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At least 253 records · Page 14Linked to original sources

A mathematical model of a blood-gas service.

A mathematical model depicting operation of a blood-gas workstation was developed by two systems analysts working closely with two clinical pathologists. This model was used to provide estimates of average as well as maximum turnaround times under various conditions of workload, specimen types (capillary vs. syringe), methodology (use of IL 513 vs. IL 313 for capillary samples), and reporting procedures (report each sample as analyzed vs. report after analysis of all samples in batch). These estimates have been validated against actual experience in our laboratory. Such an objective mathematical model can be used to plan optimal service.

Blood Gas Analysis↗

The frequency of cervical cancer screening. Comparison of a mathematical model with empirical data.

The results of a mathematical model used to analyze the frequency of the Pap smear are compared with a recently published independent empirical study of data from large screening programs in Europe and North America. The model's predictions of the reduced incidence of invasive cervical cancer achieved with different screening frequencies match the empirical results closely--the predictions were within 1% of the empirical results for screening frequencies ranging from 1 to 10 years. The data indicate that compared with annual screening, screening every 2, 3, 5, and 10 years retains 99%, 97%, 89%, and 69%, respectively, of the effectiveness measured as a reduction in frequency of invasive cancer. The mathematical model underestimated the effectiveness of screening every 3 years, compared with screening every year.

Europe↗

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↗

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↗

A mathematical model of atherogenesis as an inflammatory response.

We construct a mathematical model of the early formation of an atherosclerotic lesion based on a simplification of Russell Ross' paradigm of atherosclerosis as a chronic inflammatory response. Atherosclerosis is a disease characterized by the accumulation of lipid-laden cells in the arterial wall. This disease results in lesions within the artery that may grow into the lumen restricting blood flow and, in critical cases, can rupture causing complete, sudden occlusion of the artery resulting in heart attack, stroke and possibly death. It is now understood that when chemically modified low-density lipoproteins (LDL cholesterol) enter into the wall of the human artery, they can trigger an immune response mediated by biochemical signals sent and received by immune and other cells indigenous to the vasculature. The presence of modified LDL can also corrupt the normal immune function triggering further immune response and ultimately chronic inflammation. In the construction of our mathematical model, we focus on the inflammatory component of the pathogenesis of cardiovascular disease (CVD). Because this study centres on the interplay between chemical and cellular species in the human artery and bloodstream, we employ a model of chemotaxis first given by E. F. Keller and Lee Segel in 1970 and present our model as a coupled system of non-linear reaction diffusion equations describing the state of the various species involved in the disease process. We perform numerical simulations demonstrating that our model captures certain observed features of CVD such as the localization of immune cells, the build-up of lipids and debris and the isolation of a lesion by smooth muscle cells.

Atherosclerosis↗

[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↗

[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↗

[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↗

Mathematical modelling and controlled drug delivery: matrix systems.

This paper deals with the physical and mathematical modelling description of drug release from matrix systems. In the introduction, matrix systems are considered in the wide frame of the controlled release systems and the concept of mathematical model is briefly discussed. Then, matrix structure and topology are matched, analysing the characteristics of the three-dimensional network constituting them. In this context, drug release mechanisms are considered with particular emphasis on the key factors ruling the release kinetics, such as matrix swelling, erosion, drug dissolution (re-crystallisation), drug diffusion, drug - polymer interaction, initial drug distribution and particle size distribution (for powdered matrix systems). The mathematical modelling section firstly considers the empirical and semi-empirical models that have the great advantage of showing analytical solutions. Then, the attention is focused on theoretical approaches regarding matrix swelling equilibrium and kinetics, drug dissolution, drug diffusion, drug - polymer interaction, initial drug distribution and matrix erosion. Finally, release kinetics from polydispersed spherical particles is studied. This review points out the fact that the comprehension of the phenomena ruling drug release from matrix systems is appropriate from both the physical and modelling point of view, although further improvements are always possible and desirable.

Algorithms↗

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↗

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↗

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↗

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↗

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↗

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↗

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↗

Analysis of non-invasive ventilation effects on gastric inflation using a non-linear mathematical model.

A non-linear mathematical model of the oesophagus was developed to study the effects of non-invasive ventilation variables on the severity of gastric inflation. The model was based on the non-linear physical characteristics of biological tissue. The model simulated oesophageal mechanical function during non-invasive ventilation in cardiac arrest (2:30 ventilations/chest compressions cycles) and respiratory arrest (1:5 ventilations/s) as recommended by the European Resuscitation Council (ERC) in its 2005 guidelines for adult basic and advanced life support. Model predictions establish a strong correlation between the expiratory time and the occurrence of gastric inflation. For cardiac arrest, when using ventilation pressure lower than 12 cmH2O, expiratory time between consequent ventilations and time until the occurrence of gastric inflation were linearly dependent (r = 0.98). This linear correlation changed abruptly when airway pressure exceeded the threshold pressure of 12 cmH2O, indicating that air had entered the stomach during the first ventilation. The interval at which the pressure at the distal section of the oesophagus was above the lower oesophageal sphincter (LES) opening pressure was significantly prolonged in the model of cardiac arrest (approximately 5.5 s compared to 3 s in respiratory arrest), thus allowing a greater amount of air to enter the stomach at relatively low airway pressures. During cardiac arrest, the mean pressure at the distal section of the oesophagus and the amplitude of air backflow were higher compared to the mean pressure and amplitude during respiratory arrest. This is also due to the shorter expiratory intervals in the 2:30 ventilations/chest compressions technique. The model indicates that the time required for the air trapped in the oesophagus to completely deflate is approximately 2 s. This may be longer than the expiratory time recommended by the 2005 guidelines. Model predictions support the 2005 guidelines regarding the decrease in the tidal volume and in the inspiratory pressure in an effort to minimise gastric inflation.

Cardiopulmonary Resuscitation↗