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PubMedDate not supplied

Mathematical precision in rotational corrective osteotomy of the femur.

We used a mathematical model to determine whether the approach to derotation of the malrotated femur can be improved for use in corrective osteotomy of the femur. Rotational corrective osteotomy of the femur (RCOF) is a procedure performed by orthopedic surgeons to correct congenital femoral torsion deformities and posttraumatic femoral shaft malunions. In the conventional technique, osteotomy is performed at the malrotation site, and correction is achieved by rotating the distal segment of the femur so that the patella and toes point upward, symmetric with the normal leg when the patient is in the supine position. This approach does not ensure the rotational position of the proximal segment of the femur, and malrotation can still persist. Intraoperative muscle spasm or preoperative soft tissue contracture may alter the proximal segment rotation immediately after osteotomy. Although marked improvement in the accuracy of measuring the malrotation angle for RCOF has been made possible by the computed tomography and magnetic resonance imaging, the orthopedic surgeon does not have a defined approach for transforming this value from degrees to millimeters so that derotation of the femur can be achieved intraoperatively with precision. We carried out studies using ten cadaver femurs with malrotation angles of 15 to 44 degrees to see if this surgical technique can be improved by a mathematical model that converts the malrotation angle value (in degrees) to an equivalent value on the circle circumference (in millimeters). Our results show errors of 0.5 to 4.5 degrees in the rotation angle and virtually eliminate the error of malrotation associated with RCOF. We suggest that our model is clinically applicable and that its definitive value will arise from clinical applications.

Cadaver↗

PubMed1997

Neurosurgical trauma call: use of a mathematical simulation program to define manpower needs.

Resource criteria for trauma centers (TC) mandate a first plus backup neurosurgeon (NS) coverage, an unnecessary expense for TC treating few neurosurgery patients. This report uses a mathematical modeling system to define optimal NS trauma coverage. Random data from 749 patients treated with emergency neurosurgery operations (OR) within 24 hours of admission at 97 TC were used to create a 1-year profile of admission by month, day, and hour, operation times, and operation duration. These data were entered into a simulation program to define the frequency that a patient needing a NS consult would wait beyond 30 minutes because the NS was in the operating room at a trauma center with one, two, or three neurosurgeons on-call. One thousand iterations were done for each sample size of 25 to 300 patients in 25-patient increments. The probability that a patient could not be seen promptly by one NS in a trauma center operating on 25, 50, 75, or 100 patients per year is 0.23, 0.9, 1.6, and 3.66 patients per year. Fewer than one patient (0.75) per year will wait more than 30 min in a trauma center doing 225 emergency ORs when two neurosurgeons are on-call. One patient in 10 years would wait more than 30 min in a trauma center doing 300 ORs with a third NS on-call. Mathematical modeling of patient data helps define optimal hospital resources. Mandatory NS backup for TC performing fewer than 25 neurosurgery procedures is unneeded.

Computer Simulation↗

PubMed2002

Mathematical modeling in glucose metabolism and insulin secretion.

PURPOSE OF REVIEW: Mathematical models in the study of glucose metabolism, insulin secretion and the insulin-glucose interactions have a longstanding tradition. The recent advances in this area are reviewed, with particular emphasis on the methods for the assessment of insulin sensitivity and insulin secretion. The available models are illustrated, and their common aspects and differences discussed. RECENT FINDINGS: For the assessment of insulin sensitivity and beta-cell function, several modeling methods have recently been developed. Models for insulin sensitivity provide insulin-sensitivity indices from simple clinical tests, or a rich multiple-parameter characterization of insulin sensitivity from more elaborate experiments. Models for beta-cell function yield indices that quantify the ability of the beta-cells to respond to glucose stimuli. Furthermore, models of the insulin-glucose interactions propose interesting explanations of some experimental observations such as insulin-glucose oscillations and the progression to type 2 diabetes. SUMMARY: Mathematical models in this area continue to evolve toward more accurate and clinically applicable approaches, and should be considered as a useful resource for clinical investigators. Models also have a potentially important role for understanding the mechanisms governing the insulin-glucose regulation system.

Animals↗

PubMedDate not supplied

Functional brain imaging study of mathematical reasoning abilities in velocardiofacial syndrome (del22q11.2).

