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Theor Biol Med Model [journal]
- A selection criterion for patterns in reaction-diffusion systems. [Journal Article, Research Support, Non-U.S. Gov't]
- Theor Biol Med Model 2014.:7.
Alan Turing's work in Morphogenesis has received wide attention during the past 60 years. The central idea behind his theory is that two chemically interacting diffusible substances are able to generate stable spatial patterns, provided certain conditions are met. Ever since, extensive work on several kinds of pattern-generating reaction diffusion systems has been done. Nevertheless, prediction of specific patterns is far from being straightforward, and a great deal of interest in deciphering how to generate specific patterns under controlled conditions prevails.Techniques allowing one to predict what kind of spatial structure will emerge from reaction-diffusion systems remain unknown. In response to this need, we consider a generalized reaction diffusion system on a planar domain and provide an analytic criterion to determine whether spots or stripes will be formed. Our criterion is motivated by the existence of an associated energy function that allows bringing in the intuition provided by phase transitions phenomena.Our criterion is proved rigorously in some situations, generalizing well-known results for the scalar equation where the pattern selection process can be understood in terms of a potential. In more complex settings it is investigated numerically. Our work constitutes a first step towards rigorous pattern prediction in arbitrary geometries/conditions. Advances in this direction are highly applicable to the efficient design of Biotechnology and Developmental Biology experiments, as well as in simplifying the analysis of morphogenetic models.
- A model to determine the effect of collagen fiber alignment on heart function post myocardial infarction. [Journal Article, Research Support, N.I.H., Extramural, Research Support, U.S. Gov't, Non-P.H.S.]
- Theor Biol Med Model 2014.:6.
Adverse remodeling of the left ventricle (LV) following myocardial infarction (MI) leads to heart failure. Recent studies have shown that scar anisotropy is a determinant of cardiac function post-MI, however it remains unclear how changes in extracellular matrix (ECM) organization and structure contribute to changes in LV function. The objective of this study is to develop a model to identify potential mechanisms by which collagen structure and organization affect LV function post-MI.A four-region, multi-scale, cylindrical model of the post-MI LV was developed. The mechanical properties of the infarct region are governed by a constitutive equation based on the uncrimping of collagen fibers. The parameters of this constitutive equation include collagen orientation, angular dispersion, fiber stiffness, crimp angle, and density. Parametric variation of these parameters was used to elucidate the relationship between collagen properties and LV function.The mathematical model of the LV revealed several factors that influenced cardiac function post-MI. LV function was maximized when collagen fibers were aligned longitudinally. Increased collagen density was also found to improve stroke volume for longitudinal alignments while increased fiber stiffness decreased stroke volume for circumferential alignments.The results suggest that cardiac function post-MI is best preserved through increased circumferential compliance. Further, this study identifies several collagen fiber-level mechanisms that could potentially regulate both infarct level and organ level mechanics. Improved understanding of the multi-scale relationships between the ECM and LV function will be beneficial in the design of new diagnostic and therapeutic technologies.
- Cost-effective length and timing of school closure during an influenza pandemic depend on the severity. [Journal Article, Research Support, Non-U.S. Gov't]
- Theor Biol Med Model 2014.:5.
There has been a variation in published opinions toward the effectiveness of school closure which is implemented reactively when substantial influenza transmissions are seen at schools. Parameterizing an age-structured epidemic model using published estimates of the pandemic H1N1-2009 and accounting for the cost effectiveness, we examined if the timing and length of school closure could be optimized.Age-structured renewal equation was employed to describe the epidemic dynamics of an influenza pandemic. School closure was assumed to take place only once during the course of the pandemic, abruptly reducing child-to-child transmission for a fixed length of time and also influencing the transmission between children and adults. Public health effectiveness was measured by reduction in the cumulative incidence, and cost effectiveness was also examined by calculating the incremental cost effectiveness ratio and adopting a threshold of 1.0 × 10⁷ Japanese Yen/life-year.School closure at the epidemic peak appeared to yield the largest reduction in the final size, while the time of epidemic peak was shown to depend on the transmissibility. As the length of school closure was extended, we observed larger reduction in the cumulative incidence. Nevertheless, the cost effectiveness analysis showed that the cost of our school closure scenario with the parameters derived from H1N1-2009 was not justifiable. If the risk of death is three times or greater than that of H1N1-2009, the school closure could be regarded as cost effective.There is no fixed timing and duration of school closure that can be recommended as universal guideline for different types of influenza viruses. The effectiveness of school closure depends on the transmission dynamics of a particular influenza virus strain, especially the virulence (i.e. the infection fatality risk).
