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At least 343 records · Page 19Linked to original sources
PubMed1999

Evaluation of a mathematical model to predict intrapulmonary shunt non-invasively.

PURPOSE: We have previously published a mathematical model of oxygen transport. Using several physiological assumptions, the model provides a non-invasive estimate of intrapulmonary shunt. During a larger study of lung injury in a pig model, we had the opportunity to check the validity of our assumptions and the accuracy of the model's predictions. METHODS: We used six female pigs, average weight 12.8 kg. Following general anesthesia, tracheostomy and insertion of pulmonary venous and arterial lines, lung injury was induced by repeated saline lung lavage. Using hemodynamic measurements made at different levels of inspired oxygen, intrapulmonary shunt was calculated both by the traditional shunt equation and also by our mathematical model based on non-invasive measurements of FIO2 and SaO2. RESULTS: There was good agreement between the two methods of shunt calculation. Using linear regression the correlation coefficient was 0.95. Bland and Altman analysis showed a bias of -0.8 and precision of 12%. CONCLUSION: In a controlled setting, intrapulmonary shunt can be estimated from non-invasive measurements to a reasonable degree of accuracy. However, the calculation requires too many assumptions to be of general clinical value. The equations used provide a validated physiological model that acts as a useful tool for teaching cardiorespiratory physiology.

Animals↗
PubMed1997

A maternal screening program for congenital toxoplasmosis in Quindio, Colombia and application of mathematical models to estimate incidences using age-stratified data.

We studied 937 pregnant women from Quindio, Colombia for the presence of specific anti-Toxoplasma gondii IgG antibodies using the indirect immunofluorescence antibody technique (IFAT-IgG). Specific anti-T. gondii IgM antibodies detected using the immunosorbent agglutination assay (ISAgA-IgM) were investigated in patients with high titers in the IFAT-IgG (dilutions > or = 1:1,024). We used mathematical models based on the age prevalence results of the IFAT-IgG to estimate the number of seroconversions and these were compared with the results predicted by the IgM based-incidence results. We found 15 positive cases by ISAgA-IgM and we were able to follow the children of six mothers from this group in which we found one case of congenital toxoplasmosis with the development of a retinal scar despite prenatal and postnatal treatment. The estimation of new cases for the annual total of pregnancies (approximately 8,000) in the Quindio region was 30-120 according to the ISAgA-IgM results and 57-85 using mathematical models. Thus, mathematical models based on age prevalence can give useful estimations of the magnitude of the problem.

Adolescent↗
PubMed2000

Mathematical models for assessment of long-term persistence of antibodies after vaccination with two inactivated hepatitis A vaccines.

Very few studies with inactivated hepatitis A vaccines were designed for long-term follow-up of antibody persistence. Based on the serological data from these vaccine trials, mathematical models were developed to predict the decrease of anti-hepatitis A virus (anti-HAV) antibodies after vaccination. This study was designed to compare Avaxim (0-6 months) to Havrix 720 (0-1-6 months). In this paper, both groups of vaccinees are described considering the age, gender, and weight of the subjects at enrollment. For mathematical modelling, two different approaches were used: one starting the calculations from the geometric mean titres (GMTs) at each point in time, the other basing the calculations on individual anti-HAV titres. Both vaccines are very immunogenic, although Avaxim shows a higher GMT at each point in time. When these data are used in mathematical models to predict the persistence of anti-HAV antibodies, both vaccines (Avaxim and Havrix 720) show similar long-term antibody kinetics. Antibody levels > or = 20 mIU/ml are estimated to last on average for at least 10 years after completion of the full vaccination course. Ten years after the full course, approximately 53% of subjects are estimated to have antibody levels > or = 20 mIU/ml. At 15 years, these levels will be maintained by about 34% of vaccinees. Avaxim and Havrix 720 show a similar long-term profile of persistence of anti-HAV. A mathematical model based on GMTs appeared to give equivalent results to a model based on individual serological data. The GMT method is easier to apply than the individual based method. However, the advantage of the latter method is the possibility of calculating confidence limits for the predicted values and making estimates of the percentage of subjects having a certain level of antibody titres at a certain time.

