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At least 217 records · Page 12Linked to original sources
PubMed2003

Mathematical models of HIV and the immune system.

I describe how mathematical models have been used to elucidate the principles which govern HIV and immune system dynamics in relation to antiviral drug therapy. The review starts by introducing a basic model of virus infection and demonstrates how it was used to study HIV dynamics and to measure crucial parameters which lead to a new understanding of the disease process. Since this analysis indicates that eradication of the virus is not feasible during the lifetime of the patient, I continue to discuss mathematical models with the aim to explore how drug therapy can be used to induce long-term immunological control of the infection.

Allergy and Immunology↗
PubMed2000

A mathematical model of drug transport in human breast cancer.

A mathematical model of drug transport in tissue has been developed on the basis of a clinical study of patients with breast cancer, treated with the drug doxorubicin and of drug transport experiments using cultured human breast cancer cells. The clinical study revealed doxorubicin gradients in tumor islets of densely packed cancer cells. The mathematical model allows simultaneous drug transport through the cellular network (transcellular pathway), through the intercellular interstitium (paracellular pathway), and across the boundary between the two networks. The effective diffusion coefficient of the interstitial network is found to be much higher than that of the cellular network, in spite of the fact that the interstitium thickness is only 20-40 nm. The model simulations can be made to fit the results of the clinical study. A long-continued simulation (40 days) of drug transport into a spherical islet with a radius of 150 microm, after a bolus injection of doxorubicin, reveals that the maximum average drug concentration at the islet centre is only reached after 224 h, while it decreases by a factor 15 from the boundary to the centre of the islet. The area under the curve in a plot of the average drug concentration versus time only decreases by 10% from the boundary to the centre of the islet.

Antineoplastic Agents↗
PubMedDate not supplied

[Preliminary verification of a mathematical model for evaluating the operative risk in a personal caseload].

The authors applied a mathematical model of evaluation of operative risk to a group of patients undergoing general and obstetric-gynecologic surgery. They verified that all risk factors identified by this mathematical model really influenced operative morbidity and mortality in the present study too. In this univariate analysis, anesthetic technique was found to influence patients' outcome, so it must be included in multivariate analysis protocols. Therefore, this mathematical model showed to be of value in assessing operative risk factors.

Adolescent↗
PubMed1981

[Potential use of a mathematical modeling method for the analysis of immunological phenomena].

The paper reviews mathematical models of immunological processes associated with reactions of the total immunity system and its single formations: infectious diseases, in vivo experiments with cell cultures, cell proliferation and differentiation in the thymus, primary and secondary immune responses to the antigen, immunodeficient states, etc. It also gives models of immunological reactions in vitro: precipitation, agglutination, plaque formation, etc. The paper contains a short description of potentialities of mathematical models of biological processes.

Aerospace Medicine↗
PubMedDate not supplied

[The mathematical modelling of the processes in the natural multiplication of human lice (exemplified by the head louse population].

Methods of mathematical modelling and prediction of louse propagation processes in the natural habitation medium are presented. Theoretical and experimental data on head louse ecology served the basis for the elaboration of a mathematical model predicting the population dynamics. The model structure corresponds to 3 stages of louse development cycle (eggs, larva, lice) and parameters corresponding to natural characteristics of louse propagation process: mean lifespan of each individual during each phase of the cycle, age, fertility and so forth. The model helped to study some properties of the population, assess maximum rate of head louse population growth, detect threshold effects, establish the effects of coefficients, limiting the number of louse per unit of the body surface. The model made it possible to formulate necessary data (distribution functions) for the creation of the mathematical model of Pediculosis.

Animals↗
PubMed2002

A mathematical model of cell salvage efficiency.

UNLABELLED: Cell salvage (CS) is one of the modalities that can be used during surgery to decrease the use of allogeneic blood. Unlike acute normovolemic hemodilution, the efficiency of CS has not been mathematically modeled. In this article, we hypothesized that a mathematical model could predict the decline of hematocrit during CS. The model that was developed accounts for both the effect of decreasing the hematocrit because of blood loss and the effect of increasing hematocrit because of the readministration of washed blood in an isovolemic patient. The efficiency of CS is defined to be the maximum allowable blood loss (MABL) for a fixed blood volume and a fixed transfusion trigger. For demonstration purposes, variables used for a hypothetical patient included an estimated blood volume of 5000 mL, a presurgery hematocrit of 45%, and a transfusion trigger of 21%. The MABL in a typical case was 9600 mL, with a CS red cell recovery rate of 60%. Patient records from a convenience sample showed an average recovery rate of 57% with 20% variability. This mathematical model suggests that CS can be a highly effective blood conservation method when red blood cell collection is optimal. IMPLICATIONS: In this study, a mathematical model of cell salvage was developed. The model was then matched against real clinical cases to gain an understanding of the variables that modify cell salvage efficiency. The model illustrates that cell salvage can be a highly effective method of avoiding blood transfusion.

Algorithms↗
PubMed2000

Joint symmetry in early and late rheumatoid and psoriatic arthritis: comparison with a mathematical model.