- A model of hematopoietic stem cell proliferation under the influence of a chemotherapeutic agent in combination with a hematopoietic inducing agent. [Journal Article, Research Support, Non-U.S. Gov't]
- Theor Biol Med Model 2014.:4.
Hematopoiesis is a complex process that encompasses both pro-mitotic and anti-mitotic stimuli. Pharmacological agents used in chemotherapy have a prominent anti-mitotic effect. The approach of inhibiting cell proliferation is rational with respect to the rapidly dividing malignant cells. However, it poses a serious problem with respect to cell proliferation of cell types required for the 'house-keeping' operations of the human body. One such affected system is hematopoiesis. Chemotherapy induced anemia is an undesired side effect of chemotherapy that can lead to serious complications. Patients exhibiting anemia or leukopenia during chemotherapy are frequently administered a hematopoietic inducing agent that enhances hematopoiesis.In previous work, we derived a mathematical model consisting of a set of delay differential equations that was dependent on the effect of a hematopoietic inducing agent. The aim of the current work was to formulate a mathematical model that captures both the effect of a chemotherapeutic agent in combination with a hematopoietic inducing agent. Steady state solutions and stability analysis of the system of equations is performed and numerical simulations of the stem cell population are provided.Numerical simulations confirm that our mathematical model captures the desired result which is that the use of hematopoietic agents in conjunction with chemotherapeutic agents can decrease the negative secondary effects often experienced by patients.The proposed model indicates that the introduction of hematopoietic inducing agents have clinical potential to offset the deleterious effects of chemotherapy treatment. Furthermore, the proposed model is relevant in that it enhances the understanding of stem cell dynamics and provides insight on the stem cell kinetics.
- Metapopulation epidemic models with heterogeneous mixing and travel behaviour. [Journal Article, Research Support, Non-U.S. Gov't]
- Theor Biol Med Model 2014.:3.
Determining the pandemic potential of an emerging infectious disease and how it depends on the various epidemic and population aspects is critical for the preparation of an adequate response aimed at its control. The complex interplay between population movements in space and non-homogeneous mixing patterns have so far hindered the fundamental understanding of the conditions for spatial invasion through a general theoretical framework. To address this issue, we present an analytical modelling approach taking into account such interplay under general conditions of mobility and interactions, in the simplifying assumption of two population classes.We describe a spatially structured population with non-homogeneous mixing and travel behaviour through a multi-host stochastic epidemic metapopulation model. Different population partitions, mixing patterns and mobility structures are considered, along with a specific application for the study of the role of age partition in the early spread of the 2009 H1N1 pandemic influenza.We provide a complete mathematical formulation of the model and derive a semi-analytical expression of the threshold condition for global invasion of an emerging infectious disease in the metapopulation system. A rich solution space is found that depends on the social partition of the population, the pattern of contacts across groups and their relative social activity, the travel attitude of each class, and the topological and traffic features of the mobility network. Reducing the activity of the less social group and reducing the cross-group mixing are predicted to be the most efficient strategies for controlling the pandemic potential in the case the less active group constitutes the majority of travellers. If instead traveling is dominated by the more social class, our model predicts the existence of an optimal across-groups mixing that maximises the pandemic potential of the disease, whereas the impact of variations in the activity of each group is less important.The proposed modelling approach introduces a theoretical framework for the study of infectious diseases spread in a population with two layers of heterogeneity relevant for the local transmission and the spatial propagation of the disease. It can be used for pandemic preparedness studies to identify adequate interventions and quantitatively estimate the corresponding required effort, as well as in an emerging epidemic situation to assess the pandemic potential of the pathogen from population and early outbreak data.
- Dependency of codon usage on protein sequence patterns: a statistical study. [Journal Article]
- Theor Biol Med Model 2014.:2.
