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At least 1,639 records · Page 91Linked to original sources
PubMed2002

Intraoperative blood salvage: a mathematical perspective.

BACKGROUND: Intraoperative blood salvage (IBS) is one of several blood-conservation strategies employed to limit the use of allogeneic blood. IBS with mathematical modeling was studied to gain a better understanding of its benefits and limitations. STUDY DESIGN AND METHODS: Equations, based on a convergent geometric series, allowed the assessment of maximum allowable blood losses to avoid allogeneic RBC exposure in relationship to the fractional recovery of IBS. Such equations allowed us to calculate the potential "savings" in allogeneic RBC volume and to define better the efficiency of IBS. RESULTS: This model predicts that substantial amounts of RBCs (>2 units) can be recovered if there is large blood loss (e.g., >3000 mL) and if the minimal allowable Hct is low (e.g., 21%). As with other blood- conservation methods, this article shows that there are limits to the potential benefit of IBS for the avoidance of allogeneic RBC transfusion. CONCLUSION: IBS can be modeled with a convergent geometric series, and the amount of blood loss is dependent on the difference between the patient's starting Hct, the minimum allowable Hct, and the fractional recovery of RBCs. Such modeling illustrates the limited utility of IBS as a sole blood-conservation strategy.

Blood Loss, Surgical↗
PubMed1995

Preoperative autologous blood donation: benefit or detriment? A mathematical analysis.

BACKGROUND: Advocates of preoperative autologous blood donation (PABD) often fail to consider the needs of individual patients and the effects of donation on hematocrit. Mathematical modeling is used here to analyze PABD. STUDY DESIGN AND METHODS: A model of PABD was constructed to simulate the transfusion of red cells once a predetermined minimum hematocrit was reached. Preoperatively deposited units not needed to maintain a hematocrit at this level were not transfused. Final hematocrits were compared to the hematocrit that would be expected if the patient had not donated blood for his or her own operative use. RESULTS: For many patients, particularly those with normal initial hematocrits, large estimated blood losses must occur before the minimum hematocrit is reached. It is also known that patients donating multiple units typically cannot maintain their baseline hematocrit. In such cases, for blood losses of any volume, the final hematocrit was lower if units were collected preoperatively and transfusion did not occur. Preoperatively donating patients are more likely to be transfused earlier and more frequently than nondonating patients. Derived figures, based on individual patient values, help predict which patients will benefit most from PABD. CONCLUSION: PABD may actually lead to decreased postoperative hematocritis (with enhanced risk of ischemia) and otherwise unnecessary transfusions.

Blood Donors↗
PubMed2004

Use of a mathematical model to study the dynamics of Ctenocephalides felis populations in the home environment and the impact of various control measures.

The biology of fleas has been studied by a number of authors, as has the impact of various types of control measures. However, there are no mathematical models simulating the dynamics of a population of Ctenocephalides felis felis fleas on their host (the cat) and in their close environment (apartment). The model presented in this paper allows for integration of the numerous biological and behavioural parameters of the parasites and their hosts and for the variation of these same parameters. The various types of control measures can be programmed so that their impact over time can be studied. The model confirms the key role played by adult fleas, or emerged fleas contained in the cocoon. Only regular applications of persistent insecticides to the host animal will enable control of the parasite population. A combination of these insecticides with an IGR (Insect Growth Regulator) will accelerate decontamination of the home environment and see the disappearance of the parasites altogether if they are not reintroduced. The association of additional measures such as vacuum cleaning will accelerate the process of decontamination but will have no impact if carried out in isolation. One-off treatment with insecticide will not enable a reduction in the parasite population, even if carried out frequently. Use of insecticides on the home environment premises alone does not appear to be an adequate means of control. The present model can be used to test various integrated control measures which take into account different factors such as the number of host animals, the frequency of movement outdoors, the impact of the seasons.

Animals↗
PubMedDate not supplied

[Mathematical kinematic methods in joint prosthetics].

