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PubMed2006

Mathematical modeling of ovarian cancer treatments: sequencing of surgery and chemotherapy.

Ovarian cancer has long been one of the most common forms of cancer in women. The main treatment for ovarian cancer comprises a combination of surgery and chemotherapy. In an effort to improve treatment strategies, a variety of mathematical models have been developed in the literature. In this paper, we consider a simple mathematical model that incorporates tumor growth as well as the effects of chemotherapeutic and surgical treatments in ovarian cancer. We consider several growth models and combine them with different cell-kill hypotheses. Surgery is assumed to eliminate a fixed fraction of tumor cells instantaneously. We discuss how different models predict the optimal sequencing of chemotherapeutic and surgical treatments. This work has been carried out in the context of ovarian cancer; however, the results may also be useful for other kind of cancers.

Antineoplastic Agents↗
PubMed2005

Mathematical modeling of the hypothalamic-pituitary-adrenal system activity.

Mathematical modeling has proven to be valuable in understanding of the complex biological systems dynamics. In the present report we have developed an initial model of the hypothalamic-pituitary-adrenal system self-regulatory activity. A four-dimensional non-linear differential equation model of the hormone secretion was formulated and used to analyze plasma cortisol levels in humans. The aim of this work was to explore in greater detail the role of this system in normal, homeostatic, conditions, since it is the first and unavoidable step in further understanding of the role of this complex neuroendocrine system in pathophysiological conditions. Neither the underlying mechanisms nor the physiological significance of this system are fully understood yet.

Biological Clocks↗
PubMed1999

Mathematical modelling of stress in the hip during gait.

A mathematical model is developed for calculating the contact stress distribution in the hip for a known resultant hip force and characteristic geometrical parameters. Using a relatively simple single nonlinear algebraic equation, the model can be readily applied in clinical practice to estimate the stress distribution in the most frequent body positions of everyday activities. This is demonstrated by analyzing the data on the resultant hip force obtained from laboratory observations where a stance period of gait is considered.

Acetabulum↗
PubMed2000

Subcritical endemic steady states in mathematical models for animal infections with incomplete immunity.

Many classical mathematical models for animal infections assume that all infected animals transmit the infection at the same rate, all are equally susceptible, and the course of the infection is the same in all animals. However for some infections there is evidence that seropositives may still transmit the infection, albeit at a lower rate. Animals can also experience more than one episode of the infection although those who have already experienced it have a partial immune resistance. Animals who experience a second or subsequent period of infection may not necessarily exhibit clinical symptoms. The main example discussed is bovine respiratory syncytial virus (BRSV) amongst cattle. We consider simple models with vaccination and homogeneous and proportional mixing between seropositives and seronegatives. We derive an expression for the basic reproduction number, R(o), and perform an equilibrium and stability analysis. We find that it may be possible for there to be two endemic equilibria (one stable and one unstable) for R(o)<1 and in this case at R(o)=1 there is a backwards bifurcation of an unstable endemic equilibrium from the infection-free equilibrium. Then the implications for control strategies are considered. Finally applications to Aujesky's disease (pseudorabies virus) in pigs are discussed.

Animals↗
PubMed1998

Mathematical model for the blood coagulation prothrombin time test.

A mathematical model for the prothrombin time test is proposed. The time course of clotting factor activation during coagulation was calculated, and the sensitivity of the test to a decrease in the concentrations of coagulation proteins or their activities was studied. The model predicts that only severe coagulation disorders connected with a more than five-fold decrease in the concentrations or activities of the blood coagulation factors can be revealed by the test.

Blood Coagulation Factors↗
PubMed2000

Development and validation of a dynamic mathematical model of ammonia release in pig house.

A dynamic mathematical model of Carbon-dioxide Accelerated Ammonia Release (CAAR) was developed based on the known knowledge of the chemistry of ammonia (NH3) in liquid solution, mass transfer inside liquid and across liquid-gaseous interface, and a new concept of CAAR. It calculated the NH3 concentration, release and emission at transient and steady state conditions related to a mechanically ventilated pig house. One field experimental data set was used for estimating the proportionality coefficient in the model. Another field data set was used for model validation. The ammonia concentration and emission rate calculated in the model validation were compared with the field measurement values. R2 of 0.861 and 0.947 were obtained for NH3 concentration and emission rate, respectively. In the model validation, the pH in manure surface was found to increase from 8 at initial condition to 8.85 at dynamic equilibrium due to the co-release of CO2 from the manure. This pH change accelerated the NH3 release by 6.1-fold. The model provided a quantitative description of some new understanding of the mechanism of NH3 release in the pig house and entailed suggestions of two new techniques of NH3 emission abatement: the reduction of CO2 release and the new ventilation control strategy.

