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At least 1,711 records · Page 95Linked to original sources

Recommendations for hyperbaric oxygen therapy of cerebral air embolism based on a mathematical model of bubble absorption.

Transcranial doppler studies show that microscopic cerebral artery air emboli (CAAE) are present in virtually all patients undergoing cardiac surgery. Massive cerebral arterial air embolism is rare. If it occurs, hyperbaric oxygen therapy (HBO) is recommended as soon as surgery is completed. We used a mathematical model to predict the absorption time of CAAE, assuming that the volumes of clinically relevant CAAE vary from 10(-7) to at least 10(-1) mL. Absorption times are predicted to be at least 40 h during oxygenation using breathing gas mixtures of fraction of inspired oxygen approximately equal to 40%. When CAAE are large enough to be detected by computerized tomography, absorption times are calculated to be at least 15 h. Decreases in cerebral blood flow caused by the CAAE would make the absorption even slower. Our analysis suggests that if the diagnosis of massive CAAE is suspected, computerized tomography should be performed, and consideration should be given to HBO therapy if the CAAE are large enough to be visualized, even if patient transfer to a HBO facility will require several hours.

Absorption↗

Mathematical modeling and the redesign of a teaching ambulatory clinic.

Mathematical modeling was utilized in the planning and decision-making process involved in reorganizing a teaching clinic to effect continuity of care. The model interrelated physicians, time and space, facilitating value judgments and decisions. After examining multiple model runs, the authors finally selected a per-clinic-session doctor mix of 5 interns, 2.3 residents, and 1.6 fellows. Group productivity by model simulation was 14.6 pts/hour, utilizing 10.1 rooms. Subsequently, 90 house officers were each assigned to the clinic one-half day a week on a continuing basis. Time-motion data, from 10 sessions five months after the change, showed that during one week 353 patients were seen at a rate of 13.9 patients per hour in the rooms and time available. The fact that the reorganization was successful and the outcomes remarkably similar to model predictions has engendered confidence in the role of modeling in the planning process.

Ambulatory Care↗

The true canalicular angle: a mathematical model.

A mathematical formula that allows for the computation of the true angle between the upper and lower canaliculi using dacryocystograms is described. It was used to determine the true canalicular angle in 33 patients. The mean calculated angle at the 1.0 mm distance was 57.2 degrees +/- 13.0 degrees, and at the 0.5 mm distance was 65.2 degrees +/- 16.2 degrees. The true calculated angle was highly correlated with the angle measured in the Waters view. There was no statistically significant correlation between the right and left sides in the same patient. There was no statistically significant difference between the canalicular angle in males and females, and there was no correlation between canalicular angle and patient's age. A clinical application of this model is discussed.

Adult↗

Mathematical models of cell survival after ionizing radiation: application to radiotherapy planning.

The work described here represents an attempt to use mathematical models of single-cell survival for radiotherapy planning. The aim of the study is to develop a procedure in which the distribution of the effects achieved by optimizing physical radiation dose is implemented by taking into account radiobiological terms. An algorithmic model has been developed to evaluate the probability of tumor control and of excessive damage to normal tissue on the basis of the linear-quadratic model of cell survival. In its present preliminary form, the procedure can be used to predict differential isoeffect distributions obtained by varying the total dose and the fraction size of multifraction radiotherapy courses. This approach can also be used to extract from historical clinical results, by maximum-likelihood methods, parameters related to the cellular response to radiation (for instance, alpha and beta of the linear-quadratic model).

Cell Survival↗

An experimental and mathematical analysis of lymphopoiesis dynamics under continuous irradiation.

A mathematical model describing the dynamics of lymphopoiesis in mammals continuously exposed to ionizing radiation has been developed. It is based on the theory of chalone regulation of hematopoiesis. The model comprises a system of nine differential equations. Results from the model were compared with our experimental data for bone marrow and blood lymphocytes of rats continuously exposed to gamma radiation in a wide range of dose rates. The model reproduces the lymphopoiesis dynamics that we observed in our experiment, in particular, the radiation hormesis at low dose rates, the reduction of lymphopoiesis at intermediate dose rates, and extinction of lymphopoiesis at high dose rates of continuous radiation. The possible explanation of the hormesis is suggested by the framework of the model. The model can be used for predicting the lymphopoiesis dynamics in mammals under continuous irradiation.

