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At least 973 records · Page 54Linked to original sources
PubMed2000

A mathematical model of cancer treatment by immunotherapy.

In this paper, a detailed mathematical study of cancer immunotherapy will be presented. General principles of cancer immunotherapy and the model equations and hypotheses will be discussed. Mathematical analyses of the model equations with regard to dissipativity, boundedness of solutions, invariance of non-negativity, nature of equilibria, persistence, extinction and global stability will be analyzed. It will also be shown that bifurcations can occur, and criteria for total cure will also be derived.

Brain Neoplasms↗
PubMed1998

Mathematical procedures in data recording and processing of pupillary fatigue waves.

Spontaneous pupillary behaviour in darkness provides information about a subject's level of vigilance. To establish infrared video pupillography (IVP) as a reliable and objective test in the detection and quantification of daytime sleepiness, the definition of numerical parameters is an important precondition characterising spontaneous pupil behaviour adequately for further statistical procedures. The correct measurement of the pupil size, even if the lid or eyelashes are occluding the pupil, is of particular concern when testing vigilance. In this case many edge points of the pupil are detected and a fitting procedure is described that fits these edge points to a circle and excludes outliers. The first step of data preparation consists of a mathematical artefact management consisting of blink detection and elimination, followed by interpolation. Second, a fast Fourier transformation is carried out for frequencies from 0.0 to 0.8 Hz for each time segment of 82 s. Results are given in absolute and relative power of each frequency band per time segment and mean values over the entire record of 11 min. Third, the changes of the mean pupillary diameter per data window against time are shown graphically. An additional parameter referring to the pupil's tendency to instability, the pupillary unrest index (PUI), is defined by cumulative changes in pupil size based on mean values of consecutive data sequences. These mathematical procedures provide a high level of quality in both data collection and evaluation of IVP as an objective test of vigilance. In a pilot study, the pupillary behaviour of two groups were measured. One group rated themselves as alert (ten men), the other group as sleepy (12 men). The power and PUI were compared using the Mann-Whitney U-test. Both parameters show significant differences between the two groups.

Data Interpretation, Statistical↗
PubMed1980

Mathematical and computer assisted procedures in clinical decision making.

Numerous mathematical and computer assisted procedures have been developed and tested as aids in clinical decision making. With pressures to curtail unnecessary utilization of diagnostic tests, these models may play an increasingly important role. In practice, additional data may benefit the construction of mathematical models but may not necessarily benefit clinicians. With improvements in computer technology, laboratory medicine is in a strategic position to influence the direction of diagnostic testing and clinical decisions in a more cost effective manner.

Bayes Theorem↗
PubMed2003

Mathematical models of cell colonization of uniformly growing domains.

During the development of vertebrate embryos, cell migrations occur on an underlying tissue domain in response to some factor, such as nutrient. Over the time scale of days in which this cell migration occurs, the underlying tissue is itself growing. Consequently cell migration and colonization is strongly affected by the tissue domain growth. Numerical solutions for a mathematical model of chemotactic migration with no domain growth can lead to travelling waves of cells with constant velocity; the addition of domain growth can lead to travelling waves with nonconstant velocity. These observations suggest a mathematical approximation to the full system equations, allowing the method of characteristics to be applied to a simplified chemotactic migration model. The evolution of the leading front of the migrating cell wave is analysed. Linear, exponential and logistic uniform domain growths are considered. Successful colonization of a growing domain depends on the competition between cell migration velocity and the velocity and form of the domain growth, as well as the initial penetration distance of the cells. In some instances the cells will never successfully colonize the growing domain. These models provide an insight into cell migration during embryonic growth, and its dependence upon the form and timing of the domain growth.

Animals↗
PubMed1999

Correlation between reproductive efficiency, as determined by new mathematical indexes, and the body condition score in dairy cows.