Air Pollutants, Occupational↗
PubMedDate not supplied

Mathematical modeling of the myosin light chain kinase activation.

The mathematical model presented here describes the interactions among Ca2+, calmodulin (CaM), and myosin light chain kinase (MLCK) and consists of a kinetic scheme taking into account 7 reactions instead of 12 as proposed previously. We derive a system of 5 nonlinear ordinary differential equations. Solving it yields the prediction of active MLCK as a function of [Ca2+] whereby the active MLCK is defined to be proportional to the Ca4CaM.MLCK complex concentration. The model predictions are compared with other theoretical and experimental predictions of active MLCK as well as with the results of our previously proposed complex model.

Algorithms↗
PubMed2003

Mathematical model of peripheral blood stem cell harvest kinetics.

A mathematical model of peripheral blood stem cell harvests was developed, taking two new parameters R (number of recruited cells/minute) and E(f) (efficiency of collection) into consideration in addition to concentrations and collected amounts of cells. This model was tested on 241 harvest procedures in cancer patients (chemotherapy+G-CSF stimulation), donors of allogeneic PBSC, and platelet donors, using different collection procedures, with a Cobe Spectra Cell separator. The relationships between preapheresis concentrations, R, E(f) and harvested amounts of cells were complex, and different for different harvest procedures and populations of donors. However, invariably, recruitment played an important role and contributed significantly to the final harvest in all types of cells studied. For example, for the patient group, mean recruitment was 1.3 x 10(6) CD34+ cells/min and the amount of recruited cells corresponded to 65% of all collected cells. Recruitment was significantly influenced by pretreatment with chemo-therapy and/or radiotherapy. The mean recruitment values for the subgroups with limited, moderate, and extensive pretreatment were 1.65 x 10(6), 0.87 x 10(6), and 0.32 x 10(6) CD34+ cells released per minute, respectively. The finding of a quick and massive recruitment phenomenon may stimulate further research into hematopoiesis in order to maximize harvested cells.

Blood Component Removal↗
PubMed1987

Transport dynamics of the hepato-biliary system: a mathematical model allied to Tc 99m IDA scintigraphy.

A generalised mathematical model of hepatic biliary tracer flows is formulated in terms of physiologically identifiable transport parameters. From a particular solution derived from this, the system response to intravenous administration of Tc99m IDA biliary tracer is predicted. Minimisation procedures applied to this solution combined with experimental scintigraphic observations yield estimates for the physiological parameters pertaining to a number of patient studies. Some hepatic conditions where quantitative indicators may contribute to clinical diagnosis are discussed.

Biliary Tract↗
PubMed2003

A mathematical model of CO2 variation in the ventilated neonate.

A mathematical model of the variation of partial pressure of carbon dioxide in the arterial blood of a ventilated neonate is developed. The model comprises alveolar, arterial, pulmonary, venous and tissue compartments, with gas exchange in the lung determined by inspiration and expiration terms. Gas exchange is modelled through diffusion and convective transfer. Carbon dioxide is produced in the tissue by a metabolic term. Shunting is modelled by allowing blood flow to bypass the pulmonary compartment in which diffusion takes place. The model predicts changes in the carbon dioxide partial pressures that occur following abrupt changes in the ventilation settings, and show broad agreement with actual data obtained from novel sensing technology.

Carbon Dioxide↗
PubMed1995

A mathematical model of follicle dynamics in the human ovary.

A mathematical model has been developed to describe the rates of growth and death of follicles in human ovaries between 19 and 50 years of age. It was based on the numbers of follicles at three successive stages of development, which were obtained by counting follicles in histological sections of ovaries from 52 normal women. The model indicated that follicle dynamics were age dependent, with a transition at 38 years of age when the rate of follicle disappearance increased. The rates of follicle growth increased at successive stages but did not change with age. The annual egress from stage III (consisting of follicles with two or more granulosa cell layers) was affected by the declining numbers of small follicles, and corresponded to 31, nine and one follicles per day at 29-30, 39-40 and 49-50 years of age respectively. The rate of death at stage I (representing small, resting follicles) was the only parameter which varied significantly with age: no evidence of significant atresia was found for this stage in ovaries < or = 38 years old, but there was significant death above this age. As a consequence, only 40% of follicles leaving stage I reached stage III in older ovaries and just 1500 follicles in toto remained at 50 years of age from the 300,000 present at 19 years. This high death rate of small follicles appears to be responsible for advancing the timing of ovarian failure, and therefore of menopause, to midlife in our species.