Codon degeneracy and codon usage by organisms is an interesting and challenging problem. Researchers demonstrated the relation between codon usage and various functions or properties of genes and proteins, such as gene regulation, translation rate, translation efficiency, mRNA stability, splicing, and protein domains. Researchers usually represent segments of proteins responsible for specific functions or structures in a family of proteins as sequence patterns or motifs. We asked the question if organisms use the same codons in pattern segments as compared to the rest of the sequence.We used the likelihood ratio test, Pearson's chi-squared test, and mutual information to compare these two codon usages.We showed that codon usage, in segments of genes that code for a given pattern or motif in a group of proteins, varied from the rest of the gene. The codon usage in these segments was not random. Amino acids with larger number of codons used more specific codon ratios in these segments. We studied the number of amino acids in the pattern (pattern length). As patterns got longer, there was a slight decrease in the fraction of patterns with significant different codon usage in the pattern region as compared to codon usage in the gene region. We defined a measure of specificity of protein patterns, and studied its relation to the codon usage. The difference in the codon usage between pattern region and gene region, was less for the patterns with higher specificity.We provided a hypothesis that there are segments on genes that affect the codon usage and thus influence protein translation speed, and these regions are the regions that code protein pattern regions.
- In-silico models of stem cell and developmental systems. [Journal Article, Research Support, Non-U.S. Gov't]
- Theor Biol Med Model 2014.:1.
Understanding how developmental systems evolve over time is a key question in stem cell and developmental biology research. However, due to hurdles of existing experimental techniques, our understanding of these systems as a whole remains partial and coarse. In recent years, we have been constructing in-silico models that synthesize experimental knowledge using software engineering tools. Our approach integrates known isolated mechanisms with simplified assumptions where the knowledge is limited. This has proven to be a powerful, yet underutilized, tool to analyze the developmental process. The models provide a means to study development in-silico by altering the model's specifications, and thereby predict unforeseen phenomena to guide future experimental trials. To date, three organs from diverse evolutionary organisms have been modeled: the mouse pancreas, the C. elegans gonad, and partial rodent brain development. Analysis and execution of the models recapitulated the development of the organs, anticipated known experimental results and gave rise to novel testable predictions. Some of these results had already been validated experimentally. In this paper, I review our efforts in realistic in-silico modeling of stem cell research and developmental biology and discuss achievements and challenges. I envision that in the future, in-silico models as presented in this paper would become a common and useful technique for research in developmental biology and related research fields, particularly regenerative medicine, tissue engineering and cancer therapeutics.
- A patient-specific therapeutic approach for tumour cell population extinction and drug toxicity reduction using control systems-based dose-profile design. [Journal Article, Research Support, Non-U.S. Gov't]
- Theor Biol Med Model 2013.:68.
When anti-tumour therapy is administered to a tumour-host environment, an asymptotic tapering extremity of the tumour cell distribution is noticed. This extremity harbors a small number of residual tumour cells that later lead to secondary malignances. Thus, a method is needed that would enable the malignant population to be completely eliminated within a desired time-frame, negating the possibility of recurrence and drug-induced toxicity.In this study, we delineate a computational procedure using the inverse input-reconstruction approach to calculate the unknown drug stimulus input, when one desires a known output tissue-response (full tumour cell elimination, no excess toxicity). The asymptotic extremity is taken care of using a bias shift of tumour-cell distribution and guided control of drug administration, with toxicity limits enforced, during mutually-synchronized chemotherapy (as Temozolomide) and immunotherapy (Interleukin-2 and Cytotoxic T-lymphocyte).Quantitative modeling is done using representative characteristics of rapidly and slowly-growing tumours. Both were fully eliminated within 2 months with checks for recurrence and toxicity over a two-year time-line. The dose-time profile of the therapeutic agents has similar features across tumours: biphasic (lymphocytes), monophasic (chemotherapy) and stationary (interleukin), with terminal pulses of the three agents together ensuring elimination of all malignant cells. The model is then justified with clinical case studies and animal models of different neurooncological tumours like glioma, meningioma and glioblastoma.The conflicting oncological objectives of tumour-cell extinction and host protection can be simultaneously accommodated using the techniques of drug input reconstruction by enforcing a bias shift and guided control over the drug dose-time profile. For translational applicability, the procedure can be adapted to accommodate varying patient parameters, and for corrective clinical monitoring, to implement full tumour extinction, while maintaining the health profile of the patient.