Adolescent↗
PubMed1997

Biomechanics of the hip joint capsule -- a mathematical model and clinical implications.

OBJECTIVE: Our aim was to develop a mathematical model to calculate forces, tension and stretching in the hip joint capsule, under conditions caused by the joint effusion usually accompanying hip disease. DESIGN: A mathematical model was developed, based on experimental data from cadaver studies. BACKGROUND: Intracapsular pressure is important with respect to the degree of painless movement in the hip. Previously, we established the relations between the rotation around the axis of the neck of the femur, joint effusion, intracapsular pressure and joint stability. METHODS: In six cadaver adult hips the joint distraction, the traction force along and the rotation around the axis of the neck of the femur and the intracapsular pressure, were simultaneously monitored as the volume of intracapsularly infused saline was increased. The elasticity-constants included in the extracted formula for the fluid pressure were calculated in a designed computer software based on these experimental data. RESULTS: Presented in Figures 3-12. CONCLUSIONS: In the normal joint there is no increase in intracapsular pressure, nor any tension in the hyperboloid shape capsule within the normal range of rotation around the axis of the neck of the femur. This shape is distorted in a hip with effusion, rotation then resulting in an increased intracapsular pressure and tension in the capsule, with potential risk of ruptures.

Journal Article↗
PubMed1987

A mathematical model for determining minimal inhibitory concentrations (MICs) via diffusion assays.

A mathematical model is presented for the description of inhibition zones in a diffusion bioassay. In such an experiment the drug is placed at the center of a Petri dish containing a bacterial lawn in an agar gel and after a certain incubation period one observes a concentric ring around the center marking the toxic area. From the knowledge of the radius rtox of the toxic zone, the lower limit ctox at which the inhibitory response is observed can be readily calculated. This quantity is very important in evaluating the sensitivity of microorganisms to toxic substances. The mathematical model of the assay is given by a two-dimensional diffusion equation describing the changes in drug concentration due to diffusion, decay of the chemical and consumption by bacteria. The diffusion equation being mildly non-linear is solved numerically with the aid of a computer. For this purpose a numerical solver was developed as well as a "best-fit" simulation program that fits the parameters for which experimental values could not be obtained. The method was tested with N-methyl-N'-nitro-N-nitrosoguanidine and ethylmethanesulfonate and was seen to be fast, efficient, and inexpensive. In principle it could be used for routine quantitative screening for toxicity of chemicals.

Diffusion↗
PubMed2002

Mathematical model for assessment of radiation risk on long space missions.

A mathematical model is developed which describes the dynamics of radiation-induced mortality in mammalian populations. It relates statistical biometric functions with statistical characteristics and dynamics of an organism's critical system. In the framework of the model the effects of low and very low dose rates of chronic radiation on mice are simulated. Respectively, thrombocytopoietic and granulocytopoietic systems are considered as the critical ones. To calculate the dynamics of these systems, mathematical models are applied, too. In accordance with experimental data, the mortality model reproduces on quantitative level both increased and decreased mortality rates in populations of LAF1 mice, which were chronically exposed, respectively, to low and very low level radiation. All this makes it feasible to use the model as a basis for risk assessments of low level long-term irradiation.

Animals↗
PubMed1986

Evaluation of mathematic models to assess platelet kinetics.