OBJECTIVE: To establish a mathematical model to predict the probability of symmetry of joint involvement as a function of the number of joints involved and to compare expected with actual probabilities in psoriatic arthritis (PsA) and rheumatoid arthritis (RA) and in early and late disease. METHODS: Random involvement of joints was assumed, and the binomial theorem was used to give the frequency distribution of involved joints as a function of each joint count. Ten joint pairs were included: shoulder, elbow, wrist, metacarpophalangeal joints, proximal interphalangeal (PIP) joints of the hands, hip, knee, ankle, metatarsophalangeal joints, and PIP joints of the feet. Observed probabilities were obtained from subjects with early (duration < or =12 months) and late PsA and RA. RESULTS: The number of subjects in each of the disease subgroups was as follows: early PsA n = 33, late PsA n = 77, early RA n = 61, late RA n = 93. Observed probabilities of symmetry exceeded predicted probabilities for all disease subgroups. The median number of involved joints in each group was as follows: early PsA 4, late PsA 8, early RA 8, late RA 15 (chi2 = 95.3, 3 degrees of freedom, P = 0.0001, by Kruskal-Wallis test). After correcting for the discrepancy in the number of involved joints, no difference in joint symmetry was found between the groups (chi2 = 1.77, P = 0.62 by Friedman two-way analysis of variance). Similar results were obtained when individual hand and foot joints were analyzed separately. CONCLUSION: The pattern of joint involvement is often used to distinguish between rheumatoid and psoriatic arthritis. This study confirms that symmetry is largely a function of the total number of joints involved and that, in terms of joint pattern, differences between these disorders are more quantitative than qualitative. Both disorders have high absolute values of symmetry, particularly in the joints of the wrist and hand.

Adolescent↗
PubMedDate not supplied

Cancellation of metal-induced MRI artifacts with dual-component paramagnetic and diamagnetic material: mathematical modelization and experimental verification.

A mathematical model of dual-component paramagnetic and diamagnetic material to cancel metal-induced MRI artifacts was developed and verified experimentally. The magnetization produced by metallic material and then the gradient linearity distortion can be cancelled by using such materials with opposing paramagnetic and diamagnetic properties. This concept of dual-component materials provides a novel solution to the problem of MRI artifacts.

Artifacts↗
PubMed1983

Dependence of renal clearance on urine flow: a mathematical model and its application.

A mathematical model is developed to explain the dependence of renal clearance on urine flow rate. The model is tested using human data from the literature on compounds that are neither secreted nor reabsorbed by active or pH-sensitive mechanisms. The physiologically derived model explains and predicts the relationship between renal clearance and urine flow for a broad spectrum of compounds (i.e., butabarbital, chloramphenicol, creatinine, ethanol, theophylline, and urea) for which appropriate data are available.

Absorption↗
PubMed2000

Substrate deformation determines actin cytoskeleton reorganization: A mathematical modeling and experimental study.

A mathematical model has been developed to define the relationship between the actin cytoskeleton reorganization of a cell and substrate deformation acting on the cell. The model is based on the following major assumptions: (a) normal substrate strain, not the shear substrate strain, determines the actin cytoskeleton reorganization; (b) the normal substrate strain is transmitted to individual actin filaments; (c) each actin filament has a basal strain energy (BSE) when the cell adheres to the substrate without stretching; and (d) the actin filaments undergo disassembly when their strain energies are decreased to zero or increased to twice their BSEs. The resulting model predicts that the actin filaments are formed in the direction where their BSEs are minimally altered. This direction is therefore the one without normal substrate strain. The prediction was confirmed by experiments conducted on both fibroblasts and endothelial cells. The present model may be relevant for understanding better the effects of mechanical stimuli on the cells.

Actins↗
PubMed1996

Mechanics of feline soleus: II. Design and validation of a mathematical model.

We have developed a mathematical model to describe force production in cat soleus during steady-state activation over a range of fascicle lengths and velocities. The model was based primarily upon a three element design by Zajac but also considered the many different features present in other previously described models. We compared quantitatively the usefulness of these features and putative relationships to account for a set of force and length data from cat soleus wholemuscle described in a companion paper. Among the novel features that proved useful were the inclusion of a short-length passive force resisting compression, a new normalisation constant for connective-tissue lengths to replace the potentially troublesome slack length, and a new length dependent term for lengthening velocities in the force-velocity relationship. Each feature of this model was chosen to provide the most accurate description of the data possible without adding unneeded complexity. Previously described functions were compared with novel functions to determine the best description of the experimental data for each of the elements in the model.

Animals↗
PubMed1994

The usefulness of mathematical modeling in hydrocephalus research.

A mathematical model of the regulation of ventricular volume, which emphasizes the importance of the intrinsic properties (turgor) of the brain for the understanding of hydrocephalus, has been developed. How the model was generated is described. The use of the model for understanding the various forms of hydrocephalus is discussed. Finally, the usefulness of the model in solving difficult clinical problems, such as diffuse pediatric head injury and progressive ventriculomegaly with low intracranial pressure, is described.

Adult↗
PubMed2004

Why the lysogenic state of phage lambda is so stable: a mathematical modeling approach.

