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PubMedDate not supplied

[Development of a mathematical model for simulation of artificial ventilation].

This article describes a mathematical model for the simulation of artificial ventilation employing only the figures for air pressure and air flow between respirator and lungs. A discussion of methodological aspects of the problem shows that the model of the respiratory system can be reduced to an equivalent circuit diagram comprising only resistances and capacitances. The structure of the mathematical model is oriented to the elements of the real respiratory system, and its modularity permits ready adaptation to a variety of real-life situations. Particular emphasis was placed on the correct parametrization of the model with the aid of data originally collected from physical experiments. Finally, some selected model runs that demonstrate the range of validity and the accuracy of the model are presented.

Airway Resistance↗
PubMed2006

Mathematical description of gene regulatory units.

Revealing the control mechanisms responsible for the cell's surprisingly well-organized functions should lead directly to a better understanding of how the cell adapts to extraordinarily changing environments. A general framework for describing models that can represent diverse biochemical regulatory functions systematically would help not only systematic interpretation of the various models proposed for certain systems but also further understanding of the general control mechanism and design principles underlying different biological systems. This article presents a unified mathematical framework for describing gene regulatory units. The proposed framework is fairly compatible with the classical control theoretical framework, so it should serve as a connecting bridge between engineering control theory and biological control mechanisms. It should also provide a unified view of different regulatory units and facilitate systematic comparison of different mathematical models proposed in a variety of literature.

Animals↗
PubMed2006

A mathematical model of glioblastoma tumor spheroid invasion in a three-dimensional in vitro experiment.

Glioblastoma, the most malignant form of brain cancer, is responsible for 23% of primary brain tumors and has extremely poor outcome. Confounding the clinical management of glioblastomas is the extreme local invasiveness of these cancer cells. The mechanisms that govern invasion are poorly understood. To gain insight into glioblastoma invasion, we conducted experiments on the patterns of growth and dispersion of U87 glioblastoma tumor spheroids in a three-dimensional collagen gel. We studied two different cell lines, one with a mutation to the EGFR (U87DeltaEGFR) that is associated with increased malignancy, and one with an endogenous (wild-type) receptor (U87WT). We developed a continuum mathematical model of the dispersion behaviors with the aim of identifying and characterizing discrete cellular mechanisms underlying invasive cell motility. The mathematical model quantitatively reproduces the experimental data, and indicates that the U87WT invasive cells have a stronger directional motility bias away from the spheroid center as well as a faster rate of cell shedding compared to the U87DeltaEGFR cells. The model suggests that differences in tumor cell dispersion may be due to differences in the chemical factors produced by cells, differences in how the two cell lines remodel the gel, or different cell-cell adhesion characteristics.

Brain Neoplasms↗
PubMed2004

Combining mathematical models and statistical methods to understand and predict the dynamics of antibiotic-sensitive mutants in a population of resistant bacteria during experimental evolution.

Temporarily discontinuing the use of antibiotics has been proposed as a means to eliminate resistant bacteria by allowing sensitive clones to sweep through the population. In this study, we monitored a tetracycline-sensitive subpopulation that emerged during experimental evolution of E. coli K12 MG1655 carrying the multiresistance plasmid pB10 in the absence of antibiotics. The fraction of tetracycline-sensitive mutants increased slowly over 500 generations from 0.1 to 7%, and loss of resistance could be attributed to a recombination event that caused deletion of the tet operon. To help understand the population dynamics of these mutants, three mathematical models were developed that took into consideration recurrent mutations, increased host fitness (selection), or a combination of both mechanisms (full model). The data were best explained by the full model, which estimated a high mutation frequency (lambda = 3.11 x 10(-5)) and a significant but small selection coefficient (sigma = 0.007). This study emphasized the combined use of experimental data, mathematical models, and statistical methods to better understand and predict the dynamics of evolving bacterial populations, more specifically the possible consequences of discontinuing the use of antibiotics.

Anti-Bacterial Agents↗
PubMed2006

Mathematical modeling of cancer progression and response to chemotherapy.