PURPOSE: Children with velocardiofacial syndrome (VCFS) often have deficits in mathematical reasoning. Previous research has suggested that structural abnormalities in the parietal lobe region might underlie these deficits. The present study utilized functional magnetic resonance imaging (fMRI) to explore the relationship between brain function and mathematical performance in VCFS. METHODS: Eight children with VCFS and eight comparison subjects underwent fMRI scanning and completed an arithmetic computation task. RESULTS: In the VCFS group, increased activation was observed in the left supramarginal gyrus (LSMG) as the task difficulty increased. CONCLUSION: Aberrant LSMG activation, possibly due to structural deficits of the left parietal lobe, may explain decrements in arithmetic performance observed in VCFS.

Adolescent↗

PubMed1988

A mathematical model for the freezing process in biological tissue.

A mathematical model has been developed to study the process of freezing in biological organs. The model consists of a repetitive unit structure comprising a cylinder of tissue with an axial blood vessel (Krogh cylinder) and it is analysed by the methods of irreversible thermodynamics. The mathematical simulation of the freezing process in liver tissue compares remarkably well with experimental data on the structure of tissue frozen under controlled thermal conditions and the response of liver cells to changes in cooling rate. The study also supports the proposal that the damage mechanism responsible for the lack of success in attempts to preserve tissue in a frozen state, under conditions in which cells in suspension survive freezing, is direct mechanical damage caused by the formation of ice in the vascular system.

Animals↗

PubMed1992

Oncogenes, anti-oncogenes and the immune response to cancer: a mathematical model.

We develop a mathematical model for the initial growth of a tumour after a mutation in which either an oncogene is expressed or an anti-oncogene (i.e. tumour suppressor gene) is lost. Our model incorporates mitotic control by several biochemicals, with quite different regulatory characteristics, and we consider mutations affecting the cellular response to these control mechanisms. Our mathematical representation of these mutations reflects the current understanding of the roles of oncogenes and anti-oncogenes in controlling cell proliferation. Numerical solutions of our model, for biologically relevant parameter values, show that the different types of mutations have quite different effects. Mutations affecting the cell response to chemical regulators, or resulting in autonomy from such regulators, cause an advancing wave of tumour cells and a receding wave of normal cells. By contrast, mutations affecting the production of a mitotic regulator cause a slow localized increase in the numbers of both normal and mutant cells. We extend our model to investigate the possible effects of an immune response to cancer by including a first order removal of mutant cells. When this removal rate exceeds a critical value, the immune system can suppress tumour growth; we derive an expression for this critical value as a function of the parameters characterizing the mutation. Our results suggest that the effectiveness of the immune response after an oncogenic mutation depends crucially on the way in which the mutation affects the biochemical control of cell division.

Animals↗

PubMed2005

The mathematical significance of proof theory.

Returning to old ideas of Kreisel, I discuss how the mathematics of proof theory, often combined with tricks of the trade, can occasionally be useful in extracting hidden information from informal proofs in various areas of mathematics.

Algorithms↗

PubMed2005

Pluralism in mathematics.

We defend pluralism in mathematics, and in particular Errett Bishop's constructive approach to mathematics, on pragmatic grounds, avoiding the philosophical issues which have dissuaded many mathematicians from taking it seriously. We also explain the computational value of interval arithmetic.

Algorithms↗

PubMed2005

The justification of mathematical statements.

The uncompromising ethos of pure mathematics in the early post-war period was that any theorem should be provided with a proof which the reader could and should check. Two things have made this no longer realistic: (i) the appearance of increasingly long and complicated proofs and (ii) the involvement of computers. This paper discusses what compromises the mathematical community needs to make as a result.

Algorithms↗

PubMed1989

A mathematical model of cerebral blood flow chemical regulation--Part I: Diffusion processes.

This paper proposes a mathematical model which describes the production and diffusion of vasoactive chemical factors involved in oxygen-dependent cerebral blood flow (CBF) regulation in the rat. Partial differential equations describing the relations between input and output variables have been replaced with simpler ordinary differential equations by using mathematical approximations of the hyperbolic functions in the Laplace transform domain. This model is composed of two submodels. In the first, oxygen transport from capillary blood to cerebral tissue is analyzed to link changes in mean tissue oxygen pressure with CBF and arterial oxygen concentration changes. The second submodel presents equations describing the production of vasoactive metabolites by cerebral parenchyma, due to a lack of oxygen, and their diffusion towards pial perivascular space. These equations have been used to simulate the time dynamics of mean tissue PO2, perivascular adenosine concentration, and perivascular pH to changes in CBF. The present simulation points out that the time delay introduced by diffusion processes is negligible if compared with the other time constants of the system under study. In a subsequent work the same equations will be included in a model of the cerebral vascular bed to clarify the metabolite role in CBF regulation.