The aim of this work was to study a new mathematical model based on dynamic indexes designed to evaluate reproductive efficiency in dairy herds and to correlate the new index with the body condition score (BCS) in order to evaluate the reproductive state of the cows post partum. Four groups of dairy cows were used: 1) loose-housed Italian Friesian (loose Friesian, n = 190); 2) stanchioned Italian Friesian (stanchioned Friesian, n = 121); 3) stanchioned Italian Simmental (stanchioned Simmental, n = 120); and 4) loose-housed selected Italian Friesian cows (BCS test, n = 117). The first 3 herds were used to develop the new mathematical model while the fourth was used to correlate the method with the BCS. The new model was developed from the analysis of progesterone (P4) concentrations in whey and the frequency distribution of the cows in 3 reproductive states: cyclicity, acyclicity and pregnancy. The frequency distribution generated 3 curves, the intersections of which form a closed area. The barycenter of this closed area gives a simple static representation of the reproductive efficiency of each herd. We also studied the movement of the barycenter with time (dynamic index) for each reproductive status curve. The dynamic index allowed for evaluation of the reproductive efficiency of a group of cows at 40 d after calving, by analyzing the evolution of the different reproductive states post partum. A reproductive index called Cycle Time was characterized in a 240-d period of observation as the interval needed to bring all the animals from acyclic to pregnant status. The loose Friesian cows had the best reproductive efficiency. The BCS test was used to divide cows into 3 groups depending on the percentage loss of BCS due to the negative energy balance at 30 d post partum. Cows which lost more than 20% in BCS had the lowest reproductive efficiency. The following protocol was devised to monitor herds in order to identify cows that were likely to have reproductive problems: 1) measure BCS 10 d before calving; 2) monitor progesterone in whey starting 5 d after calving; 3) measure BCS 30 d after calving; 4) isolate cows that lost more than 20% of BCS; 5) measure progesterone only in the cows that lose more than 20% of BCS; 6) activate appropriate feeding strategies to help prevent excessive mobilization of body fat reserves.

Animal Feed↗
PubMed1998

Implications derived from a mathematical model for eradication of pseudorabies virus.

Simple mathematical models based on experimental and observational data were applied to evaluate the feasibility of eradicating pseudorabies virus (PRV) regionally by vaccination and to determine which factors can jeopardise eradication. As much as possible, the models were uncomplicated and our conclusions were based on mathematical analysis. For complicated situations, Monte-Carlo simulation was used to support the conclusions. For eradication, it is sufficient that the reproduction ratio R (the number of units infected by one infectious unit) is < 1. However, R can be determined at different scales: at one end the region with the herds as units and at the other end compartments with the pigs as units. Results from modelling within herds showed that contacts between groups within a herd is important whenever R between individuals (R(ind)) is > 1 in one or more groups. This is the case within finishing herds. In addition, if the R(ind) is more than 1 within a herd, the size of the herd determines whether PRV can persist in the herd and determines the duration of persistence. Moreover, when reactivation of PRV in well-vaccinated sows is taken into account, R(ind) in sow herds is still less than 1. In sow herds with group-housing systems, it is possible that in those groups R(ind) is > 1. Results from modelling between herds showed that whether or not Rherd is < 1 in a particular region is determined by two factors: (1) the transmission of infection between nucleus herds and rearing herds through transfer of animals and (2) contacts among finishing herds and among rearing herds. The transmission between herds can be reduced by reduction of the contact rate between herds. reduction of the herd size, and reduction of the transmission within herds.

Animals↗
PubMed2000

Mathematical modeling of chronical hypoxia in tumors considering potential doubling time and hypoxic cell lifetime.

PURPOSE: To model mathematically how potential doubling time and hypoxic cell lifetime affect the extent of chronical hypoxia in tumor tissue segments. Three capillary geometries were modeled under idealized steady state conditions. MATERIALS AND METHODS: The capillary geometries are: tissue surrounding an axial capillary, tissue enclosed by a cylindrical capillary network, and tissue enclosed by a spherical capillary network. The tissue segments are modeled as three-compartment systems, where well nourished cells proliferate near the vasculature and, in so doing, displace 'older' cells into a quiescent compartment and, ultimately into a hypoxic region. The extent of the hypoxic zone is the distance traversed by cells during their hypoxic lifetime before becoming necrotic. The steady state situation, where the necrotic cell loss equals the cell gain caused by cell proliferation was investigated. RESULTS: The hypoxic fraction, HF, was found to be inversely proportional to the potential doubling time of the tumor segment, T(pot), and proportional to the hypoxic cell lifetime, T(hypox). The extent of the oxygenated zone depends only on the capillary geometry, the capillary radius, the intracapillary oxygen tension, and the tissue respiration rate. The extent of the hypoxic zone in addition depends on T(pot) and T(hypox). CONCLUSIONS: Mathematical modeling of idealized steady state conditions shows that the ratio of hypoxic cell lifetime and potential doubling time, T(hypox)/T(pot), determines the hypoxic fraction, HF, in tumor segments. The extents of the oxygenated and the hypoxic zones can be predicted from the models.