The complex, constantly evolving and multifaceted nature of cancer has made it difficult to identify unique molecular and pathophysiological signatures for each disease variant, consequently hindering development of effective therapies. Mathematical modeling and computer simulation are tools that can provide a robust framework to better understand cancer progression and response to chemotherapy. Successful therapeutic agents must overcome biological barriers occurring at multiple space and time scales and still reach targets at sufficient concentrations. A multiscale computer simulator founded on the integration of experimental data and mathematical models can provide valuable insights into these processes and establish a technology platform for analyzing the effectiveness of chemotherapeutic drugs, with the potential to cost-effectively and efficiently screen drug candidates during the drug-development process.

Antineoplastic Agents↗
PubMed2001

A mathematical model for malaria transmission relating global warming and local socioeconomic conditions.

OBJECTIVE: Sensitivity analysis was applied to a mathematical model describing malaria transmission relating global warming and local socioeconomic conditions. METHODS: A previous compartment model was proposed to describe the overall transmission of malaria. This model was built up on several parameters and the prevalence of malaria in a community was characterized by the values assigned to them. To assess the control efforts, the model parameters can vary on broad intervals. RESULTS: By performing the sensitivity analysis on equilibrium points, which represent the level of malaria infection in a community, the different possible scenarios are obtained when the parameters are changed. CONCLUSIONS: Depending on malaria risk, the efforts to control its transmission can be guided by a subset of parameters used in the mathematical model.

Animals↗
PubMed1998

Quantitative description of the morphology of the human palate by a mathematical equation.

OBJECTIVE: To derive a three-dimensional mathematical description of normal human hard tissue palatal size and shape. METHODS: The maxillary dental casts of 30 adolescents free from respiratory problems, who had a complete (28 teeth) permanent sound dentition with normal occlusion, were studied. The x, y, z coordinates of several standardized palatal and dental landmarks were obtained with a computerized three-dimensional digitizer. Palatal landmarks were used to derive a mathematical equation of palatal shape in the frontal and sagittal planes. Palatal width, length, frontal and sagittal heights, and sagittal slope, as well as dental arch transverse and anteroposterior dimensions, were computed. RESULTS: Neither the size nor the shape of the palate was significantly influenced by gender. Only the intercanine distance was larger (p < .025) in males than in females. CONCLUSIONS: Data collected in the present investigation could represent a first database for the quantitative description of normal human palatal morphology in subjects with a complete permanent dentition.

Adolescent↗
PubMed2005

Mathematical models of oxygen and carbon dioxide storage and transport: the acid-base chemistry of blood.

This article describes a mathematical model of the acid-base chemistry of blood. The model is formulated from first principles by considering the "components" of blood and the reaction equations in the plasma and erythrocyte fractions. Equations are formulated to describe the total concentration of blood components, the physicochemical properties, and the equilibrium position of reactions. The model includes 28 equations and 12 parameters. All equations can be solved from six variables included in the model. The model uses simple mathematics, without introducing intermediate concepts or linear coefficients necessary for algebraic solution. Model equations are solved simultaneously using numerical methods. Model parameters are estimated and the model verified for plasma, fully oxygenated blood, and deoxygenated blood. Published data are used to estimate model parameters and normal conditions and to verify model simulations. The model reproduces experimental results, including addition or removal of CO2, or strong acid to plasma; CO2, strong acid or haemoglobin to blood; and the effects of deoxygenating blood. The model can also be used as the basis for models of whole body CO2 transport as illustrated in the accompanying article. As such, it is possible to simulate the effects on blood of physiological changes in ventilation or metabolism.

Acid-Base Equilibrium↗
PubMed2002

Mathematical methods for quantification and comparison of dissolution testing data.