By the use of mathematical and cinematical methods a new understanding for the construction as well as for the implantation-techniques for endoprosthesis can be developed. With these methods the size of the natural motion and the process of the natural motion can be studied. So we get better informations about the natural motion and we can deduce criterions for the construction of endoprosthesis, for we can compare the motion of a model with the natural way of motion. So we can estimate preoperative the efficiency and the maximal load of the prosthesis as a result of incorrect motions. Such incorrect motions can be caused or can be avoid by the construction of the endoprosthesis as well as the implantation techniques.

Biomechanical Phenomena↗
PubMedDate not supplied

[Rotation movements of the knee joint. A mathematical-kinematic model].

The kinematics of rotational motion of the knee joint is described by a three-dimensional mathematical model. It is on principle supposed, that cruciate ligaments interact in concert to guide motion. This concept is based on the idea to explain movement in the sagittal and horizontal plane by a four-bar kinematic chain. The path of the instantaneous centers of rotation is shown with the help of this concept.

Biomechanical Phenomena↗
PubMed2002

GATA-3 transcriptional imprinting in Th2 lymphocytes: a mathematical model.

Immunological memory involves the fast recall of cytokine expression by T helper (Th) lymphocytes. Two distinct profiles of cytokine expression, Th1 and Th2, can be induced by antigen and polarizing signals during activation of naive Th cells and can subsequently be reexpressed on stimulation by antigen alone. The transcription factor GATA-3 induces Th2 development. GATA-3 is activated by the Th2-polarizing stimulus, IL-4, and has recently been observed to autoactivate its transcription. Based on these experimental data, we developed a mathematical model of GATA-3 expression that assumes independent activation of GATA-3 transcription by IL-4 and by GATA-3. Cooperativity of GATA-3 transcriptional activation is shown to create a threshold for autoactivation, resulting in the coexistence of two distinct GATA-3 expression states: a state of basal expression and a state of high expression sustained by autoactivation. Suprathreshold IL-4 signals induce a transition from basal to high GATA-3 expression. Thus, GATA-3 autoactivation creates a bistable system that can memorize a transient inductive signal. The model further predicts conditions under which the state of high GATA-3 expression can be abolished, which may extinguish the Th2 cytokine memory.

Animals↗
PubMed1979

Mathematical model for studying genetic variation in terms of restriction endonucleases.

A mathematical model for the evolutionary change of restriction sites in mitochondrial DNA is developed. Formulas based on this model are presented for estimating the number of nucleotide substitutions between two populations or species. To express the degree of polymorphism in a population at the nucleotide level, a measure called "nucleotide diversity" is proposed.

Base Sequence↗
PubMed1989

Ordered appearance of antigenic variants of African trypanosomes explained in a mathematical model based on a stochastic switch process and immune-selection against putative switch intermediates.

Antigenic variation of African trypanosomes results from the periodic activation of a single new variant cell surface glycoprotein (VSG) gene out of a repertoire of about a 1000 VSG genes. In spite of the apparently random genetic basis of the process of antigenic variation, the relapsing parasitemias are characterized by an as yet unexplained order of appearance of major VSG variants. Here we mathematically test hypotheses concerning the blood-based parasitemia. In our model the antigenic switches occur at random at the DNA level. A variable proportion of the switches has a short intermediate phase in which two different VSGs simultaneously occur on the cell surface. We show that, in a theoretical population of 230 single expressor variants in an immunocompetent or in an immunodeficient host, it is not possible to explain the ordered appearance of variants by affecting the growth coefficients of single expressors or double expressors or by affecting the antigen switch probabilities. Rather, a realistic parasitemia can be obtained if the majority of switches has a double expressor switch-intermediate phase and if the double expressors have a differential susceptibility to the immune control. This study is significant in providing a theoretical basis for the ordered appearance of variants and in explaining previously unresolved discrepancies between the rate of appearance of new variants in culture and in vivo. In addition, testable predictions as to the development of the infections, switch rate of variants, fraction of double expressors, and parasite mortality coefficients are generated.

Animals↗
PubMed1994

Evolution of gene networks by gene duplications: a mathematical model and its implications on genome organization.