Adult↗
PubMed1991

Drugs, sex and HIV: a mathematical model for New York City.

A data-based mathematical model was formulated to assess the epidemiological consequences of heterosexual, intravenous drug use (IVDU) and perinatal transmission in New York City (NYC). The model was analysed to clarify the relationship between heterosexual and IVDU transmission and to provide qualitative and quantitative insights into the HIV epidemic in NYC. The results demonstrated the significance of the dynamic interaction of heterosexual and IVDU transmission. Scenario analysis of the model was used to suggest a new explanation for the stabilization of the seroprevalence level that has been observed in the NYC IVDU community; the proposed explanation does not rely upon any IVDU or sexual behavioural changes. Gender-specific risks of heterosexual transmission in IVDUs were also explored by scenario analysis. The results showed that the effect of the heterosexual transmission risk factor on increasing the risk of HIV infection depends upon the level of IVDU. The model was used to predict future numbers of adult and pediatric AIDS cases; a sensitivity analysis of the model showed that the confidence intervals on these prediction estimates were extremely wide. This prediction variability was due to the uncertainty in estimating the values of the models' thirty variables (twenty biological-behavioural transmission parameters and the initial sizes of ten subgroups). However, the sensitivity analysis revealed that only a few key variables were significant in contributing to the AIDS case prediction variability; partial rank correlation coefficients were calculated and used to identify and to rank the importance of these key variables. The results suggest that long-term precise estimates of the future number of AIDS cases will only be possible once the values of these key variables have been evaluated accurately.

Female↗
PubMed1999

A mathematical model of the carotid baroregulation in pulsating conditions.

A mathematical model of short-term arterial pressure control by the carotid baroreceptors in vagotomized subjects is presented. It includes an elastance variable description of the left and right heart, the systemic and pulmonary circulations, the afferent carotid baroreceptor pathway, a central elaboration unit, and the action of five effector mechanisms. Simulation results suggest that the carotid baroreflex is able to significantly modulate the cardiac function curve, but this effect is masked in vivo by changes in arterial pressure and atrial pressure. During heart pacing, cardiac output increases with frequency at moderate levels of heart rate, then fails to increase further due to a reduction in stroke volume. Shifting from nonpulsatile to pulsatile perfusion of the carotid sinuses decreases the overall baroreflex gain. Finally, a sensitivity analysis suggests that venous unstressed volume control plays the major role in the early hemodynamic response to acute hemorrhage, whereas systemic resistance control is less important. In all cases, there has been satisfactory agreement between model and experimental results.

Baroreflex↗
PubMed2004

A mathematical model of immunohistochemical preparations, which provides quantitative predictions.

A mathematical model of the reaction between primary antibody and epitope is described using the Law of Mass Action to define the reaction quantitatively. The model explains some of the peculiar properties of immunohistochemical preparations. It also predicts that antibody excess over epitope will not increase staining intensity for very avid primary antibodies. This property can be exploited to measure the amount of epitope in histological sections. The assumptions of the model are not specific to immunohistochemistry, and such reasoning should be widely applicable to tests based on highly avid detection systems with high amplification of the initial signal.

Antibodies↗
PubMed1990

Analysis of stomach cancer incidence by histologic subtypes based on a mathematical model of multistage cancer induction and exponential growth.