In recent years, drug release/dissolution from solid dosage forms has been the subject of intense and profitable scientific developments. Whenever a new solid dosage form is developed or produced, it is necessary to ensure that drug dissolution occurs in an appropriate manner. The pharmaceutical industry and the registration authorities do focus, nowadays, on drug dissolution studies. The quantitative analysis of the values obtained in dissolution/release tests is easier when mathematical formulas that express the dissolution results as a function of some of the dosage forms characteristics are used. This work discusses the analysis of data obtained for dissolution profiles under different media pH conditions using mathematical methods of analysis described by Moore and Flanner. These authors have described difference factor (f1) and similarity factor (f2), which can be used to characterise drug dissolution/release profiles. In this work we have used these formulas for evaluation of dissolution profiles of the conventional tablets in different pH of dissolution medium (range of physiological variations).

Journal Article↗
PubMed1995

Dynamics of beta-cell mass in the growing rat pancreas. Estimation with a simple mathematical model.

The growth and development of the endocrine pancreas has been studied for many years, but questions remain concerning the regulation of the mass of insulin-producing beta-cells both in the normal growing pancreas and during the pathogenesis of diabetes. The homeostatic control of beta-cell mass in both normal and pathophysiological conditions is based on the balance of cell proliferation, cell growth, and cell death. To gain insight into the relative contribution of each of these dynamic processes, we first mathematically analyzed the data available on the components involved in the maintenance of beta-cell mass, including rates of replication, beta-cell volume, and the beta-cell mass itself, at various ages in normal Sprague-Dawley rats. Then these data were combined in a simple mass balance equation to construct a mathematical model of the dynamics of the beta-cell mass in the normal growing rat pancreas. Such a model has allowed us to infer the contributions of fluxes that cannot be measured, i.e., neogenesis and cell death, to the known mass of beta-cells. Another important contribution of this model is to raise unanswered questions concerning the control of the balance of cell death and cell renewal in the endocrine pancreas.

Aging↗
PubMed1998

Evaluation of selected mathematical approaches to the kinetics of protein degradation in situ.

A linear model, two mathematical nonlinear models, and a curve-peeling procedure were used to estimate rate and extent of ruminal CP degradation of meat and bone meal (MBM) and soybean meal (SBM) from data obtained using the in situ Dacron polyester bag technique. Most of the values for extent of CP degradation of MBM were lowest when determined using curve peeling or the nonlinear models. In general, rates and extents of CP degradation of MBM estimated using the linear model and including ruminal incubations up to 12 h were greater than those obtained with the linear model and including ruminal incubations up to 24 h or up to 72 h. In addition, the models ranked the MBM samples differently for rate and extent of CP degradation. The results of the lack-of-fit test indicated that the linear model was inappropriate for estimating rate of degradation of MBM. However, CP degradation for SBM could be described by the linear model if long ruminal incubation times (greater than 48 h) were included in the calculations. Regression analyses were conducted to evaluate various compositional characteristics as predictors of CP degradation for MBM. Most of the correlation coefficients between CP degradation and the same independent variables were greater when the nonlinear models and curve peeling were used compared with the linear model. In general, the correlation coefficients between extent of CP degradation and the independent variables obtained with the linear model increased as the duration of ruminal incubations included in the model increased. Lysine concentrations, followed by CP solubility and ash content, were the best predictors of ruminal degradation of MBM protein. When using a specific mathematical model to predict CP degradation, analysis of residuals vs fitted and lack-of-fit tests should be performed to assess the validity of the model to describe the degradation patterns of the protein source under consideration. Also, long (at least 48 h) ruminal incubation times may be needed to correctly describe the pattern of CP degradation for MBM.

Animal Feed↗
PubMedDate not supplied

Auditory brainstem response (ABR) latency: relative importance of age, sex and sensorineural hearing-loss using a mathematical model of the audiogram.

Influences of age, sex and audiogram on ABR latencies have been studied. Using a mathematical model of audiogram, the analysis of data finds a relative importance of age, sex and audiogram similar to previous studies. Audiogram slope was correlated only with the latencies of waves I and V, and multiple regression analyses indicate the slope effect is relatively weak compared to that of the other parameters. Using a mathematical model of audiogram did not improve the ABR variance across subjects, underscoring the need to discover other relevant variables to explain ABR latency.

