creates a framework for incorporating
explicit mechanics, simulated by finite element analysis, into a theoretical
biology framework
Modeling and Simulation of the Effects of Cyclic Loading on Articular Cartilage Lesion Formation
We present a model of articular cartilage lesion formation to simulate the
effects of cyclic loading. This model extends and modifies the
reaction-diffusion-delay model by Graham et al. 2012 for the spread of a lesion
formed though a single traumatic event. Our model represents "implicitly" the
effects of loading, meaning through a cyclic sink term in the equations for
live cells.
Our model forms the basis for in silico studies of cartilage damage relevant
to questions in osteoarthritis, for example, that may not be easily answered
through in vivo or in vitro studies.
Computational results are presented that indicate the impact of differing
levels of EPO on articular cartilage lesion abatement
A mathematical model of <i>Bacteroides thetaiotaomicron</i>, <i>Methanobrevibacter smithii</i>, and <i>Eubacterium rectale</i> interactions in the human gut
The human gut microbiota is a complex ecosystem that affects a range of human physiology. In order to explore the dynamics of the human gut microbiota, we used a system of ordinary differential equations to model mathematically the biomass of three microorganism populations: Bacteroides thetaiotaomicron, Eubacterium rectale, and Methanobrevibacter smithii. Additionally, we modeled the concentrations of relevant nutrients necessary to sustain these populations over time. Our model highlights the interactions and the competition among these three species. These three microorganisms were specifically chosen due to the system’s end product, butyrate, which is a short chain fatty acid that aids in developing and maintaining the intestinal barrier in the human gut. The basis of our mathematical model assumes the gut is structured such that bacteria and nutrients exit the gut at a rate proportional to its volume, the rate of volumetric flow, and the biomass or concentration of the particular population or nutrient. We performed global sensitivity analyses using Sobol’ sensitivities to estimate the relative importance of model parameters on simulation results
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