Capillaries↗
PubMed1997

A mathematical model that reproduces vertical ocular following responses from visual stimuli by reproducing the simple spike firing frequency of Purkinje cells in the cerebellum.

A mathematical model that accurately reproduces eye movements from visual stimuli and incorporates intermediate neural signals is useful for quantitative analysis of the neural mechanisms involved in transforming visual stimuli to eye movements. Here we describe a mathematical model consisting of two systems: a non-linear system that relates retinal slip to simple spike firing frequency of Purkinje cells in the ventral paraflocculus (VPFL) and a linear system that relates VPFL simple spike firing frequency to eye movement. This model accurately reproduced the firing frequency of Purkinje cells and ocular following responses from visual stimulation paradigms used in physiological experiments.

Action Potentials↗
PubMed1998

Mathematical modeling of deposition and disposition of drugs administered via the nose.

This articles reviews the mathematical models of deposition and disposition of drugs administered into the human nasal cavity for systemic activity. The modeling of the disposition kinetics includes drug release from carriers, translocation within the nasal cavity and into the gastrointestinal tract, drug decomposition, and drug absorption during the transit through the nose and the gastrointestinal tract. The uses of such mathematical models for design and analysis of nasal delivery systems are illustrated, with particular reference to the new therapeutic materials and excipients.

Journal Article↗
PubMed2001

A three-dimensional mathematical model of temporomandibular joint loading.

OBJECTIVE: A mathematical model of the temporomandibular joint was developed to study the magnitude and direction of the compressive loading experienced at the temporomandibular joint during clenching. DESIGN: The model was based on the principles of static equilibrium in three dimensions. BACKGROUND: Direct measurement of temporomandibular joint loading in humans is extremely difficult. Animal models have provided an alternative in the past. However, evidence suggests that primates are not the most accurate human analogues for temporomandibular joint studies. A mathematical model was used as an alternative to direct measurement. METHODS: The EMG activity of two masticatory muscles was combined with their cross-sectional areas to calculate the force exerted by each muscle. Experimentally determined forces were implemented into a quadratic programming model to solve for the compressive forces on the joint. Two objective functions were chosen and their ability to predict muscle and joint forces was evaluated. RESULTS: The maximum bite forces for normal men, normal women, and women with temporomandibular joint disorders were 300 N (SD 102 N), 210 N (SD 57.7 N), and 120 N (SD 77.1 N), respectively. The calculated joint force for normal males was 260 N (SD 84.1 N). Normal females and female temporomandibular joint disorder patients produced temporomandibular joint forces of 172 N (SD 37.5 N) and 152 N (SD 44.2 N), respectively.

Electromyography↗
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↗
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↗
PubMed1999

A mathematical model predicting the frequency of aberrant rearrangements in the T-cell receptor gene.

The T-cell receptor (TCR) genetic loci undergo an orderly process of recombination in ontogeny in order to generate a diverse array of antigen receptors. Normally occurring, out-of-frame and incomplete rearrangements produce non-productive TCR transcripts. Abnormalities in the rearrangement process occur at very low frequencies but may predominate in inborn errors of recombination. Detecting these abnormalities in surviving pools of lymphocytes is difficult and typically focuses on identification of abnormally rearranged alleles or on detecting abnormalities in recombinase proteins. Thus, there currently exists no rapid screening method to identify aberrant V(D)J recombination. To address this issue, a mathematical model was developed to predict the error rate from the measured proportions of different non-productive TCR alleles. Since the proportions of different non-productive rearrangements vary in a characteristic fashion in response to abnormalities in the recombination process, the mathematical model presented here provides a tool to indirectly assess the error rate of TCR recombination. The model was applied to a group of patients with Omenn's syndrome, most of whom had an unknown primary defect. The results indicate that these patients had a > 90% rate of aberrant TCR recombination.

Alleles↗
PubMed2000

Investigation of mathematical methods for efficient optimisation of aqueous two-phase extraction.

Mathematical strategies were applied to optimise the extraction of recombinant leucine dehydrogenase from E. coli homogenates and endoglucanase 1 from culture filtrates of Trichoderma reesei in polyethylene glycol-phosphate systems. The goal was to test mathematical tools which could facilitate the optimisation procedure in aqueous two-phase systems. A modified simplex approach, the method of steepest ascent and a genetic algorithm were successfully applied and compared. The methods differ in the height of the optimum found, the number of experiments and the time required. The genetic algorithm proved to be an optimisation procedure which can be used well in aqueous two-phase systems. The simplex procedure has to be further improved.