Networks of transcriptional regulators have key roles in metazoan development. Important forces in the evolution of these networks are gene duplications and gene deletions, events that may change the spatiotemporal expression pattern of network genes. A measure for the probability of such changes after gene-duplication events is proposed. This measure is based on a simple mathematical model that describes such networks as dynamical systems and on properties of ensembles of these dynamical systems. It is predicted that this probability depends only on the fraction of genes duplicated in a single event and that it is largest if approximately 40% of the genes in a network are duplicated. This property is robust with respect to variations in model parameters. On these grounds, it is argued that (i) evolution of gene networks should preferentially occur either by duplication of single genes or by duplication of all genes involved in a network, and that (ii) tight linkage ("clustering") or strong dispersal are the two evolutionarily most favorable forms of genomic organization of genes forming such networks.

Animals↗
PubMed2001

From cell death to embryo arrest: mathematical models of human preimplantation embryo development.

Human preimplantation embryos exhibit high levels of apoptotic cells and high rates of developmental arrest during the first week in vitro. The relation between the two is unclear and difficult to determine by conventional experimental approaches, partly because of limited numbers of embryos. We apply a mixture of experiment and mathematical modeling to show that observed levels of cell death can be reconciled with the high levels of embryo arrest seen in the human only if the developmental competence of embryos is already established at the zygote stage, and environmental factors merely modulate this. This suggests that research on improving in vitro fertilization success rates should move from its current concentration on optimizing culture media to focus more on the generation of a healthy zygote and on understanding the mechanisms that cause chromosomal and other abnormalities during early cleavage stages.

Apoptosis↗
PubMed2001

Overview of mathematical computer models of striated sphincter muscles.

The present paper compares current mathematical striated sphincter models. Current models are subdivided in four categories: (1) simple models, (2) implementations of the urethral resistance relation, (3) models with realistic muscle dynamics and (4) finite element models. In our research group a neural network model, representing Onuf's nucleus, the spinal motor nucleus that innervates the external urethral and anal sphincters, was developed. A realistic sphincter model is needed to test the neural network. To decide whether or not a model is applicable in our research two requirements should be fulfilled: (1) the presence of realistic muscle dynamics preferably by implementation of a Huxley type muscle model and (2) the model should consist of more than one muscle unit to form a more dimensional model. Reviewing the literature, if a myogenic sphincter is modelled, mainly the Hill-equation is applied. Moreover, single muscle unit models are published. In general a multi-unit muscle model of the sphincter is lacking, prohibiting the study of the inherent properties of sphincter muscles, which could give information on the realistic behaviour of elements in circular muscles. It is concluded that the functionality of current sphincter models is limited for our purpose.

Animals↗
PubMed2003

An improved mathematical model of the ovulatory cycle of the laying hen.

1. The mathematical model of the hen's ovulatory cycle proposed by Etches and Schoch (British Poultry Science, 25: 65-76, 1984) predicts ovulation times for sequences of 2 to 9 ovulations only. 2. Continuous functions have been produced, representing the changes required to the parameters lambda1, lambda2, S1, S2, b1, b2 and b3, such that the prediction of any sequence length is now possible. 3. This improved ovulation model is capable of predicting ovulation times and intra-sequence ovulation intervals for any ovulation rate between 0.5 and 1.0. 4. The improved ovulatory model lends itself to stochasticity. The rate of lay of a population of hens at a time may be modelled with the use of means and standard errors for each of the parameters in the model. 5. Age-related changes in the ovulation rate of the population may be predicted using a combination of three methods, which are consistent with published theories that account for the decline in performance with time.

Animals↗
PubMed2002

Language and mathematical problem solving among bilinguals.

Does using a bilingual's 1st or 2nd language have an effect on problem solving in semantically rich domains like school mathematics? The author conducted a study to determine whether Filipino-English bilingual students' understanding and solving of word problems in arithmetic differed when the problems were in the students' 1st and 2nd languages. Two groups participated-students whose 1st language was Filipino and students whose 1st language was English-and easy and difficult arithmetic problems were used. The author used a recall paradigm to assess how students understood the word problems and coded the solution accuracy to assess problem solving. The results indicated a 1st-language advantage; that is, the students were better able to understand and solve problems in their 1st language, whether the 1st language was English or Filipino. Moreover, the advantage was more marked with the easy problems. The theoretical and practical implications of the results are discussed.