A mathematical model incorporating the processes of both cancer induction and subsequent tumor growth has been developed. The model was applied to incidence data of stomach classified into histologic subtypes: papillary adenocarcinoma (PAP), well and moderately differentiated tubular adenocarcinomas (WEL and MOD), poorly differentiated adenocarcinoma (POR), mucinous adenocarcinoma (MUC) and signet-ring cell carcinoma (SIG). The multistage theory was assumed for cancer induction as in the Armitage-Doll model. For the period of growth, exponential growth was assumed and clinical surfacing was formulated as a stochastic process related to tumor diameter. The number of stages in cancer induction and the tumor growth rate were simultaneously estimated for each histologic subtype using the maximum likelihood procedure. The present model showed better fits than the Armitage-Doll model in most histologic subtypes except WEL, PAP, WEL and MOD, which are characterized as differentiated subtypes with less mucous production, showed different features from POR, MUC and SIG: 1) the number of stages was estimated to be larger, 2) the differences in incidence rates between males and females were more marked, and 3) males tended to have larger growth rates in PAP and MOD, while in POR, MUC and SIG, females had larger values. The present study showed that an analysis by histologic subtypes is of importance in stomach cancer and that the period of tumor growth should not be ignored when formulating a model of the natural history of stomach cancer.

Adenocarcinoma↗
PubMedDate not supplied

Photographic patterns in macular images: representation by a mathematical model.

Normal macular photographic patterns are geometrically described and mathematically modeled. Forty normal color fundus photographs were digitized. The green channel gray-level data were filtered and contrast enhanced, then analyzed for concentricity, convexity, and radial resolution. The foveal data for five images were fit with elliptic quadratic polynomials in two zones: a central ellipse and a surrounding annulus. The ability of the model to reconstruct the entire foveal data from selected pixel values was tested. The gray-level patterns were nested sets of concentric ellipses. Gray levels increased radially, with retinal vessels changing the patterns to star shaped in the peripheral fovea. The elliptic polynomial model could fit a high-resolution green channel foveal image with mean absolute errors of 6.1% of the gray-level range. Foveal images were reconstructed from small numbers of selected pixel values with mean errors of 7.2%. Digital analysis of normal fundus photographs shows finely resolved concentric elliptical foveal and star-shaped parafoveal patterns, which are consistent with anatomical structures. A two-zone elliptic quadratic polynomial model can approximate foveal data, and can also reconstruct it from small subsets, allowing improved macular image analysis.

Adult↗
PubMed2002

Dynamical description of sinoatrial node pacemaking: improved mathematical model for primary pacemaker cell.

We developed an improved mathematical model for a single primary pacemaker cell of the rabbit sinoatrial node. Original features of our model include 1) incorporation of the sustained inward current (I(st)) recently identified in primary pacemaker cells, 2) reformulation of voltage- and Ca(2+)-dependent inactivation of the L-type Ca(2+) channel current (I(Ca,L)), 3) new expressions for activation kinetics of the rapidly activating delayed rectifier K(+) channel current (I(Kr)), and 4) incorporation of the subsarcolemmal space as a diffusion barrier for Ca(2+). We compared the simulated dynamics of our model with those of previous models, as well as with experimental data, and examined whether the models could accurately simulate the effects of modulating sarcolemmal ionic currents or intracellular Ca(2+) dynamics on pacemaker activity. Our model represents significant improvements over the previous models, because it can 1) simulate whole cell voltage-clamp data for I(Ca,L), I(Kr), and I(st); 2) reproduce the waveshapes of spontaneous action potentials and ionic currents during action potential clamp recordings; and 3) mimic the effects of channel blockers or Ca(2+) buffers on pacemaker activity more accurately than the previous models.

4-Aminopyridine↗
PubMed1992

A mathematical model of life-threatening hyperthermia during infancy.

A mathematical model was created to test the hypothesis that a partially covered febrile infant may develop potentially lethal temperature elevation. Infants may be at special risk to develop hyperthermia because, unlike older children, infants may not be able to remove blankets in response to temperature elevation. The model compared heat production (MTsk) with heat loss (Qtot). The difference between these terms is the excess energy (E): MTsk - Qtot = E. In most situations the simulated infant transfers heat to the environment as rapidly as it is produced (E less than 0), so hyperthermia does not result. In some situations, heat production exceeds heat loss (E greater than 0), causing progressive warming. The time was calculated for the simulated infant to progress from 41 to 43.4 degrees C (defined as a lethal end point). In certain circumstances, this may occur in less than 90 min. An infant at high risk of hyperthermia may not appear to be covered by a conspicuous excess of insulation (less than or equal to 3.5 cm may be sufficient). In many situations, heat loss is more closely determined by exposed body surface area than by blanket thickness. These findings have important implications for understanding the antecedents of hyperthermia in infants and may help in understanding the role of hyperthermia in certain pediatric illnesses.

Bedding and Linens↗