Animals↗

PubMed1989

A mathematical model of cerebral blood flow chemical regulation--Part II: Reactivity of cerebral vascular bed.

In the present paper an original mathematical model of the chemical oxygen-dependent cerebral blood flow (CBF) regulation in the rat is proposed. Taking into account recent experimental works, the model assumes that oxygen acts on cerebral vessels through an indirect mechanism, mediated by the release of two metabolic substances (adenosine and H+) from tissue, and that any change in perivascular concentration of these substances affects the diameter of both the medium and small pial arteries as well as of intracerebral arterioles. The model is composed of several submodels, each closely related to a different physiological event. mathematical equations, which describe the reaction of the vasoactive portion of the cerebral vascular bed, are reported in detail and justified. The model permits the simulation of the role played by chemical factors in the control of CBF under many different physiological and pathological conditions in an attempt to clarify their relevance. Several events associated with an alteration in oxygen supply to tissue (auto-regulation to changes in arterial and venous pressure, reactive hyperemia following on cerebral ischemia, arterial hypoxia) have been simulated with the model. The results suggest that chemical factors, adenosine and H+, play a significant but not exclusive role in the regulation of the cerebral vascular bed. The action of other mechanisms (which are probably neurogenic) must be hypothesized to explain completely the CBF changes occurring in vivo.

Animals↗

PubMed2006

A mathematical formulation of DNA computation.

DNA computation is to use DNA molecules for information storing and processing. The task is accomplished by encoding and interpreting DNA molecules in suspended solutions before and after the complementary binding reactions. DNA computation is attractive, due to its fast parallel information processing, remarkable energy efficiency, and high storing capacity. Challenges currently faced by DNA computation are: 1) lack of theoretical computational models for applications and 2) high error rate for implementation. This paper attempts to address these problems from mathematical modeling and genetic coding aspects. The first part of this paper presents a mathematical formulation of DNA computation. The model may serve as a theoretical framework for DNA computation. In the second part, a genetic code based DNA computation approach is presented to reduce error rate for implementation, which has been a major concern for DNA computation. The method provides a promising alternative to reduce error rate for DNA computation.

Base Sequence↗

PubMed2001

A mathematical analysis of the interactions between immunogenic tumor cells and cytotoxic T lymphocytes.

Recent developments of biotechnology have enabled us to use immunotherapy against certain kinds of tumors in patients. However, it is reasonable to doubt if the immunotherapy can completely aid the rejection of tumors that have escaped from the immune system. In this paper, we propose a new mathematical model of tumor immunity by tumor-specific cytotoxic T lymphocytes (CTLs), since tumor-specific CTLs play an important role in tumor immunity. Using this model, we have mathematically investigated the interactions between immunogenic tumor cells (TCs) and tumor-specific CTLs and evaluated the availability of immunotherapies for tumors. The findings herein demonstrate that three kinds of dynamics of tumor immunity exist: i.e. (1) TCs continue to proliferate with CTLs; (2) TCs are rejected by CTLs; and (3) TCs equilibrate with CTLs, but with little possibility of the equilibrium. The findings also demonstrate that a sufficient increase in CTLs by immunotherapy can aid the rejection of TCs, but an insufficient increase in CTLs by immunotherapy causes only a transient regression of TCs. Clinically the findings mean that increasing tumor-specific CTLs, e.g., by vaccination or adoptive transfer of tumor-specific CTLs expanded ex vivo, can theoretically aid the rejection of TCs.

Humans↗

PubMed1989

A mathematical model of erythropoiesis in mice and rats. Part 1: Structure of the model.

