Mathematical biosciences
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Mathematical biosciences · Jan 2010
An optimization study of a mathematical model of the urine concentrating mechanism of the rat kidney.
The rat kidney's morphological and transepithelial transport properties may change in response to different physiologic conditions. To better understand those processes, we used a non-linear optimization technique to estimate parameter sets that maximize key measures that assess the effectiveness and efficiency of a mathematical model of the rat urine concentrating mechanism (UCM). We considered two related measures of UCM effectiveness: the urine-to-plasma osmolality (U/P) ratio and free-water absorption rate (FWA). ⋯ To study that scenario, the optimization algorithm separately sought parameter sets that attained maximum (U/P)(rho) and (U/P)/TAT. Those parameter sets increased urine osmolality by 55.4% and 44.5%, respectively, above base-case value; the outer-medullary concentrating capability was increased by 64.6% and 35.5%, respectively, above base case; and the inner-medullary concentrating capability was increased by 73.1% and 70.8%, respectively, above base case. The corresponding urine flow rate and the concentrations of NaCl and urea are all within or near reported experimental ranges.
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Mathematical biosciences · Oct 2005
Role of structural organization in the urine concentrating mechanism of an avian kidney.
The organization of tubules and blood vessels in the quail medullary cone is highly structured. This structural organization may result in preferential interactions among tubules and vessels, interactions that may enhance urine concentrating capability. ⋯ The model equations are based on standard expressions for transmural transport and on solute and water conservation. Model results suggest that the preferential interactions among tubules enhance the urine concentration capacity of short medullary cones by reducing the diluting effect of the descending limbs on the region of the interstitium where the collecting ducts are located; however, the effects on longer cones are unclear.
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Mathematical biosciences · Jan 2002
Detection of hormesis effect in longevity: simulation approach for heterogeneous population.
Manifestation of hormesis in longevity was modelled by modification of the mortality rate during and after the period of a stress factor action. In heterogeneous population this can lead to observation of unchanged mortality during action of the stress and decrease in mortality after stress period. Stochastic simulations were made to investigate the possibility of detecting the hormesis effect on the basis of the stress-control longitudinal data. ⋯ In case of 'weak' effect the hormesis phenomenon is not detected in a 'highly heterogeneous' population even in a group composed of 1000 subjects. In a 'low heterogeneous' population the hormesis phenomenon is detected with probability higher than 70% when the group size is not less than 200 subjects. Information about the survival in control group did not play a critical role in all experiments and exact survival curve may be replaced by the traditional Kaplan-Meier estimate.
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Mathematical biosciences · May 2000
Keratinocyte growth factor signalling: a mathematical model of dermal-epidermal interaction in epidermal wound healing.
A wealth of growth factors are known to regulate the various cell functions involved in the repair process. An understanding of their therapeutic value is essential to achieve improved wound healing. Keratinocyte growth factor (KGF) seems to have a unique role as a mediator of mesenchymal-epithelial interactions: it originates from mesenchymal cells, yet acts exclusively on epithelial cells. ⋯ We then incorporate the effect of KGF on cell proliferation, and using travelling wave analysis we obtain an approximation for the rate of healing. Our modelling shows that the large up-regulation of KGF post-wounding extends the KGF signal range but is above optimal for the rate of wound closure. We predict that other functions of KGF may be more important than its role as a mitogen for the healing process.
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We derive attraction theorems for a cycle connecting nonempty compact (isolated) invariant sets using an average Lyapunov function. An application is given to a concrete system having such a cycle with the object to obtain the impermanence of the system.