Animals↗

Modeling the distribution and dosimetry of internal emitters: a review of mathematical procedures using matrix methods.

This paper reviews the mathematical procedures for an analytical representation of linear compartmental systems and the radiation dosimetry of internal organs in terms of matrices and vectors. The features characteristic for internal dosimetry, such as the various forms of intakes, subsystems (e.g., lung, gastro-intestinal tract), and decay products are also discussed. The ICRP concept of internal dose calculation is translated into matrix notation and its application demonstrated by calculating the radiation doses from the ingestion of 40K.

Humans↗

Mathematical analysis of arterial enhancement and optimization of bolus geometry for CT angiography using the discrete fourier transform.

PURPOSE: The goal of this work was to develop a clinically applicable mathematical algorithm to analyze and optimize individual arterial enhancement in CT angiography (CTA). METHOD: Assuming a time-invariant linear system, the discrete Fourier transform was used to calculate the transfer function of the system ("patient function") from the arterial time-attenuation response to a test bolus. The patient function was subsequently used to predict aortic enhancement in five select patients and to calculate optimized biphasic injection protocols in two of these patients undergoing CTA of the abdominal aorta. RESULTS: Arterial time-attenuation curves were accurately predicted in all patients. Optimized biphasic contrast agent injection protocols resulted in uniform aortic enhancement at the predefined level over the entire scanning period in both subjects despite markedly different contrast agent volumes and injection rates used. CONCLUSION: Fourier analysis of the time-attenuation response to a test bolus is a simple and feasible approach to optimize arterial enhancement in CTA.

Angiography↗

Mathematically directed single-cut osteotomy for correction of tibial malunion.

In 1986 and 1987, four patients with tibial malunion involving both angular and torsional misalignment underwent surgical correction by a single-cut technique based on a mathematical model of long bone deformity. The technique involved a single surgical cut, followed by rotation of the two fragments along the osteotomy plane. The orientation of the osteotomy is based on a computer-assisted design. The deformity is measured on radiographs, computed tomography, and clinical exam and is then plotted on graphs to find the osteotomy orientation. The deformity involved varus and extension in four cases, internal rotation in 2, and external rotation in two. The deformities ranged from 9 to 26 degrees. The cutting angle of the osteotomy ranged from 50 to 66 degrees as measured from the transverse plane. Actual lengthening of 1 cm and functional lengthening over 1.5 cm was obtained without the use of bone graft. As no wedge of bone was removed, all corrected bones were easily suited to rigid internal fixation across the cut surface. In all cases, the desired correction was obtained within measurable error, and union was obtained with minimal immobilization. There were no soft tissue or joint contractures, and no neurovascular complications. In one patient, who had had four prior surgical procedures on the involved limb, an infection developed 6 weeks postoperatively that required debridement and delayed primary closure. As the technique involves only one cut, no wedge of bone is removed, no shortening occurs, and the osteotomy is highly suitable for rigid internal fixation. The described technique is the first to integrate in a precise way the correction of torsion with the correction of angular deformity.(ABSTRACT TRUNCATED AT 250 WORDS)

Biomechanical Phenomena↗

Mathematical model for predicting dioptric effects of optical parameter changes in the eye.

Changes in refractive status induced by contact lenses have been attributed to changes in various intraocular comonents. Limitation of previous mathematical attempts to quantify the effects of changes in these components are discussed. A series of simple ray-tracing equations is developed which avoids these limitations and provides a practical means of relating calculations to clinical measurements.

Anterior Chamber↗

AIDS vaccines that allow HIV-1 to infect and escape immunologic control: a mathematic analysis of mass vaccination.