Twelve mathematic methods used to calculate the mean platelet survival time were compared by determining the "goodness of fit" of the models to the platelet survival curves of 15 reference subjects and 54 patients. Platelets were labeled with [111In]oxine. The linear (LN), exponential, weighted mean, multiple hit (MH), Dornhorst (DH), Meuleman (ML), alpha order (AO), and polynomial (PO) mathematic models were investigated. The goodness of fit for the exponential model was determined by the nonlinear least squares method (EP), and also by the linear least squares method on logarithmically transformed data (EX) as is recommended. The modified weighted mean (MWM) and the usual weighted mean method (WM) obtained with these exponential models were tested. The Dornhorst (DH10) and Meuleman (ML10) models, where the potential age-dependent platelet survival times were kept constant at 10 days, were also evaluated. The goodness of fit results, expressed as % s.d. indicated that the LN (5.2%), EX (5.0%), EP (4.4%), WM (3.7%), DH10 (3.7%), and ML10 (3.7%) models all fitted the data significantly worse than the MWM, MH, DH, ML, AO, and PO models (range 3.2-3.3%). The mean platelet survival time determined with the MH model differed significantly from the results with the DH, ML, and AO models. The results of mean platelet survival time calculated with different mathematic models cannot, therefore, be compared directly. The models that fitted the platelet survival curve well varied slightly in sensitivity to noise as is indicated by the coefficient of variation of the mean platelet survival time estimates for the reference subjects (range 7.9-12.0%). Fitting data to at least two mathematic models has definite advantages. Data on which the calculations are based are probably invalid if the following are true: (a) if the mean platelet survival time estimated with the alpha order model is shorter than that estimated with the EP, MWM, or MH models, or (b) the mean platelet survival time estimated with either the DH, ML, AO, or PO models, is longer than the LN, MWM, or MH estimate of the mean platelet survival time. We conclude that the mean platelet survival time can be reliably estimated by fitting the data to either the MWM method (if limited computing facilities are available) or the MH model. Confidence in the result will be increased if considered in conjunction with the finding obtained with one other model; in those cases where the platelet survival time is very short, the alpha order model is recommended.(ABSTRACT TRUNCATED AT 400 WORDS)

Blood Platelets↗
PubMed2004

Improving methods for epidemiological control of canine visceral leishmaniasis based on a mathematical model. Impact on the incidence of the canine and human disease.

The mathematical model described by Dye (1996) condemned the epidemiological canine visceral leishmaniasis control campaign, considering it non-efficient. Using this model, we mathematically demonstrate that the control is not efficient, only at low kappa values (rate at which latent and infectious dogs are lost by the destruction program) which match the canine seropositivity observed in the field by the immunofluorescency (IF) blood eluates analysis. With higher k values, corresponding to IF (kappa = 0.07) or ELISA (kappa = 0.25) results in sera samples, the number of infectious dogs declines to a Ro =1 or Ro =0, respectively, interrupting the transmission and the advancement of epidemics. We also experimentally demonstrate that the dog removal, following the results of IF of sera, instead of eluates lead to a 57% (p < 0.005) decrease in canine cases and 87.5% (p < 0.005) in human cases. Our mathematical and experimental results indicate that the control campaign become more efficient by enhancing the sensitivity of the diagnostic assay.

Animals↗
PubMedDate not supplied

Mathematical model for the effects of epidermal growth factor receptor trafficking dynamics on fibroblast proliferation responses.