Acoustic Stimulation↗
PubMed1999

A mathematical model of in situ freezing in liquid nitrogen.

In situ freezing is a procedure, typically applied in neuroscience, to halt metabolism and diffusion. However, the freezing process is not instantaneous, and the regional concentrations of a compound under study may change before the tissue is completely frozen. Knowing the local freezing time, metabolic rate and the diffusion coefficient of the compound of interest, it should be possible to reconstruct the spatial concentration profile prevailing before the object was placed in the cryogen. A mathematical model for calculating the temperature changes at different depths in rabbit and rat heads cooled in liquid nitrogen has been developed. By comparing with experimental results it has been found that the mathematical model can be used for prediction of the local freezing time with a small error.

Animals↗
PubMed1991

An application of mathematical models for decision making to the selection of policies on testing for drug use.

The object of the paper is to provide the basis to decide whether testing for drug use should be used, taking into consideration individual and social benefits and costs that the results of the tests could originate. In the analysis, special attention is paid to the fact that the actual costs of the tests themselves are not the most important elements of the social costs of a testing program. The most important costs are those generated by the defective results of the tests. They can provide false positive results, meaning that a nonuser is identified as a user, or false negative results in which a user is not identified as such. Social costs of the false positive results range from lowered worker morale to legal suits, while the false negative results eliminate any benefit that the identification of drug users could have. Combining all these elements, Correa and Woods specify a mathematical procedure as a decision tool to be used for determining whether a testing program should be implemented in specific industries or groups of industries. A complete implementation of the model is not carried out due to the lack of the required statistical information. However, preliminary trials showed that the conceptual and mathematical framework is operational, and that the model prepared could be used as a guideline for collecting the most appropriate data for decision making.

Adult↗
PubMed2000

Mathematical theory of stereotactic coordinate transformation: elimination of rotational targeting error by addition of a third reference point. Technical note.

All frame-based stereotactic procedures require localization of an anatomical target within the coordinate system of the stereotactic frame. If the target is defined by its coordinates given in a stereotactic atlas (indirect localization), the neurosurgeon faces the mathematical task of transforming atlas coordinates into frame coordinates. In the method usually used, the frame coordinates of two reference points (the anterior and posterior commissures) are obtained from computerized tomography or magnetic resonance images, and serve as the basis for the coordinate transformation. This two-point algorithm relies on the additional assumption that the frame sits on the patient's head without exhibiting roll, that is, rotation about the anteroposterior axis (y axis). Usually this assumption is nearly, but not exactly, correct. An amount of roll as small as 3 degrees can cause a targeting error on the order of 1 mm when a two-point algorithm is used. This potential source of error can be eliminated by using a new method of coordinate transformation, the derivation of which is mathematically reported in this article. The new method requires a third reference point located in the midsagittal plane, in addition to the two commissural reference points.

Algorithms↗
PubMed1979

[A Mathematical Approach To The Mode Of Transmission Of Clonorchiasis In The Inhabitants Of Nak-Dong And Han River Basin]

To understand the mode of transmission in clonorchiasis, a survey was made in Kim-hae Goon, South Kyong-sang Do (=Province). The mathematical analysis of the age prevalence was done on the egg positive rates. And another analysis for the comparison was also made to the cited data from two areas, North Kyong-sang Do and Ko-yang Goon, Kyong-gi Do. Some catalytic models of H. Muench (1959) were applied to the observed age prevalence. Because the both parameters, such as force of infection(a) and loss of positivity(b) were considered to be constant for a long period in the surveyed area, the two stage catalytic model by Muench was chosen to the analysis. In the surveyed area, Kim-hae Goon where the egg positive rates were 56.2% and 61.2% (by Kim, 1974), the constant values of 'a' were found to be 0.051 and 0.089 respectively. In other words, the force of infection was 51, 89 per 1,000 susceptibles. The values of 'b' were found to be 0.006 and 0.005. This means that the rates of disappearance from egg positive cases to negative were 6 and 5 per annum per l,000 positive cases in above area. Therefore, the two catalytic curves were expressed by the following equations, y = 1.133 {e(-0.006t) - e(-0.051t)} and y = 1.047 {e(-0.005t) - e(-0.089t)} respectively. In the cases of North Kyong-sang Do and Ko-yang Goon, Kyong-gi Do where the egg positive rates of clonorchis shown as 27.7% and 15.2% by Shin (1964) and Kim (l974), the curves were expressed by y = 1.769 {e(-0.010t) - e(-0.034t)} and y = 2.857 {e(-0.020t) - e(-0.027t)} respectively. From the above mathematical analyses by age prevalence in clonorchiasis, it was considered that the mode of transmission of clonorchiasis in the surveyed area, Kim-hae Goon presented more rapid pattern than those of North Kyong-sang Do and Ko-yang Goon, Kyong-gi Do.