- Changes in geometric configuration and biomechanical parameters of a rapidly growing abdominal aortic aneurysm may provide insight in aneurysms natural history and rupture risk. [Journal Article, Research Support, Non-U.S. Gov't]
- Theor Biol Med Model 2013.:67.
Abdominal aortic aneurysms (AAA) are currently being treated based on the maximum diameter criterion which has often been proven insufficient to determine rupture risk in case of every AAA. We analyzed a rare case of an AAA which presented an extremely fast growth focusing on biomechanical determinants that may indicate a high risk profile. The examination of such a case is expected to motivate future research towards patient-specific rupture risk estimations.An initially small AAA (maximum diameter: 4.5 cm) was followed-up and presented a growth of 1 cm in only 6-months of surveillance becoming suitable for surgical repair. Changes of morphometric characteristics regarding AAA, thrombus and lumen volumes, cross-sectional areas, thrombus maximum thickness and eccentricity, and maximum centerline curvature were recorded. Moreover biomechanical variables concerning Peak Wall Stress, AAA surface area exposed to high stress and redistribution of stress during follow-up were also assessed.Total aneurysm volume increased from 85 to 120 ml which regarded thrombus deposition since lumen volume remained stable. Thrombus deposition was eccentric regarding anterior AAA segment while its thickness increased from 0.3 cm to 1.6 cm. Moreover there was an anterior bulging over time as depicted by an increase in maximum centerline curvature from 0.4 cm-1 to 0.5 cm-1. Peak Wall Stress (PWS) exerted on aneurysm wall did not change significantly over time, slightly decreasing from 22 N/cm2 to 21 N/cm2. At the same time the area under high wall stress remained practically constant (9.9 cm2 at initial vs 9.7 cm2 at final examination) but there was a marked redistribution of wall stress against the posterior aneurysmal wall over time.Aneurysm area under high stress and redistribution of stress against the posterior wall due to changes in geometric configuration and thrombus deposition over time may have implications to aneurysms natural history and rupture risk.
- A calibrated agent-based computer model of stochastic cell dynamics in normal human colon crypts useful for in silico experiments. [Journal Article]
- Theor Biol Med Model 2013.:66.
Normal colon crypts consist of stem cells, proliferating cells, and differentiated cells. Abnormal rates of proliferation and differentiation can initiate colon cancer. We have measured the variation in the number of each of these cell types in multiple crypts in normal human biopsy specimens. This has provided the opportunity to produce a calibrated computational model that simulates cell dynamics in normal human crypts, and by changing model parameter values, to simulate the initiation and treatment of colon cancer.An agent-based model of stochastic cell dynamics in human colon crypts was developed in the multi-platform open-source application NetLogo. It was assumed that each cell's probability of proliferation and probability of death is determined by its position in two gradients along the crypt axis, a divide gradient and in a die gradient. A cell's type is not intrinsic, but rather is determined by its position in the divide gradient. Cell types are dynamic, plastic, and inter-convertible. Parameter values were determined for the shape of each of the gradients, and for a cell's response to the gradients. This was done by parameter sweeps that indicated the values that reproduced the measured number and variation of each cell type, and produced quasi-stationary stochastic dynamics. The behavior of the model was verified by its ability to reproduce the experimentally observed monocolonal conversion by neutral drift, the formation of adenomas resulting from mutations either at the top or bottom of the crypt, and by the robust ability of crypts to recover from perturbation by cytotoxic agents. One use of the virtual crypt model was demonstrated by evaluating different cancer chemotherapy and radiation scheduling protocols.A virtual crypt has been developed that simulates the quasi-stationary stochastic cell dynamics of normal human colon crypts. It is unique in that it has been calibrated with measurements of human biopsy specimens, and it can simulate the variation of cell types in addition to the average number of each cell type. The utility of the model was demonstrated with in silico experiments that evaluated cancer therapy protocols. The model is available for others to conduct additional experiments.