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PubMed1993

An approach to QRS complex detection using mathematical morphology.

An approach to QRS complex detection based on mathematical morphology is presented in this communication. QRS complexes are detected by the application of a simple morphological operator. This operator works as a peak-valley extractor and it is controlled by the shape of the structuring element. A set (horizontal line segment) is used as structuring element resulting in very fast execution times. The accuracy of this approach has been tested using a standard ECG library; a sensitivity of 99.38% and a positive predictivity of 99.48% have been achieved.

Decision Support Techniques↗

PubMed1993

Mathematical analysis and computer simulation of the respiratory system in the newborn infant.

A mathematical model of neonatal respiratory control is proposed which can be used to stimulate the system under different physiological conditions. The model consists of a continuous plant and a discrete controller. Included in the plant are lungs, body tissue, brain tissue, a cerebrospinal fluid compartment, and central and peripheral receptors. The effect of shunt in the lungs is included in the model and the lung volume and the dead space are time varying. The controller utilizes outputs from peripheral and central receptors to adjust the depth and rate of breathing and the effects of prematurity of peripheral receptors are included in the system. Hering-Breuer type reflexes are embodied in the controller to accomplish respiratory synchronization. The model is examined and its simulation results under test conditions in hypoxia and hypercapnia are presented.

Blood Gas Analysis↗

PubMed1995

Intracranial pressure dynamics in patients with acute brain damage: a critical analysis with the aid of a mathematical model.

The time pattern of intracranial pressure (ICP) in response to typical clinical tests (i.e., bolus injection and bolus withdrawal of 1 to 4 mL of saline in the craniospinal space) was studied in 18 patients with acute brain damage by means of a mathematical model. The model includes the main biomechanical factors assumed to affect intracranial pressure, particularly cerebrospinal fluid (CSF) dynamics, intracranial compliance, and cerebral hemodynamics. Best fitting between model simulation curves and clinical tracings was achieved using the Powell minimization algorithm and a least-square criterion function. The simulation results demonstrate that, in most patients, the ICP time pattern cannot be explained merely on the basis of CSF dynamics but also requires consideration of the contribution of cerebral hemodynamics and blood volume alterations. In particular, only in a few patients (about 40% of total) the ICP monotonically returns toward baseline following the clinical maneuver. In most of the examined cases (about 60%), ICP exhibits an anomalous response to the same maneuver, characterized by a delayed increase after bolus injection and a delayed decrease after withdrawal. The model is able to explain these responses, imputing them to active intracranial blood volume changes induced by mechanisms controlling cerebral blood flow. Finally, the role of the main intracranial biomechanical parameters in the genesis of the ICP time pattern is discussed and a comparison with previous theoretical studies performed.

Acute Disease↗

PubMed2004

Recognition of online handwritten mathematical expressions.

This paper aims at automatic understanding of online handwritten mathematical expressions (MEs) written on an electronic tablet. The proposed technique involves two major stages: symbol recognition and structural analysis. Combination of two different classifiers have been used to achieve high accuracy for the recognition of symbols. Several online and offline features are used in the structural analysis phase to identify the spatial relationships among symbols. A context-free grammar has been designed to convert the input expressions into their corresponding T(E)X strings which are subsequently converted into MathML format. Contextual information has been used to correct several structure interpretation errors. A new method for evaluating performance of the proposed system has been formulated. Experiments on a dataset of considerable size strongly support the feasibility of the proposed system.

Algorithms↗

PubMed1979

A mathematical model of thrombopoiesis in rats.

A mathematical model of thrombopoiesis in rats is presented. This has four compartments; stem cells, megakaryocytes, thrombocytes and thrombopoietin. A high thrombopoietin concentration influences bone marrow proliferation in three ways. Firstly the stem cells are stimulated and a slow increase in megakaryocyte number follows. Secondly there are additional endomitoses in the (early) megakaryocytes resulting in an increase in megakaryocyte volume. Thirdly the megakaryocyte maturation time is shortened. The parameters of the model are determined from experimental values for the normal, maximum and minimum proliferation rates, maturation times and destruction rates. The model is tested by comparing simulated results for acute and chronic thrombocytopenia and thrombocytosis with experimental curves from the literature. The model and data agree within the limits of experimental error. Not all of the thrombopoietic regulatory system is known yet, so some important alternative hypotheses are investigated and compared with the model. Several hypotheses have been excluded in this way.

Animals↗

PubMed1980

A comprehensive mathematical model of stem cell proliferation which reproduces most of the published experimental results.

