Current Pharmaceutical Design - Volume 13, Issue 15, 2007

In recent years, biomedical research and drug design became one of the fastest growing branches of scientific and industrial development. The tremendous scale (number of projects and volume of information to process) promoted by trillions of dollars invested in these fields called for completely new approaches to obtain, analyze, and apply information to clinical practice, pharmacological research and the medical industry. This issue was put together as a result of our long-standing interest in the various aspects of research and drug design. It is dedicated to the use of new mathematical models in various fields of medical research. Our previous Current Pharmaceutical Design issue (2004) addressed the concept of multi-functional drug targets in diverse model systems [1]. This issue, accordingly, continues our inquiry into various types of models used in research and the subsequent creation of novel agents and improved therapies. This issue aims to give the reader an inside view into the concepts of intelligent research design and biomedical information processing. In Part-1 of this topic, we began with articles on the use of mathematics in basic science research to uncover the processes underlining the most complex events that are so crucial to understand in order to successfully conduct medical research, design drugs and simply practice medicine nowadays. Then, we began discussing the prediction capabilities of using mathematical models in biomedical research and in medicine, such as the prediction of drug delivery efficiency or patient treatment outcome. In Part-2, Jadhav, Eggleton and Konstantopoulos [2] address the application of mathematical modeling of cell adhesion in shear flow in order to target drug delivery for the treatment of inflammation and cancer metastasis. They conclude that these multiscale mathematical models can be employed to predict optimal drug carrier-cell binding through isolated parameter studies and engineering optimization schemes, which will be essential for developing effective drug carriers for delivery of therapeutic agents to afflicted sites of the host. Then, Dvorchik and his co-authors [3] analyze prognostic models in hepatocellular carcinoma (HCC) and the statistical methodologies behind them. These methods are evolving at a very fast pace and are extremely promising. The symbiosis of microarrays analysis, genotyping techniques and statistical modeling presents a powerful tool to further advance our knowledge of cancer development and progression. In the next section, two reviews [4, 5] delve into the use of mathematical models in the analysis of treatment results and potential optimization of outcomes. First, Qazi, DuMez and Uckun [4] describe the use of a parametric lognormal model to calculate and compare survival statistics in the clinical treatment of advanced/metastatic pancreatic, breast and colon cancers. Then Apolloni, Bassis, Gaito and Malchiodi [5] propose a new statistical framework, called Algorithmic Inference, for overcoming crucial difficulties usually met when computing confidence intervals about medical treatment or pollution effectiveness and abandoning general simplifying hypotheses such as errors’ Gaussian distribution. In the final review [6], Tsibulsky and Norman give insight into the mathematical modeling of behaviors of the animal models used in biomedical research. We would like to thank all the authors for their contributions and hope that this issue will stimulate new communication and collaborations. References [1] Current Pharmaceutical Design, Volume 10, Number 15, June 2004. [2] Jadhav S, Eggleton CD, Konstantopoulos, K. Mathematical Modeling of Cell Adhesion in Shear Flow: Application to Targeted Drug Delivery in Inflammation and Cancer Metastasis. Curr Pharm Des 2007; 13(15): 1511-1526. [3] Dvorchik I, Demetris AJ, Geller DA, Carr BI, Fontes P, Finkelstein, SD, Cappella NK, Marsh JW.Prognostic Models in Hepatocellular Carcinoma (HCC) and Statistical Methodologies Behind Them. Curr Pharm Des 2007; 13(15): 1527-1532. [4] Qazi S, DuMez D, Uckun FM. Meta analysis of advanced cancer survival data using lognormal parametric fitting: A statistical method to identify effective treatment protocols. Curr Pharm Des 2007; 13(15): 1533-1544. [5] Apolloni B, Bassis B, Gaito S, Malchiodi D. Appreciation of medical treatments through confidence intervals. Curr Pharm Des 2007; 13(15): 1545-1570. [6] Tsibulsky VL, Norman AB. Mathematical models of behavior of an individual animal. Curr Pharm Des 2007; 13(15): 1571- 1595.

Cell adhesion plays a pivotal role in diverse biological processes that occur in the dynamic setting of the vasculature, including inflammation and cancer metastasis. Although complex, the naturally occurring processes that have evolved to allow for cell adhesion in the vasculature can be exploited to direct drug carriers to targeted cells and tissues. Fluid (blood) flow influences cell adhesion at the mesoscale by affecting the mechanical response of cell membrane, the intercellular contact area and collisional frequency, and at the nanoscale level by modulating the kinetics and mechanics of receptor-ligand interactions. Consequently, elucidating the molecular and biophysical nature of cell adhesion requires a multidisciplinary approach involving the synthesis of fundamentals from hydrodynamic flow, molecular kinetics and cell mechanics with biochemistry/molecular cell biology. To date, significant advances have been made in the identification and characterization of the critical cell adhesion molecules involved in inflammatory disorders, and, to a lesser degree, in cancer metastasis. Experimental work at the nanoscale level to determine the lifetime, interaction distance and strain responses of adhesion receptor-ligand bonds has been spurred by the advent of atomic force microscopy and biomolecular force probes, although our current knowledge in this area is far from complete. Micropipette aspiration assays along with theoretical frameworks have provided vital information on cell mechanics. Progress in each of the aforementioned research areas is key to the development of mathematical models of cell adhesion that incorporate the appropriate biological, kinetic and mechanical parameters that would lead to reliable qualitative and quantitative predictions. These multiscale mathematical models can be employed to predict optimal drug carrier-cell binding through isolated parameter studies and engineering optimization schemes, which will be essential for developing effective drug carriers for delivery of therapeutic agents to afflicted sites of the host.

