Mohammad A. Tabatabai

Hyperbolastic modeling of wound healing

A new mathematical model for wound healing is introduced and applied to three sets of experimental data. The model is easy to implement but can accommodate a wide range of factors affecting the wound healing process. The data sets represent the areas of trace elements, diabetic wounds, growth factors, and nutrition within the field of wound healing. The model produces an explicit function accurately representing the time course of healing wounds from a given data set. Such a function is used to study variations in the healing velocity among different types of wounds and at different stages in the healing process. A new multivariable model of wound healing capable of analyzing the effects of several variables on accelerating the wound healing process is also introduced. Such a model can help to formulate appropriate strategies to treat wounds. It also would enable us to evaluate the efficacy of different treatment modalities during the inflammatory, proliferative, and tissue remodeling phases.

Mathematical Modeling Of Stem Cell Proliferation

The mathematical models prevalently used to represent stem cell proliferation do not have the level of accuracy that might be desired. The hyperbolastic growth models promise a greater degree of precision in representing data of stem cell proliferation. The hyperbolastic growth model H3 is applied to experimental data in both embryonic stem cells and adult mesenchymal stem cells. In the embryonic stem cells the results are compared with other popular models, including the Deasy model, which is used prevalently for stem cell growth. In the case of modelling adult mesenchymal stem cells, H3 is also successfully applied to describe the proliferative index. We demonstrated that H3 can accurately represent the dynamics of stem cell proliferation for both embryonic and adult mesenchymal stem cells. We also recognize the importance of additional factors, such as cytokines, in determining the rate of growth. We propose the question of how to extend H3 to a multivariable model that can include the influence of growth factors.

Hypertabastic survival model

A new two-parameter probability distribution called hypertabastic is introduced to model the survival or time-to-event data. A simulation study was carried out to evaluate the performance of the hypertabastic distribution in comparison with popular distributions. We then demonstrate the application of the hypertabastic survival model by applying it to data from two motivating studies. The first one demonstrates the proportional hazards version of the model by applying it to a data set from multiple myeloma study. The second one demonstrates an accelerated failure time version of the model by applying it to data from a randomized study of glioma patients who underwent radiotherapy treatment with and without radiosensitizer misonidazole. Based on the results from the simulation study and two applications, the proposed model shows to be a flexible and promising alternative to practitioners in this field.

Reliability of Bridge Decks in Wisconsin

An accurate reliability model for bridge decks is important for effective long-term bridge deck management. The main objectives of this paper are to identify the most suitable reliability model for bridge decks in Wisconsin, and to utilize that model for detailed analyzes of bridge deck reliability and failure rates. The 2005 National Bridge Inventory (NBI) data for the State of Wisconsin were used. In this paper, the hypertabastic, Weibull, log logistic, and lognormal distributions are investigated. The end of service life is defined as the age of deck when rehabilitation or replacement is required (herein defined as a deck rating of between 4 and 5). The effects on NBI deck rating of average daily traffic (ADT), type of bridge superstructure (steel or concrete), and the deck surface area were considered. Based on the Akaike information criteria, the hypertabastic accelerated failure time model was selected as the most appropriate model for this study. Results show that deck area, type of superstructure ...

Hyperbolastic modeling of tumor growth with a combined treatment of iodoacetate and dimethylsulphoxide

BackgroundAn understanding of growth dynamics of tumors is important in understanding progression of cancer and designing appropriate treatment strategies. We perform a comparative study of the hyperbolastic growth models with the Weibull and Gompertz models, which are prevalently used in the field of tumor growth.MethodsThe hyperbolastic growth models H1, H2, and H3 are applied to growth of solid Ehrlich carcinoma under several different treatments. These are compared with results from Gompertz and Weibull models for the combined treatment.ResultsThe growth dynamics of the solid Ehrlich carcinoma with the combined treatment are studied using models H1, H2, and H3, and the models are highly accurate in representing the growth. The growth dynamics are also compared with the untreated tumor, the tumor treated with only iodoacetate, and the tumor treated with only dimethylsulfoxide, and the combined treatment.ConclusionsThe hyperbolastic models prove to be effective in representing and analyzing the growth dynamics of the solid Ehrlich carcinoma. These models are more precise than Gompertz and Weibull and show less error for this data set. The precision of H3 allows for its use in a comparative analysis of tumor growth rates between the various treatments.