On the basis of experimental knowledge about haemopoietic stem cells a catalogue of fundamental statements is formulated. From this a simple mathematical model of haemopoietic regulation mechanisms is developed. The functional net effects of regulatory processes which are still unknown or unmeasurable are estimated using evolution arguments. The model is developed in three steps. It allows description of the self-replication of stem cells after direct destruction as well as their reaction to increased or reduced needs in the erythropoietic system. The most important experimental data about changes in CFUs, BFUe and CFUe after acute or chronic irradiation, anaemia, hypoxia, hypertransfusion or direct erythropoietic stimulation can be reproduced within the model. The model allows us to understand most of the results of experimental stem cell research. Furthermore, it can be applied for a more precise analysis of the existing data. Predictions about the results of certain experiments can be made.

Animals↗

PubMed1981

A mathematical model for analysing cellular age-response functions in terms of physiological age.

A mathematical model is presented which facilitates the analysis of cellular age-response functions in terms of the physiological ages of the cells. Age-response functions are generally determined by obtaining synchronous cohorts of cells and measuring the sensitivity of the cohorts to the treatment agent at different times after selection (i.e., several different chronological ages). The model described here uses data on the [3H]TdR labelling patterns of the cell population to determine the distribution of physiological ages for the cohorts at the times of treatment. The age-response function data are then analysed in terms of the physiological ages of the cells. The compartments used in the analysis may be chosen according to the biology of the system and the wishes of the experimenters and not imposed by the variability of the phase durations. The application of the model is illustrated using the age-response functions for EMT6 cells exposed to radiation and HeLa cells exposed to hydroxyurea.

Animals↗

PubMed1982

Kinetics of protein and DNA synthesis studied by mathematical modelling of flow cytometric protein and DNA histograms.

Mathematical models for histograms of cellular protein content as measured by flow cytometry were developed, based on theoretical protein distributions. These were derived from the age distribution of cells and the accumulation function for cellular protein content as a function of age within the cell cycle. A model assuming an exponential age distribution and an exponential protein accumulation function was found to give the best representation of protein histograms of exponentially growing NHIK 3025 cells. This is in good agreement with the known kinetic behaviour of such cells. By the combined use of the protein histogram model and a similar model for DNA content, and assuming linear DNA accumulation during S, the fraction of cells in S, as a function of cellular protein content, was simulated. This function showed good agreement with values of the [3H]TdR labelling index scored in cells sorted by flow cytometry from 5-channel intervals of the protein histogram. The protein and DNA histogram models were combined into a two-dimensional model for correlated protein/DNA measurements. Comparison between simulated data and experimentally derived two-dimensional protein/DNA histograms gave further support to the cell kinetic assumptions underlying the models, but also identified some minor deviations which could not be recognized in the analysis of the one-dimensional histograms.

Cell Cycle↗

PubMed1982

Evidence for discrete cell kinetic subpopulations in mouse epidermis based on mathematical analysis.

Continuous (repeated) labelling studies in mouse epidermis indicate that nearly all cells are labelled after about 100 hr. Percentage labelled mitoses studies ([3H]TdR at 15.00 and 03.00 hours) have a first peak that does not reach 100% and has a half-width of about 10 hr. Small second and third peaks can be detected at about 90 and 180 hr. respectively. The changes with time in the number of labelled cells show a difference dependent on the time of day of [3H]TdR administration. Both curves show an early doubling in labelled cells which then decline, forming a peak of labelled cells. A second peak occurs at about 120 hr. This is followed by a progressive decline with no further peak until values of about 1% labelling are obtained at 340 hr. These experiments have been investigated mathematically. A computer programme has been devized that permits all three types of experiments to be analyzed simultaneously. More importantly, it can analyse situations with a heterogeneity in cell cycle parameters in all proliferative subpopulations. Various models for epidermal cell replacement have been considered. The data as a whole can best be explained if the basal layer contains at least two distinct subpopulations of cells and an exponentially decaying post-mitotic population with a half-life of about 30 hr. The proliferative sub-populations must be characterized by near integer differences in the length of cycle, the precursor (stem) compartment having the longer cycle. An inverse relationship is required for the length of S, i.e. the shortest time for the stem cells. A full range of cell kinetic parameters can be calculated and are tabulated for the most appropriate model system which is one involving three transit proliferating subpopulations.

Animals↗

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↗

PubMed1986

Mathematical model for human myeloma relating growth kinetics and drug resistance.