Cytotoxic T lymphocyte (CTL)-based HIV vaccine concepts shown to reduce viremia and postpone disease but not to prevent infection in monkeys are currently in human phase 1 trials. To evaluate the potential efficacy of vaccines that cannot prevent HIV-1 to infect and escape immunologic control, we designed a mathematic model that correlates the level of viremia to both infectiousness and disease progression. We speculate that vaccinees will have a virologic set point and disease progression rates comparable to untreated HIV-1-infected individuals with the best prognosis. Our model (illustrated with R0 = 3) shows that a sexually active population can ultimately be reduced to 26% of its initial size as a result of AIDS-related mortality in the absence of treatment or vaccination. Start of vaccination when HIV-1 prevalence is still low might postpone the peak incidence of infection and the dramatic decline in population size by up to 22 years. In conclusion, CTL-based vaccines that do not prevent HIV-1 infection but do postpone the time to onset of AIDS have considerable potential to curb the spread of HIV-1 and to postpone high AIDS-related mortality on a population level. The number of long-term survivors is substantially increased only when vaccination is initiated early in an AIDS epidemic, however.

AIDS Vaccines↗

What is the best method for assessing the rate of wound healing? A comparison of 3 mathematical formulas.

OBJECTIVE: To identify and evaluate current mathematical formulas used to assess the rate of wound healing. DATA SOURCES: MEDLINE, CINAHL, and Cochrane Systematic Review databases, from 1965 to 2004. STUDY SELECTION: Papers selected for the study met the following inclusion criteria: (1) participants had chronic venous, neuropathic, pressure, or ischemic wounds; (2) the wounds were objectively measured; and (3) the investigators described and used an objective measurement of wound healing rate, either as an absolute reduction in area over time, a percentage change, or a linear advancement of wound edge. Papers were excluded if they were (1) not written in English, (2) duplicated from other sources, or (3) unpublished. CONCLUSIONS: In clinical trials, measurement of the rate of wound healing over time by using the equation for the linear advancement of wound margins toward the center of the wound controls for confounding introduced by differing baseline ulcer sizes and shapes. Use of this assessment method after 4 weeks of healing may prove to be of value in predicting time to complete healing. Further research is required to develop standard healing rates for wounds of different etiologies.

Anthropometry↗

Addressing current challenges in cancer immunotherapy with mathematical and computational modelling.

The goal of cancer immunotherapy is to boost a patient's immune response to a tumour. Yet, the design of an effective immunotherapy is complicated by various factors, including a potentially immunosuppressive tumour microenvironment, immune-modulating effects of conventional treatments and therapy-related toxicities. These complexities can be incorporated into mathematical and computational models of cancer immunotherapy that can then be used to aid in rational therapy design. In this review, we survey modelling approaches under the umbrella of the major challenges facing immunotherapy development, which encompass tumour classification, optimal treatment scheduling and combination therapy design. Although overlapping, each challenge has presented unique opportunities for modellers to make contributions using analytical and numerical analysis of model outcomes, as well as optimization algorithms. We discuss several examples of models that have grown in complexity as more biological information has become available, showcasing how model development is a dynamic process interlinked with the rapid advances in tumour-immune biology. We conclude the review with recommendations for modellers both with respect to methodology and biological direction that might help keep modellers at the forefront of cancer immunotherapy development.

Computer Simulation↗

A mathematical model for collagen fibre formation during foetal and adult dermal wound healing.

Adult dermal wounds, in contrast to foetal wounds, heal with the formation of scar tissue. A crucial factor in determining the nature of the healed tissue is the ratio of collagen 1 to collagen 3, which regulates the diameter of collagen fibres. We develop a mathematical model which focuses on the stimulus for collagen synthesis due to the secretion of the different isoforms of the regulatory chemical transforming growth factor beta. Numerical simulations of the model lead to a value of this ratio consistent with that of healthy tissue for the foetus but corresponding to scarring in adult wound healing. We investigate the effect of topical application of TGF beta isoforms during healing and determine the key parameters which control the difference between adult and foetal repair.

Animals↗

League tables and school effectiveness: a mathematical model.

'School performance tables', an alphabetical list of secondary schools along with aggregates of their pupils' performances in national tests, have been published in the UK since 1992. Inevitably, the media have responded by publishing ranked 'league tables'. Despite concern over the potentially divisive effect of such tables, the current government has continued to publish this information in the same form. The effect of this information on standards and on the social make-up of the community has been keenly debated. Since there is no control group available that would allow us to investigate this issue directly, we present here a simple mathematical model. Our results indicate that, while random fluctuations from year to year can cause large distortions in the league-table positions, some schools still establish themselves as 'desirable'. To our surprise, we found that 'value-added' tables were no more accurate than tables based on raw exam scores, while a different method of drawing up the tables, in which exam results are averaged over a period of time, appears to give a much more reliable measure of school performance.