Journal Article↗
PubMed1996

Mathematical curves for the description of input and output variables of the daily production process in aviary housing systems for laying hens.

The objectives of this study were 1) to compute appropriate mathematical curves that describe the daily production process by the input variables daily feed consumption, water consumption, ambient temperature, and output variables hen-day egg production, egg weight, second grade eggs, floor eggs, cumulative mortality, body weight, and flock uniformity; and 2) to obtain insights into the daily variations in these variables, in order to support the poultry farmer with an aviary housing system in his daily management. Literature and research data attained from six unmolted flocks that were housed in aviary systems were used to formulate the mathematical curves. The curves were a function of the number of days in the laying period. Curves for cumulative mortality, hen-day egg production, egg weight, body weight, and percentage of floor eggs described individual flock results well (0.72 < R2adj < 1.00). The coefficients of determination for feed consumption, water consumption, flock uniformity, and percentage of second grade eggs were in general low (0.33 < R2adj < 0.54), which implies that the form of the curve differs between flocks. Egg weight, body weight, cumulative mortality, and hen-day egg production had the lowest minimum coefficients of variation (0.8 to 1.9), followed by feed consumption, water consumption, and flock uniformity (2.8 to 3.6). Ambient temperature, percentage floor eggs, and percentage of second grade eggs had the highest minimum coefficients of variation (4.8 to 9.1).

Animals↗
PubMed1989

Towards the development of a mathematical model for acupuncture meridians.

Traditional concepts of classical acupuncture and Chinese medicine come from a culture which is very different from ours, and there has been considerable problems in their accurate presentation. Our approach is to attempt the development of a mathematical language that links these traditional concepts theoretically to models that can be experimentally tested. We first review some of Manaka's findings, confirmed also by our results, having to do with low intensity stimuli. In particular, Manaka applied polarized agents such as Cu(+) and Zn(-) to nonacupuncture points on a meridian and to the so called "mother and child" points on a meridian. In both cases he observed the pressure pain reaction which increased for one orientation of Cu and Zn on the meridian and decreased for the opposite orientation. Note that in the case of "mother and child" points the observed reaction was in agreement with the so called "five phase (five element)" theory. Also, in the case of the "mother and child" points the effect usually lasted considerably longer than in the case of nonacupuncture points on a meridian. Taking into account the connection between Manaka's results and skin electrical measurements by some electrodermal diagnostic instruments such as Motoyama's AMI, we discuss some equivalent electric circuits for a single meridian and relate them to the nervous system response. In particular, an electrical circuit model similar to the synapse membrane with two ionic channels seems to be especially useful when we try to explain Manaka's clinical results and Motoyama's results on the velocity of propagation of electrical impulses along meridians. We also develop a mathematical model in the form of a linear five dimensional dynamical system of the so called "five phase (five element)" laws such as "creative" cycle, "controlling" cycle, etc., in the case of a single meridian. We connect this model with the membrane type model mentioned above by assuming a simple mass action law, for the dependence of the conductances in the ionic channels on the input signals. This combined model is used to describe the development of a "disease" and its treatment according to the "five phase" theory. Here we interpret the "disease" as a blockage in a meridian, while the treatment initiates the unblocking process.

Acupuncture Therapy↗