We present a computer-based mathematical model that can simulate characteristic features of the clinical time course of human myeloma. It asserts that therapy resistance in myeloma cells is an inherited trait associated with the longer inter-mitotic times of some cells and that the strength of this trait affects tumour growth characteristics. These kinetic differences within the malignant cell clone may also influence therapeutic efficacy. In the model, the same total therapy, administered in different time-dose fractions, could be 'curative' or 'minimally effective' depending on kinetic properties. For example, as others have shown, in myeloma pulsed intermittent therapy is often more effective than low dose continuous therapy. According to our model this finding is compatible with a high coefficient of inheritability of resistance from one cell generation to the next. The model also suggests that if there are subclones of varying resistance, a therapy must have some effect on each of them if it is to be employed in a curative fashion. While many aspects of the model are not yet clinically testable, exploration of its concepts might increase knowledge about fundamental neoplastic mechanisms.

Antineoplastic Agents↗

PubMed1988

Mathematical analysis of haemopoietic grafted cell renewal and migration through the allogeneic or syngeneic mouse host.

A mathematical analysis of results from kinetic studies of 125-iododeoxyuridine uptake and loss in almost all the lymphoid and non-lymphoid organs of mice is described. Applied to data gathered from a graft-versus-host reaction experiment, this analysis affords quantitative precision on the differential effects of organ alloantigens on the proliferating grafted cells. It is shown that, depending on the organ and the post-graft period, cell growth can be ascribed to alloantigen-driven cell renewal or to alloantigen-driven trapping or sequestration. Possible applications of the present approach in graft rejection monitoring are discussed.

Animals↗

PubMed1988

Turnover and maturation kinetics in the hairless mouse epidermis. Continuous [3H]TdR labelling and mathematical model analyses.

Hairless mice were continuously labelled with 10 microCi of tritiated thymidine ([3H]TdR) every 4 h for 8 d, and the proportions of labelled basal and differentiating cells were recorded separately. The mitotic rate was measured by the stathmokinetic method and the cell cycle distributions were measured by flow cytometry of isolated basal cells at intervals during the labelling period. The mitotic rate of the [3H]TdR-injected animals did not deviate from control values during the first 5 d. Computer simulations of the data based on various mathematical models were made, and three main conclusions were obtained: (1) a large spread in transit times through the G1 phase was found, together with a very narrow distribution in maturation time of differentiating cells; (2) about 20% of the differentiating cells were estimated to leave the basal cell layer directly after mitosis. This is consistent with results obtained from different sets of data; and (3) during continuous labelling more than 90% of the cells are labelled during each passage through the S phase.

Animals↗

PubMed1989

A mathematical model of erythropoiesis in mice and rats. Part 3: Suppressed erythropoiesis.

A mathematical model of erythropoietic cell production and its regulation process has been proposed in a preceding paper. It is primarily based on the assumption that the number of cell divisions taking place in the CFU-E and erythropoietic precursor stages can be regulated depending on the oxygen supply to the tissue. Here we provide evidence that this model adequately describes situations of suppressed erythropoiesis. In detail this implies a quantitative description of the following processes: (1) changes in tissue oxygen tension (Pto2) due to increase in red cell numbers (red cell transfusion, posthypoxia), decrease in plasma volume (dehydration) or increase in atmospheric oxygen pressure (hyperoxia), (2) Pto2 dependent reduction of erythropoietin (EPO) production, (3) dose-response of reduced EPO-levels on erythropoietic amplification (omission of three to five mitoses). Model simulations are compared to experimental data obtained from red cell transfusion, posthypoxia, hyperoxia and dehydration. A satisfactory agreement suggests that the model adequately describes and correlates different ways to suppress erythropoiesis. It quantifies the role and relative contribution of the haematocrit, haemoglobin concentration, atmospheric oxygen pressure, tissue oxygen pressure and plasma volume as triggers in erythropoietic suppression under various conditions. In conjunction with the preceding two papers it could be shown that one unique set of model parameters is sufficient to describe erythropoiesis in steady state, stimulation and suppression. Limitations of the model are discussed and experiments for a more detailed investigation of the feedback mechanisms are proposed.

Animals↗

PubMed1990

A mathematical model of erythropoiesis in mice and rats. Part 4: Differences between bone marrow and spleen.