Hepatocellular carcinoma (HCC) is estimated to be responsible for 250,000 deaths worldwide yearly. Aggressive surgical resection or liver transplantation still remain the only viable curative options for patients suffering the disease despite the multitude of emerging therapies for HCC. However, even with the most aggressive surgical intervention, survival varies widely within each particular stage of HCC. In order to improve utilization of available therapeutic modalities, a number of outcome prognostic models have been developed. This manuscript reviews the prognostic models most commonly utilized in clinical practice and the statistical methodologies on which these models are based. A multitude of statistical and mathematical techniques can be used for prognostic model development. The most common methodologies used for HCC prognostic model development can be generally divided into four groups: survival, artificial neural networks, analysis of variance, and cluster analysis. Survival methodologies (such as Cox proportional hazard model) are commonly employed for estimation of relative significance of risk factors for patient survival or cancer recurrence. Artificial neural networks (such as back-propagation network) can be supreme approximation tools for any continuous or binary function, and as such can be employed for prognostication of HCC recurrence (death). Analysis of variance and cluster analysis are the most common statistical tools of recently evolved microarrays technology, which, in turn, is one of the most promising tools available to the cancer researcher.

We describe the use of a parametric lognormal model to calculate and compare survival statistics in the clinical treatment of advanced/metastatic pancreatic, breast and colon cancers. The fit using the lognormal model explained greater than 90% (R2 ranged from 0.917 to 0.998 for a total of the 51 arms from published studies) of the variation in the cumulative survival statistics of patients treated for advanced cancers. A meta-analytic Q-test was performed to test whether there were significant differences between different studies. For all three cancer types, the Q-test showed highly significant differences between the survival arms (p<0.0001 for pancreatic, breast and colon cancers). The z-values expressed the difference of the average of lognormal means relative to each study in terms of deviation expressed in standard errors. The treatments that were most effective ranked with the highest z-value: Doxorubicin plus docetaxel for pancreatic cancer (z-value = 4.1); Capecitabine plus paclitaxel for breast cancer (z-value = 3); irinotecan, fluorouracil and folinate for colon cancer (z-value = 7.4).

The typical way of judging about either the efficacy of a new treatment or, on the contrary, the damage of a pollutant agent is through a test of hypothesis having its ineffectiveness as null hypothesis. This is the typical operational field of Kolmogorov’s statistical framework where wastes of data (for instance non significant deaths in a polluted region) represent the main drawback. Instead, confidence intervals about treatment/pollution effectiveness are a way of exploiting all data, whatever their number is. We recently proposed a new statistical framework, called Algorithmic Inference, for overcoming crucial difficulties usually met when computing these intervals and abandoning general simplifying hypotheses such as errors’ Gaussian distribution. When effectiveness is expressed in terms of regression curves between observed data we come to a learning problem that we solve by identifying a region where the whole curve lies with a given confidence. The approach to inference we propose is very suitable for identifying these regions with great accuracy, even in the case of nonlinear regression models and/or a limited size of the observed sample, provided that a normally powered computing station is available. In the paper we discuss this new way of extracting functions from the experimental data and drawing conclusions about the treatments originating them. From an operational perspective, we give the general layout of the procedure for computing confidence regions as well as some applications on real data.

This review is focused on mathematical modeling of behaviors of a whole organism with special emphasis on models with a clearly scientific approach to the problem that helps to understand the mechanisms underlying behavior. The aim is to provide an overview of old and contemporary mathematical models without complex mathematical details. Only deterministic and stochastic, but not statistical models are reviewed. All mathematical models of behavior can be divided into two main classes. First, models that are based on the principle of teleological determinism assume that subjects choose the behavior that will lead them to a better payoff in the future. Examples are game theories and operant behavior models both of which are based on the matching law. The second class of models are based on the principle of causal determinism, which assume that subjects do not choose from a set of possibilities but rather are compelled to perform a predetermined behavior in response to specific stimuli. Examples are perception and discrimination models, drug effects models and individual-based population models. A brief overview of the utility of each mathematical model is provided for each section.

Ionotropic glutamate receptors contain three subtypes: NMDA, AMPA and kainate receptors. The former two receptor subtypes have well defined roles in nociception, while the role of kainate receptors in pain is not as well characterized. Kainate receptors are expressed in nociceptive pathways, including the dorsal root ganglion, spinal cord, thalamus and cortex. Electrophysiological studies show that functional kainate receptors are located postsynaptically, where they mediate a portion of excitatory synaptic transmission, or are located presynaptically, where they modulate excitatory or inhibitory neurotransmission. Recent genetic and pharmacological studies suggest that kainate receptors can regulate nociceptive responses. These results highlight kainate receptors as a target for the development of new treatments for chronic pain.

Heparin is a glycosaminoglycan mixture currently used in prophylaxis and treatment of thrombosis. Heparin possesses non-anticoagulant properties, including modulation of various proteases, interactions with fibroblast growth factors, and anti-inflammatory actions. Senile dementia of Alzheimer’s type is accompanied by inflammatory responses contributing to irreversible changes in neuronal viability and brain function. Vascular factors are also involved in the pathogenesis of senile dementia. Inflammation, endogenous proteoglycans, and assembly of senile plagues and neurofibrillary tangles contribute directly and indirectly to further neuronal damage. Neuron salvage can be achieved by antiinflammation and the competitive inhibition of proteoglycans accumulation. The complexity of the pathology of senile dementia provides numerous potential targets for therapeutic interventions designed to modulate inflammation and proteoglycan assembly. Heparin and related oligosaccharides are known to exhibit anti-inflammatory effects as well as inhibitory effects on proteoglycan assembly and may prove useful as neuroprotective agents.