We apply a mathematical model for receptor-mediated cell uptake and processing of epidermal growth factor (EGF) to analyze and predict proliferation responses to fibroblastic cells transfected with various forms of the EGF receptor (EGFR) to EGF. The underlying conceptual hypothesis is that the mitogenic signal generated by EGF/EGFR binding on the cell surface, via stimulation of receptor tyrosine kinase activity, is attenuated when the receptors are downregulated and growth factor is depleted by endocytic internalization and subsequent intracellular degradation. Hence, the cell proliferation rate ought to depend on receptor/ligand binding and trafficking parameters as well as on intrinsic receptor signal transduction properties. The goal of our modeling efforts is to formulate this hypothesis in quantitative terms. The mathematical model consists of kinetic equations for binding, internalization, degradation, and recycling of EGF and EGFR, along with an expression relating DNA synthesis rate to EGF/EGFR complex levels. Parameter values have been previously determined from independent binding and trafficking kinetic experiments on B82 fibroblasts transfected with wild-type and mutant EGFR. We show that this model can successfully interpret literature data for EGF-dependent growth of NR6 fibroblasts transfected with wild-type EGFR. Moreover, it successfully predicts the literature observation that NR6 cells transfected with a delta 973 truncation mutant EGFR, which is kinase-active but internalization-deficient, require an order of magnitude lower EGF concentration than cells with wild-type EGFR for half-maximal proliferation rate. This result demonstrates that it may be feasible to genetically engineer mammalian cell lines with reduced growth factor requirements by a rational, nonempirical approach. We explore by further model computations the possibility of exploiting other varieties of EGFR mutants to alter growth properties of fibroblastic cells, based on relationships between changes in the primary structure of the EGF receptor and the rates of specific receptor/ligand binding and trafficking processes. Our studies show that the ability to predict cell proliferation as a function of serum growth factors such as EGF could lead to the designed development of cells with optimized growth responses. This approach may also aid in elucidation of mechanisms underlying loss of normal cell proliferation control in malignant transformation, by demonstrating that receptor trafficking dynamics may in some cases play as important a role as intrinsic signal transduction in determining the overall resulting mitogenic response.

Cell Division↗
PubMed1990

[Evolutionary and prognostic studies of patients with primary liver cancer. II. Multifactorial analysis using a stepped-regression mathematical model and graphics].

The subject of this study is the evolution and prognosis of 63 patients with primary liver carcinoma assessed bu multifactor regression mathematical model realized with the aid of the program 2R of the statistical package VMDR and by graphic expression of the functions of survival, mortality, speed of mortality function growth and graphic assessment of survival according to Okuda's method. The step regression analysis in 2 steps of the regression mathematical model of the clinical indices pointed out the factors age, edema and liver encephalopathy. By 7 steps in the regression mathematical model of the combined clinical and clinico-chemical indices as basic prognostic factors were selected: prothrombin time, liver encephalopathy, direct bilirubin, age, GGTP and sex.

Adult↗
PubMed1992

Mathematical modeling and spectrum analysis of the physiological patello-femoral pulse train produced by slow knee movement.

Analysis of vibration signals emitted by the knee joint has the potential for the development of a noninvasive procedure for the diagnosis and monitoring of knee pathology. In order to obtain as much information as possible from the power density spectrum of the knee vibration signal, it is necessary to identify the physiological factors (or physiologically relevant parameters) that shape the spectrum. This paper presents a mathematical model for knee vibration signals, in particular the physiological patello-femoral pulse (PFP) train produced by slow knee movement. It demonstrates through the mathematical model that the repetition rate of the physiological PFP train introduces repeated peaks in the power spectrum, and that it affects the spectrum mainly at low frequencies. The theoretical results also show that the spectral peaks at multiples of the PFP repetition rate become more evident when the variance of the interpulse interval (IPI) is small, and that these spectral peaks shift toward higher frequencies with increasing PFP repetition rates. To evaluate the mathematical model, a simulation algorithm was developed, which generates PFP signals with adjustable repetition rate and IPI variance. Signals generated by simulation were seen to possess representative spectral characteristics typically observed in physiological PFP signals. This simulation procedure allows an interactive examination of several factors which affect the PFP train spectrum. Finally, in vivo measurements of physiological PFP signals of normal volunteers are presented. Results of simulations and analysis of signals recorded from human subjects support the mathematical model's prediction that the IPI statistics play a very significant role in determining the low-end power spectrum of the physiological PFP signal.(ABSTRACT TRUNCATED AT 250 WORDS)

Algorithms↗
PubMed2004

A mathematical model of cell salvage compared and combined with normovolemic hemodilution.