Analysis of Variance↗
PubMed1999

Gender and racial differences in mathematical performance.

The authors examined gender and racial differences in mathematics performance among 5th- and 8th-grade students in the United States. Math performance was assessed by scores on the math-concepts and math-computation sections of the California Achievement Test (CTB/McGraw-Hill, 1986) given at the end of the previous year. There were no significant gender differences, but in both grades, the White students scored significantly higher than the Black students. The racial differences were more pronounced in the scores for concepts than in the scores for computation. Responses to a parent questionnaire showed significant relationships between parents' self-reported math anxiety, parents' most advanced math course, and parents' education level in relation to the child's math performance. Differences in these relationships suggest that, although parents' beliefs and attitudes about math influence their child's math performance, the relationship is complex and may vary with race.

Achievement↗
PubMed1980

Mathematical model of synaptic plasticity: II. Habituation.

A mathematical model of the phenomenon of habituation as a homosynaptic depression of the amount of transmitter release is proposed. The model is based on the physiological studies of habituation in invertebrates and in the spinal cord of vertebrates, where a single synapse has been isolated and some of the physiological mechanisms of this process have been elucidated. The model simulates the following properties of habituation: (1) reduced amount of transmitter release attributed to a repetitive stimulus through changes in the membrane permeability to Ca2+ ions; (2) spontaneous recovery by rest; (3) the amplitude and frequency dependence of habituation; (4) modulation of habituation: sensitization, through an increase in membrane Ca2+ permeability, and presynaptic inhibition, through a reduced depolarization of the physiological stimulus; (5) long-term habituation attributed to repetitive trials of habituation and spontaneous recovery.

Animals↗
PubMed1980

Mathematical model of synaptic plasticity: III. Heterosynaptic changes.

A mathematical model, using differential equations, of heterosynaptic plasticity is proposed. The model is based on physiological studies of invertebrates in which nonspecific conditioning, such as sensitization and heterosynaptic inhibition, starts to be elucidated and behavioral studies of classical and instrumental conditioning, which we postulate to have the same mechanisms as those found in nonspecific conditioning. The model permits us to simulate the following heterosynaptic changes: sensitization, heterosynaptic inhibition, classical and instrumental conditioning--including short- and long-term memory--extinction and recuperation--spontaneously and by stimulation.

Animals↗
PubMed2002

A mathematical analysis of the 4 x 100 m relay.

In this study, we examined aspects of the 4 x 100 m relay that are amenable to mathematical analysis. We looked at factors that affect the time required to complete the relay, focusing on the performance of elite male athletes. Factors over which the individual athletes, and the team coach, can exercise some control are: the starting positions of the runners on legs 2, 3 and 4, the positions at which baton exchanges occur, the free distances at the baton exchanges and the running order of the athletes. The lane draw is shown to have an important influence on the relay time, although it is outside the control of the team coach. Teams drawn in the outside lanes benefit from the inverse relation between bend radius of curvature and running speed. For teams composed of athletes with different times over 100 m, we show that the fastest relay times are achieved with the fastest athlete taking the first leg, with the slowest two runners allocated to the final two legs.

Energy Metabolism↗
PubMed1995

Determination of physiological data from a mathematical analysis of the running performance of elite female athletes.

A method of analysis developed and applied to male athletes is used to determine physiological data for female athletes. The analytical method rests on the construction of an energy balance incorporating a mathematical representation of each of the major terms in the balance. By recasting the energy balance, a relationship between race distance and running time is derived. Excellent agreement with results for female athletes from recent Olympic Games for distances from 100 to 10,000 m is established. From the analysis, representative values of the maximum anaerobic power, the maximum aerobic power and the rate of degradation of mechanical energy into heat are derived for elite female athletes.

Adult↗