Algorithms↗
PubMed1998

New mathematical approach for the evaluation of drug binding to human serum albumin by high-performance liquid affinity chromatography.

A novel mathematical approach for investigation of drug-human serum albumin (HSA) interactions by means of high-performance liquid affinity chromatography is developed. The model is based on the assumption that two types of competitive binding sites exist on the HSA molecule. The widely used single-site binding equation is extended and a proper mathematical analysis is proposed allowing the determination of the major parameters characterizing the multisite binding (cobinding) process. The utility of the new approach is proved by competitive studies on HSA binding of two model drugs, diazepam and diclofenac.

Anti-Anxiety Agents↗
PubMed2002

The value of mathematical modelling in understanding contrast enhancement in CT with particular reference to the detection of hypovascular liver metastases.

OBJECTIVE: Few subjects in body imaging have generated such intensive debate as that surrounding the optimising of strategies for the detection of liver metastases using contrast-enhanced Computed Tomography (CT). Despite this, research on the subject has been almost entirely focused on experimental studies, little attention having been paid to the value of theoretical analyses. The authors' aim was to develop a relatively simple and robust mathematical model which could be implemented on a personal computer. METHODS: Simple differential equations describing the distribution of contrast agent between intra- and extra-vascular spaces during an infusion are set up. An analytic solution is obtained for the plasma/blood concentrations as a fraction of time and a solution for the interstitial concentrations as a fraction of time is obtained by converting the differential equations to difference equations which are solved in a stepwise manner. RESULTS: Vascular and hepatic parenchymal enhancement-time curves are generated which are in close agreement with expectations. The model may be used to compare different infusion regimes, e.g. lower versus higher dose, faster versus slower infusions, monophasic versus biphasic infusions and scan start delay. The implications of the results of the model for clinical protocol design are discussed and the special value of spiral/helical technology indicated. CONCLUSION: A simple mathematical model has been developed to model blood and tissue contrast enhancement in CT during contrast infusion. The model clarifies a number of issues related to contrast enhancement regimes for the study of the liver and these have been discussed.

Contrast Media↗
PubMed2002

Mathematical modeling of the forces between an intraocular lens and the capsule.

PURPOSE: To model the pressure relationship between an intraocular lens (IOL) and the capsular bag. SETTING: Department of Physics, Kings' College, London University, London, United Kingdom. METHODS: A mathematical model was made of the forces between the capsule and IOL showing that the pressure related to the local radius of curvature of the IOL at any given point. The local radius of curvature for round-edged and square-edged IOLs was measured from electron micrographs of the IOL profiles, and the corresponding pressure profiles were calculated and compared. RESULTS: The pressure between an IOL and the capsular bag was proportional to the quotient of the tension in the capsule divided by the local radius of curvature of the IOL, with a constant of proportionality that depended on the coefficient of friction between the capsule and IOL. Measuring the local radius of curvature of the 2 IOL types suggested a pressure increase of at least 69% +/- 6% at the optic edge with the square-edged IOL. CONCLUSIONS: The mathematical model predicted that IOLs with square-edged optic profiles exerts higher pressure on the posterior capsule than IOLs with round-edged optic profiles. The higher pressure may form a physical barrier to lens epithelial cell migration onto the posterior capsule.

Humans↗
PubMed1992

Arch length considerations due to the curve of Spee: a mathematical model.

Arch length analysis should consider discrepancies not only within the sagittal plane but also within the vertical and transverse planes. The vertical deviation of the occlusal plane from a flat plane is known as the curve of Spee. The purpose of this study was to produce a mathematical model of the mandibular arch form in three planes of space and to determine the effect that the curve of Spee has on arch circumference. Two mandibular arch forms, the catenary and the Bonwill-Hawley, were examined. The curve of Spee was modeled as a cylinder perpendicular to the midsagittal plane centered on the arch anteroposteriorly. A mathematical distance formula was used to calculate arch circumferences from the central fossa of the first molars for 10 arches with curves of Spee ranging from 0 to 10 mm. This procedure was repeated for arch circumferences extending from the central fossa of the second molars. Plots for the difference in arch circumferences verses depth of the curve of Spee showed that the relationship between these two variables is not linear and is less than one to one. This model showed that clinical practice of allowing 1 mm of arch circumference for leveling each millimeter of curve of Spee overestimates the amount of arch circumference needed to flatten the curve of Spee.

Child↗