We develop a mathematical model of the phage lambda lysis/lysogeny switch, taking into account recent experimental evidence demonstrating enhanced cooperativity between the left and right operator regions. Model parameters are estimated from available experimental data. The model is shown to have a single stable steady state for these estimated parameter values, and this steady state corresponds to the lysogenic state. When the CI degradation rate (gammacI) is slightly increased from its normal value (gammacI approximately 0.0 min(-1)), two additional steady states appear (through a saddle-node bifurcation) in addition to the lysogenic state. One of these new steady states is stable and corresponds to the lytic state. The other steady state is an (unstable) saddle node. The coexistence these two globally stable steady states (the lytic and lysogenic states) is maintained with further increases of gammacI until gammacI approximately 0.35 min(-1), when the lysogenic steady state and the saddle node collide and vanish (through a reverse saddle node bifurcation) leaving only the lytic state surviving. These results allow us to understand the high degree of stability of the lysogenic state because, normally, it is the only steady state. Further implications of these results for the stability of the phage lambda switch are discussed, as well as possible experimental tests of the model.

Bacteriophage lambda↗
PubMed1998

Evaluation of bovine viral diarrhea virus control using a mathematical model of infection dynamics.

A mathematical model for infection with bovine viral diarrhea virus (BVDV) was created comprising a series of coupled differential equations. The model architecture is a development of the traditional model framework using susceptible, infectious and removed animals (the SIR model). The model predicts 1.2% persistent infection (within the range of field estimates) and is fairly insensitive to alterations of structure or parameter values. This model allows us to draw important conclusions regarding the control of BVD, particularly with respect to the importance of persistently infected (PI) animals in maintaining BVD as an endemic entity in the herd. Herds without PI animals are likely to experience episodic reproductive losses at intervals of two to three years, unlike herds with PI animals which will not see such marked episodic manifestations of infection. Instead, these herds will experience an initial peak of disease which will settle to low-level chronic reproductive losses. The model indicates that vaccine coverage for herd immunity (to avoid episodic manifestations of disease) need be only 57% without PI animals, although 97% coverage is required when PI animals are present. Analysis of model behavior suggests a program of detection and removal of PI animals may enhance the effectiveness of a vaccine program provided these animals are in the herd for 10 days or less. The best results would be seen with PI animals in the herd for 5 or fewer days.

Animals↗
PubMed1998

Plant growth influenced by photosynthetic irradiance and temperature. Part I: Mathematical model for standard conditions.

The mathematical model of plant growth based on the analysis of photosynthesis has been developed. In the analysis, the leaf was treated as a control system, where the photosynthetically active radiation is an input value of the system and the leaf or plant dry mass is an output one. Environmental factors which influence plant growth are treated as disturbances. Part I presents the theory for standard plant growth conditions. Theoretical and experimental results were compared for lettuce cultivated in a greenhouse and phytotron. Part II develops the model for nonstandard conditions.

Lactuca↗
PubMed1989

The simulation of continuous arteriovenous hemodialysis with a mathematical model.

We have developed a mathematical model that predicts the performance of continuous arteriovenous hemodialysis. Given patient (plasma protein concentration, hematocrit, mean arterial pressure, central venous pressure) and circuit (flow resistance, membrane hydraulic permeability, dialyzer mass transfer coefficient, ultrafiltrate column height, dialysate flow rate) characteristics as inputs, predictions of hydraulic and oncotic pressure distribution, filtration rate, blood flow, total, diffusive, and convective urea clearances are provided. The model was tested by perfusing a circuit with bovine blood under conditions of pure ultrafiltration, zero net ultrafiltration and dialysis, or combined ultrafiltration and dialysis (countercurrent dialysate flow at rates of 10, 20, and 30 ml/min). In order to permit computation, membrane hydraulic permeability and flow resistances were measured. Dialyzer mass transfer coefficient for urea could not be measured directly and so was determined by fitting model predictions to measured urea clearances. For all conditions of operation, a urea mass transfer coefficient of 0.014 cm/min successfully simulated the data. Predictions of blood flow, filtrate generation rate, and circuit pressure distribution were accurate. At lower dialysate flow rates, urea clearance approximated the sum of dialysate flow and filtration rate. At higher dialysate flows, however, departure from this ideal blood-dialysate equilibrium was observed. Model predictions regarding the relative contributions of diffusion and convection to urea clearance were explored. Under conditions of nearly perfect equilibration of urea between blood and dialysate at the blood inlet, the model predicts that the diffusive clearance of urea will increase with increasing rate of filtration and may exceed the rate of dialysate inflow.

Hemofiltration↗
PubMed1989

Optimal insulin infusion resulting from a mathematical model of blood glucose dynamics.

Mathematical optimization techniques are applied to a simplified mathematical model of blood glucose dynamics to derive insulin infusion programs for the control of blood glucose levels in diabetic individuals. Two particular cases are discussed. First, the insulin infusion program which results in an initially high blood glucose level being reduced to acceptable levels. Second, the control of blood glucose levels following a meal, prior to which blood glucose and net blood-glycemic hormone were at their fasting levels.

Blood Glucose↗