A mathematical model has been developed which describes the regulation of erythropoiesis in mice and rats. The main model assumptions are: (1) Regulation is mediated by erythropoietin (EPO). (2) The production of EPO depends exponentially on the tissue oxygen pressure (e.g. in the renal production sites). (3) There are sigmoidal dose-response curves relating the EPO concentration in the plasma to the mitotic activity of CFU-E and proliferative erythropoietic precursors. For maximum stimulation two to four additional mitoses may occur, while for an absent stimulus three to five mitoses may be omitted. (4) The normal precursor transit time of three to four days may be shortened by more than 50% during maximum stimulation. (5) The erythrocytes have a normal lifespan of 42-56 days, which may be reduced to 15-20 days under erythropoietic stimulation. Among these assumptions, the dose-response relationships between EPO and the mitotic activity of CFU-E and the proliferative erythropoietic precursors are the most important hypotheses of the model. This is the first of a series of three papers and gives a description of the mathematical formalism and the parameters used. In the subsequent papers computer simulations on erythropoietic stimulation and suppression are presented.

Animals↗

PubMed1996

Comparison of mathematical formulas used for estimation of DNA synthesis time of bromodeoxyuridine-labelled cell populations with different proliferative characteristics.

Growth kinetic data of human tumours, obtained by flow cytometric analysis of cells labelled with bromodeoxyuridine (BrdUrd) might provide prognostic information and allow prediction of response to radio- and chemotherapy. However, the theoretical models applied for calculation of growth kinetic data are not fully evaluated. The purpose of this study was to investigate the dependence of the estimation of DNA synthesis time (Ts) on sampling time after BrdUrd labelling, using four different mathematical formulas (Begg et al., White & Meistrich, White et al. and Johansson et al.) which have been developed for the evaluation of flow cytometry-derived data of BrdUrd-labelled cells. In addition, we have investigated the influence of the growth kinetic properties of the cell populations using two cultured cell lines (one slow and one fast growing), and two hetero-transplanted human tumours. The dependence of the estimation of Ts on sampling time was more or less pronounced, depending on the cell population examined and on the formula used. In the fast growing cell line, the estimates of Ts did not vary significantly with sampling time when using the formulas by White et al., whereas in the slow growing cell line, the estimates of Ts did not show any significant dependence on sampling time when using the formula by Johansson et al. In the tumours, the estimation of Ts depended on sampling time with all formulas used, although to different degrees. In one of the tumours, this was mainly caused by the influence of mouse cells, as we demonstrate. Our results indicate that the proliferative characteristics of a cell population should be taken into consideration when choosing a mathematical formula in order to attain Ts values that are independent of sampling time.

Adenocarcinoma↗

PubMed1981

An approach to mathematical literacy for medical students.

Mathematical literacy is defined as the ability to read and interpret information of a mathematical nature. Based on the empirically determined needs of medical students in this area, a set of instructional materials (tests, text, and technical manual) were produced and successfully used. These results are described here as are considerations bearing on the generalizability of the described approach.

Educational Status↗

PubMed1989

Student/teacher relations and attitudes toward mathematics before and after the transition to junior high school.

In a longitudinal study of 1,301 students and the teachers they had for mathematics before and after the transition to junior high school, we assessed whether changes across the transition in students' perceptions of their teachers' supportiveness were related to changes in their valuing of mathematics. Using repeated-measures multivariate analysis of variance, we found that when students moved from elementary teachers they perceived to be low in support to junior high teachers they perceived to be high in support, the intrinsic value of math was enhanced, while students who moved from teachers they perceived to be high in support to teachers they perceived to be low in support experienced a sharp decline in both the intrinsic value and perceived usefulness and importance of math. For students' perceptions of the usefulness and importance of math there was an interaction with achievement level. Math values decreased more sharply during the first year of junior high for low-achieving students who moved from more supportive to less supportive teachers than for high-achieving students who experienced the same change.

Achievement↗

PubMed1984

Mathematical expression of relationship between auditory brainstem transmission time and age.

Brainstem transmission time (BTT) was studied in 71 subjects ranging in age from one day to 29 years in order to find a mathematical expression to best describe the relationship between BTT and age. The mathematical function which relates BTT to age is exponential. Using this data, the BTT confidence limit was calculated for subjects from birth through to eight years. Repeated recordings of auditory brainstem responses were performed in several children as they grew older and these verified the normal maturational processes of the brainstem structures in the developing infant and young child.

Age Factors↗