TELBS robust linear regression method

Correspondence: WM Eby Department of Mathematical Sciences, Cameron University, Lawton, OK, USA Tel +1 580 581 2395 Fax +1 580 581 2616 Email weby@cameron.edu Abstract: Ordinary least squares estimates can behave badly when outliers are present. An alternative is to use a robust regression technique that can handle outliers and influential observations. We introduce a new robust estimation method called TELBS robust regression method. We also introduce a new measurement called S h (i) for detecting influential observations. In addition, a new measure for goodness of fit, called R RFPR , is introduced. We provide an algorithm to perform the TELBS estimation of regression parameters. Real and simulated data sets are used to assess the performance of this new estimator. In simulated data with outliers, the TELBS estimator of regression parameters performs better in comparison with least squares, M and MM estimators, with respect to both bias and mean squared error. For rat liver weights data, none of the estimators (least squares, M, and MM) are able to estimate the parameters accurately. However, TELBS does give an accurate estimate. Using real data for brain imaging, the TELBS and MM methods were equally accurate. In both of these real data sets, the S h (i) measure was very effective in identifying influential observations. The robustness and simplicity of computations of TELBS model parameters make this method an appropriate one for analysis of linear regression. Algorithms and programs have been provided for ease in implementation, including all relevant statistics necessary to perform a complete analysis of linear regression.

T model of growth and its application in systems of tumor-immune dynamics.

In this paper we introduce a new growth model called T growth model. This model is capable of representing sigmoidal growth as well as biphasic growth. This dual capability is achieved without introducing additional parameters. The T model is useful in modeling cellular proliferation or regression of cancer cells, stem cells, bacterial growth and drug dose-response relationships. We recommend usage of the T growth model for the growth of tumors as part of any system of differential equations. Use of this model within a system will allow more flexibility in representing the natural rate of tumor growth. For illustration, we examine some systems of tumor-immune interaction in which the T growth rate is applied. We also apply the model to a set of tumor growth data.

Role of Metastasis in Hypertabastic Survival Analysis of Breast Cancer: Interaction with Clinical and Gene Expression Variables

This paper analyzes the survival of breast cancer patients, exploring the role of a metastasis variable in combination with clinical and gene expression variables. We use the hypertabastic model in a detailed analysis of 295 breast cancer patients from the Netherlands Cancer Institute given in.1 In comparison to Cox regression the increase in accuracy is complemented by the ability to analyze the time course of the disease progression using the explicitly described hazard and survival curves. We also demonstrate the ability to compute deciles for survival and probability of survival to a given time. Our primary concern in this article is the introduction of a variable representing the existence of metastasis and the effects on the other clinical and gene expression variables. In addition to making a quantitative assessment of the impact of metastasis on the prospects for survival, we are able to look at its interactions with the other prognostic variables. The estrogen receptor status increase in importance, while the significance of the gene expression variables used in the combined model diminishes. When considering only the subgroup of patients who experienced metastasis, the covariates in the model are only the clinical variables for estrogen receptor status and tumor grade.

Clinical and multiple gene expression variables in survival analysis of breast cancer: analysis with the hypertabastic survival model.

BackgroundWe explore the benefits of applying a new proportional hazard model to analyze survival of breast cancer patients. As a parametric model, the hypertabastic survival model offers a closer fit to experimental data than Cox regression, and furthermore provides explicit survival and hazard functions which can be used as additional tools in the survival analysis. In addition, one of our main concerns is utilization of multiple gene expression variables. Our analysis treats the important issue of interaction of different gene signatures in the survival analysis.MethodsThe hypertabastic proportional hazards model was applied in survival analysis of breast cancer patients. This model was compared, using statistical measures of goodness of fit, with models based on the semi-parametric Cox proportional hazards model and the parametric log-logistic and Weibull models. The explicit functions for hazard and survival were then used to analyze the dynamic behavior of hazard and survival functions.ResultsThe hypertabastic model provided the best fit among all the models considered. Use of multiple gene expression variables also provided a considerable improvement in the goodness of fit of the model, as compared to use of only one. By utilizing the explicit survival and hazard functions provided by the model, we were able to determine the magnitude of the maximum rate of increase in hazard, and the maximum rate of decrease in survival, as well as the times when these occurred. We explore the influence of each gene expression variable on these extrema. Furthermore, in the cases of continuous gene expression variables, represented by a measure of correlation, we were able to investigate the dynamics with respect to changes in gene expression.ConclusionsWe observed that use of three different gene signatures in the model provided a greater combined effect and allowed us to assess the relative importance of each in determination of outcome in this data set. These results point to the potential to combine gene signatures to a greater effect in cases where each gene signature represents some distinct aspect of the cancer biology. Furthermore we conclude that the hypertabastic survival models can be an effective survival analysis tool for breast cancer patients.

A flexible multivariable model for Phytoplankton growth

We introduce a new multivariable model to be used to study the growth dynamics of phytoplankton as a function of both time and the concentration of nutrients. This model is applied to a set of experimental data which describes the rate of growth as a function of these two variables. The form of the model allows easy extension to additional variables. Thus, the model can be used to analyze experimental data regarding the effects of various factors on phytoplankton growth rate. Such a model will also be useful in analysis of the role of concentration of various nutrients or trace elements, temperature, and light intensity, or other important explanatory variables, or combinations of such variables, in analyzing phytoplankton growth dynamics.