Adolescent↗

Mathematical models in physiology.

Computational modelling of biological processes and systems has witnessed a remarkable development in recent years. The search-term (modelling OR modeling) yields over 58000 entries in PubMed, with more than 34000 since the year 2000: thus, almost two-thirds of papers appeared in the last 5-6 years, compared to only about one-third in the preceding 5-6 decades. The development is fuelled both by the continuously improving tools and techniques available for bio-mathematical modelling and by the increasing demand in quantitative assessment of element inter-relations in complex biological systems. This has given rise to a worldwide public domain effort to build a computational framework that provides a comprehensive theoretical representation of integrated biological function-the Physiome. The current and next issues of this journal are devoted to a small sub-set of this initiative and address biocomputation and modelling in physiology, illustrating the breadth and depth of experimental data-based model development in biological research from sub-cellular events to whole organ simulations.

Computer Simulation↗

Some physical, mathematical and evolutionary aspects of biological pattern formation.

An important mechanism in the generation of biological structures is the production of defined spatial patterns within initially near-uniform cells and tissues. This process can be modelled on the basis of conventional molecular kinetics if there is a short-range activating effect in conjunction with depletion or inhibition extending over a wider range ('lateral inhibition'). Such pattern-generating systems exhibit simple self-regulatory properties empirically observed in developmental biology such as polarity effects, proportion regulation and the inducibility of secondary centres. Autocatalysis and lateral inhibition have been shown to be mathematically necessary for the simplest two-factor case. Certain generalizations of these conditions to multi-component systems are possible; they are suitable for modelling intercalary regeneration. The evolution of higher organisms seems to be determined to a considerable extent by many small changes of patterns and proportions. While evolution proceeds at varying rates in the course of time, the rate-limiting steps may be due to mutations of low selection pressure. A semi-quantitative argument suggests that there might be an upper limit of evolutionarily effective genetic complexity.

Animals↗

A mathematical method for analysing plasmid stability in micro-organisms.

A mathematical model describing the instability of plasmids in micro-organisms has been developed. The model is based on the assumption that the overall causes of plasmid instability are described by the segregational instability of the plasmid, R (i.e. the rate at which plasmid-free cells are generated from plasmid-bearing cells), and the growth rate difference, d mu (i.e. the difference in growth rate between plasmid-free and plasmid-bearing cells). A method for determining the values of R and d mu (accompanied by 95% confidence limits) for any plasmid-bearing micro-organism is described. This method is based on the observation that, depending on the plasmid, various exponential patterns of plasmid instability are observed. The stability of Escherichia coli 1B373(pMG169), where d mu much greater than R, and E. coli RV308(pHSG415), where R much greater than d mu, are analysed in order to demonstrate the method.

Escherichia coli↗

Mathematical analysis of catabolic function loss in a population of Pseudomonas putida mt-2 during non-limited growth on benzoate.

Pseudomonas putida mt-2, harbouring the TOL plasmid PWW0, was grown continuously on benzoate in a phauxostat at a non-limited rate. The gradual decrease in the population carrying the complete TOL plasmid was caused predominantly by a growth-rate advantage of spontaneous mutants carrying a partially deleted plasmid (TOL- cells). The growth-rate difference (v) was quantified both by measuring the increase in the dilution rate (from 0.68 to 0.79 h-1; v = 0.11 h-1) and by mathematical analysis of the ingrowth of TOL- cells (v = 0.12 h-1). The latter procedure also established that the segregation rate was of the order of magnitude 10(-5) h-1. Similar values for the growth-rate advantage and the segregation rate were found when both benzoate and succinate were present in non-limiting concentrations. It is suggested that the growth-rate disadvantage of the wild-type strain is caused by inhibitory effects of an intermediate in the degradation of benzoate via the plasmid-encoded meta-pathway.

Benzoates↗