BACKGROUND: Mathematical models have been used to describe the factors that affect cell salvage (CS) and normovolemic hemodilution (ANH). Here, the CS and ANH models were used to compare these two techniques alone or in combination with each other. STUDY DESIGN AND METHODS: Variables used for a hypothetical patient included an estimated blood volume of 5000 mL, a presurgery hematocrit (Hct) of 45 percent, and a transfusion trigger of 21 percent. The model accounts for both the effect of decreasing the Hct due to blood loss and the effect of increasing Hct due to the readministration of blood in an isovolemic patient. The efficacy of CS and ANH is defined to be the maximum allowable blood loss for a fixed blood volume and a fixed transfusion trigger. RESULTS: Comparison of CS with ANH showed that 3 units of ANH was comparable to CS when CS recovery rates ranged from 19 to 24 percent. For a patient with a blood volume of 5000 mL and a starting Hct of 40 percent, 3 units of ANH would allow for 3972 mL of blood to be lost before crossing a 21-percent transfusion trigger, whereas CS with a 125-mL bowl would allow for 7611 mL. CONCLUSION: When comparing ANH to CS, this mathematical model would suggest that CS has the potential to offer significantly greater red blood cell avoidance than does ANH; however, the combination of ANH with CS may offer allogeneic avoidance superior to either technique alone.

Blood Loss, Surgical↗
PubMed2000

Hepatitis C kinetics: mathematical modeling of viral response to therapy.

Mathematical models have been used to study the dynamics of HIV. Using these same principles, the dynamics of hepatitis C virus (HCV) are reviewed during interferon (IFN) therapy. After initiating IFN treatment, there is an IFN dose-dependent exponential decline in viral RNA levels within the first 48 hours. This rapid 1.0 to 2.0 log decline was best explained by an effect of IFN in inhibiting viral production with a varying degree of effectiveness. By applying mathematical principles, viral serum half-life was estimated to be 3.0 hours and viral production rat was calculated to be 1.0 x 10(12) virions per day. After this rapid first-phase decline there was a slower second phase decline in viral levels that was highly variable between subjects. This phase was dependent on the rate of elimination of HCV-infected liver cells. The rapidity of the second phase proved to be the best predictor of early viral clearance. The use of these models to understand the life cycle of viruses and their response to therapy is reviewed.

Antiviral Agents↗
PubMed1987

[Mathematical model of the immunostimulation of tumor growth].

A mathematical model of immune system that takes into consideration the subpopulation of suppressor lymphocytes was proposed. The possibility of stable balance in the process of carcinogenesis is shown. The prospects of mathematical formalization of the immune processes are discussed.

Humans↗
PubMed1984

On the equivalence of mathematical models for cell proliferation kinetics.

Various types of mathematical models, such as partial differential equations, ordinary differential equations and difference equations, are available in the literature to describe the kinetics of cell proliferation, and different studies of cell kinetic phenomena have been conducted using these models. This paper discusses the equivalence between the different models identifying the conditions and approximations under which one type of models may be derived from another. Such an equivalence study is highly useful for an integration of the diverse results that have been obtained using different models in order to gain a more complete understanding of cell kinetic phenomena.

Animals↗
PubMedDate not supplied

[Mathematical model of the otolith].

This paper describes a mathematical model of the otolith of mammals represented as a system with parameters of distribution. Two versions of the model are analyzed and the lowest frequencies of natural oscillations of the system are evaluated.

Animals↗
PubMed1988

A contribution to mathematical modelling of immunological tolerance.

The original simple mathematical model describing the kinetics of B cell tolerance was extended by the inclusion of Th cell tolerance. It anticipates the existence of two compartments of B and Th cells reactive to the antigen--the immature cells and the mature ones. It is assumed that tolerance is induced by irreversible inactivation of the antigen-reactive cells and the escape from tolerance is due to their differentiation from the precursors. There is also considered the situation, where two categories of Th cells cooperate with the same B cells. Besides that, suppressive activity on Th cells is included in the model. The simulated values are compared with experimental data.

Animals↗