Current
Pharmaceutical Design
ISSN: 1381-6128
Current Pharmaceutical Design
Volume 13, Number 15, 2007
Contents
Part-II
Ground-Breaking Mathematical Models for Basic and Applied
Research
Executive Editors: A.O. Vassilev and H.E. Tibbles
Editorial: Pp. 1509
Mathematical Modeling of Cell Adhesion in Shear
Flow: Application to Targeted Drug Delivery in Inflammation
and Cancer Metastasis Pp. 1511-1526
S. Jadhav, C.D. Eggleton and K. Konstantopoulos
[Abstract]
Prognostic Models in Hepatocellular Carcinoma (HCC)
and Statistical Methodologies Behind Them Pp. 1527-1532
I. Dvorchik, A.J. Demetris, D.A. Geller, B.I. Carr, P.
Fontes, S.D. Finkelstein, N.K. Cappella and J.W. Marsh
[Abstract]
Meta Analysis of Advanced Cancer Survival Data Using
Lognormal Parametric Fitting: A Statistical Method to Identify
Effective Treatment Protocols Pp. 1533-1544
S. Qazi, D. DuMez and F.M. Uckun
[Abstract]
Appreciation of Medical Treatments Through Confidence
Intervals Pp. 1545-1570
B. Apolloni, S. Bassis, S. Gaito and D. Malchiodi
[Abstract]
Mathematical Models of Behavior of An Individual Animal
Pp. 1571-1595
V.L. Tsibulsky and A.B. Norman
[Abstract]
General Articles
Kainate Receptors and Pain: From Dorsal Root Ganglion to the
Anterior Cingulate Cortex Pp. 1597-1605
L.-J. Wu, S.W. Ko and M. Zhuo
[Abstract]
Heparin Oligosaccharides as Potential Therapeutic
Agents in Senile Dementia Pp. 1607-1616
Q. Ma, U. Cornelli, I. Hanin, W.P. Jeske, R.J. Linhardt,
J.M. Walenga, J. Fareed and J.M. Lee
[Abstract]
Abstracts
[Back to top]
Editorial: Ground-Breaking Mathematical Models for
Basic and Applied Research
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.
Alexei O. Vassilev Ph.D
avassilev@hotmail.com
Heather E. Tibbles
tibbles_2@hotmail.com
[Back to top]
Mathematical Modeling of Cell Adhesion in Shear Flow: Application
to Targeted Drug Delivery in Inflammation and Cancer Metastasis
S. Jadhav, C.D. Eggleton and K. Konstantopoulos
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.
[Back to top]
Prognostic Models in Hepatocellular Carcinoma (HCC)
and Statistical Methodologies Behind Them
I. Dvorchik, A.J. Demetris, D.A. Geller, B.I. Carr, P.
Fontes, S.D. Finkelstein, N.K. Cappella and J.W. Marsh
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.
[Back to top]
Meta Analysis of Advanced Cancer Survival Data Using
Lognormal Parametric Fitting: A Statistical Method to Identify
Effective Treatment Protocols
S. Qazi, D. DuMez and F.M. Uckun
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).
[Back to top]
Appreciation of Medical Treatments Through Confidence
Intervals
B. Apolloni, S. Bassis, S. Gaito and D. Malchiodi
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.
[Back to top]
Mathematical Models of Behavior of An Individual Animal
V.L. Tsibulsky and A.B. Norman
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.
[Back to top]
Kainate Receptors and Pain: From Dorsal Root Ganglion to the
Anterior Cingulate Cortex
L.-J. Wu, S.W. Ko and M. Zhuo
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.
[Back to top]
Heparin Oligosaccharides as Potential Therapeutic
Agents in Senile Dementia
Q. Ma, U. Cornelli, I. Hanin, W.P. Jeske, R.J. Linhardt,
J.M. Walenga, J. Fareed and J.M. Lee
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 anti-inflammation 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.
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