In a preceding analysis we hypothesized that the most important parameter controlled by erythropoietic regulation in vivo is the degree of amplification (number of cell divisions) in the CFU-E and erythroblast cell stages. It was concluded that erythropoietic amplification in vivo is controlled according to a sigmoidal dose-response relationship with respect to the control parameter which is the haematocrit (or haemoglobin concentration). Here, this hypothesis is extended to include the differences in murine bone marrow and splenic erythropoiesis that are described and quantified by different dose-response relationships. Comparing several sets of experimental data with mathematical model simulations, this approach leads to the following conclusions: (i) in the unperturbed normal steady state at least one extra erythropoietic cell division takes place in the spleen compared with the bone marrow; (ii) a strong erythropoietic stimulus, such as severe bleeding or hypoxia, can induce five to six additional cell divisions in the spleen but only two to three additional divisions in the bone marrow; this results in a considerable increase in the spleen's contribution to erythropoiesis from about 10% in normal animals to over 40% during strong stimulation; (iii) under erythropoietic suppression, such as red cell transfusion, a similar number of cell divisions is skipped in both organs and the splenic contribution to erythropoiesis remains unchanged. In conclusion, the concept that bone marrow and spleen microenvironments differ in the dose-response relationship for erythropoietic regulation provides an explanation for the changing contribution of splenic murine erythropoiesis following a variety of experimental treatments.

Animals↗

PubMed1992

Mathematical modelling of microenvironment and growth in EMT6/Ro multicellular tumour spheroids.

In order to determine the role of micromilieu in tumour spheroid growth, a mathematical model was developed to predict EMT6/Ro spheroid growth and microenvironment based upon numerical solution of the diffusion/reaction equation for oxygen, glucose, lactate ion, carbon dioxide, bicarbonate ion, chlorine ion and hydrogen ion along with the equation of electroneutrality. This model takes into account the effects of oxygen concentration, glucose concentration and extracellular pH on cell growth and metabolism. Since independent measurements of EMT6/Ro single cell growth and metabolic rates, spheroid diffusion constants, and spinner flask mass transfer coefficients are available, model predictions using these parameters were compared with published data on EMT6/Ro spheroid growth and micro-environment. The model predictions of reduced spheroid growth due to reduced cell growth rates and cell shedding fit experimental spheroid growth data below 700 microns, but overestimated the spheroid growth rate at larger diameters. Predicted viable rim thicknesses based on predicted near zero glucose concentrations fit published viable rim thickness data for 1000 microns spheroids grown at medium glucose concentrations of 5.5 mM or less. However, the model did not accurately predict the onset of necrosis. Moreover, the model could not predict the observed decreases in oxygen and glucose metabolism seen in spheroids with time, nor could it predict the observed growth plateau. This suggests that other unknown factors, such as inhibitors or cell-cell contact effects, must also be important in affecting spheroid growth and cellular metabolism.

Animals↗

PubMed1983

Hazard analysis applied to microbial growth in foods: development of mathematical models describing the effect of water activity.

Mathematical models have been developed which describe the effect of lowering the water activity on the growth kinetics of Staphylococcus aureus and Salmonella typhimurium. By treating the lag phase and exponential phase kinetics separately predictions can be made on the extent of microbial growth over successive time/temperature cycles. Staph. aureus was far more tolerant than Salm. typhimurium to lowered water activity and under near growth limiting conditions of water activity and temperature was showing lag periods as long as ca 40 d. The maximum lag period observed for Salm. typhimurium was ca 5 d. Under these conditions the predicted generation times for Staph. aureus were 2-3 d and for Salm. typhimurium.

Animals↗

PubMed1976

Particle size-shape distributions: the general spheroid problem. I. Mathematical model.

The development of stereological methods for the study of dilute phases of particles, voids or organelles embedded in a matrix, from measurements made on plane or linear intercepts through the aggregate, has deserved a great deal of effort. With almost no exception, the problem of describing the particulate phase is reduced to that of identifying the statistical distribution--histogram in practice--of a relevant size parameter, with the previous assumption that the particles are modelled by geometrical objects of a constant shape (e.g. spheres). Therefore, particles exhibiting a random variation about a given type of shape as well as a random variation in size, escape previous analyses. Such is the case of unequiaxed particles modelled by triaxial ellipsoids of variable size and eccentricity parameters. It has been conjectured (Moran, 1972) that this problem is indetermined in its generally (i.e. the elliptical sections do not furnish a sufficient information which permits a complete description of the ellipsoids). A proof of this conjecture is given in the Appendix. When the ellipsoids are biaxial (spheroids) and of the same type (prolate or oblate), the problem is identifiable. Previous attempts to solve it assume statistical independence between size and shape. A complete, theoretical solution of the spheroids problem--with the independence condition relaxed--is presented. A number of exact relationships--some of them of a striking simplicity--linking particle properties (e.g. mean-mean caliper length, mean axial ratio, correlation coefficient between principal diameters, etc.) on the one hand, with the major and minor dimensions of the ellipses of section on the other, emerge, and natural, consistent estimators of the mentioned properties are made easily accessible for practical computation. Finally, the scope and limitations of the mathematical model are discussed.

Mathematics↗