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Title: "Identification
of Stochastic Systems with Random Parameters With
Particular Reference to Recirculating
Lymphocytes in
the Immune System".
Abstract: It is available below and at the following IEEE link:
ieeexplore.ieee.org/iel5/37/24291/01105346.pdf?arnumber=1105346
AN
ABSTRACT OF THE DISSERTATION OF
Zarreen H
Farooqi
for the
degree of
Doctor of
Philosophy
in
Electrical
& Computer Engineering
presented on
December 17,1986.
Title:
Identification
of Stochastic Systems With
Random Parameters With
Particular Reference to the Recirculating
Lymphocytes
in the Immune System.
Interest in stochastic nature
of
models is reflected in identification and estimation of stochastic
systems
especially nonlinear ones, which are closer to natural systems. This is
seen in
the increasing role of nonlinear (in general, and bilinear in
particular) time
series and also in the interest in robust methods.
Many models have been
developed
related to the immune response at several hierarchical levels including
the subcellular and
cellular levels. This dissertation is
concerned with phenomena in the immune system which functionally link
together
many processes at the cellular level, thus physically and
physiologically
conveying information and providing defense. These phenomena include
the
recirculation of lymphocytes, which is composed of many processes. The
particular event in recirculation that will be focussed
on here is the distribution of lymphocytes in various organs, lymphoid
and
non-lymphoid, throughout the body. Such distribution gains importance
because i) it is
consequential in effective defense of the body,
and ii) lymphocyte maldistribution
may be a symptom
of a disease state.
This is an attempt to collect
various mathematical and physiological items and to combine them in a
happy
marriage. Certain deterministic models of lymphocyte distribution have
been
published previously. Process of cell distribution though inherently
continuous
in time has imposed on it the process of observation which is usually
discrete.
In view of this, here discrete-time and continuous-time stochastic
models will
be developed and their parameters interpreted. It turns out that these
models
are also stiff. The class of models studied here are compartmental. The
derived
mathematical structures are bilinear time series with two inputs (or
random
coefficient autoregression)
and vector stochastic differential
equation, respectively, for the discrete and the continuous cases. The
existence, uniqueness, stability and stationarity
properties of their solutions are studied.
Parameter estimation for a
reduced, 7-compartment system is done using nonlinear optimization with
weighted least squares and -2 ln
likelihood criteria
(assuming Gaussianity
for convenience, though not
realistic). The outputs of the models are statistically examined
against best
available experimental data. This data has some missing values and the
observations have been recorded irregularly (i.e., at unequally spaced
time
intervals) for 13 organs.
The discrepancies in the two
(experimental and estimated values) are analyzed for proximity of fit,
validity
of the models, Gaussianity,
and stationarity.
Multiple comparisons are performed to test lack of fit of individual
compartments and in so doing major sources of error in estimation are
assessed.
1. Mohler, R.R.,
Farooqi, Z.H., and Heilig,
T., 1984, "An
Immune Lymphocyte Circulation Model," In: Thoft-Christensen,
P., (Ed.), System Modelling
and Optimization,
(Lecture Notes in Control and Information Sciences, Vol. 59),
2. Mohler, R.R.,
Farooqi, Z.H., and Heilig,
T., 1986,
"Lymphocyte Distribution and Lymphatic Dynamics," In: Balakrishnan, A.V., Dorodnitsyn,
A.A., and Lions, J.L., (Eds.), Vistas in Applied Mathematics:
Numerical
Mathematics, Atmospheric Sciences, Immunology, (A Volume dedicated to
Academician G.I. Marchuk
on the occasion of his 60th
birthday), NY: Optimization Software, Publications Division.
3. Mohler, R.R.,
Farooqi, Z.H., and Heilig,
T., 1986, "On
Migratory Lymphocyte Models," In: Hoffman, G.W. and Hraba,
T., (Eds.), Immunology and Epidemiology,
Proceedings of an International
Conference held in Mogilany,
Poland, Feb. 18-25,
1985, (Lecture Notes in Biomathematics, Vol. 65), Berlin: Springer-Verlag.
4. Yang, X.S., Mohler,
R.R., and Farooqi, Z.H., 1987, "Immune Control
System Modelling and
Identification", Proceedings of IFAC
1987 held in July 1987 in
5. Mohler, R.R.,
and Farooqi, Z.H., 1988, "On Immune Process
Stochastic
Structure", In: Perelson,
A.S., (Ed.), Theoretical
Immunology, (Proceedings of the DOE Workshop on Theoretical
Immunology held
in June 1987 in Santa Fe, NM, USA), NY: Addison-Wesley.
6. Farooqi,
Z.H. and Mohler,
R.R., 1988, "Stochastic Recirculating
Lymphocyte Models," In: Mohler,
R.R. (Ed.), Non-linear
Time Series and Signal Processing, (Lecture Notes in Control
and
information Sciences, Vol. 106),
7. Mohler, R.R.,
and Farooqi, Z.H., 1989, "Distribution of Recirculating
Lymphocytes: A Stochastic Model Foundation," Acta
Applicandae Mathematicae,
14(1/2): 143-153. This issue of the journal was
later published as the
following special edition: Kurzhanski,
A.B. and
Sigmund, K. (Eds.), Evolution and Control in Biological
Systems,
(Proceedings of the IIASA Workshop held 30 November-4 December 1987 in Laxenburg, Austria),
8. Farooqi,
Z.H. and Mohler,
R.R., 1989, "Distribution Models of Recirculating
Lymphocytes," IEEE Trans. Biomedical
Engineering, Vol. BME-36(3): 355-362.
9. Farooqi,
Z.H., 1989, "A
Markov Process Based Model of the Neurotransmitter-Receptor Binding
Process in
the Brain --- Comment," Drug Design and Delivery, 4:
257-259.
10. Farooqi,
Z.H. and Lambrecht,
R.M., 1990, "Modelling
Delays in Pharmacokinetics", In: Maddalena,
D.J., Snowdon, G.M.,
and Boniface, G.R., (Eds.), Advances
in Radiopharmacology,
(Proceedings of at the 6th
International Symposium on Radiopharmacy,
held 23-26
Aug., 1989 in Sydney, Australia) Wollongong, Australia: Wollongong
University Printery
Services.
11. Farooqi,
Z.H., 1990,
"Model of Acute Leukemia Regrowth
After Autologous Bone
Marrow Transplantation", Proceedings
of the International Seminar on Modeling and Signal Processing of
Cellular
Systems, held 28-30 October, 1990 at Internationales
Institut Schloss Reisensburg,
Gunzburg, Germany
(to be published).
12. Farooqi,
Z.H. and Aboul-Enein,
H.Y., 1992, "The Influence of Different
Configurations of a Cyclohexyl
Moiety on the
Conformational Flexibility of Cyclohexylaminoglutethimide:
A Potent Aromatase
Inhibitor", Toxicological
& Environmental Chemistry, 36:
189-193.
13. Farooqi,
Z.H. and Aboul-Enein,
H.Y., 1993, "The Influence of a Cyclohexyl
Moiety on the Conformational Flexibility of Aminoglutethimide",
Toxicological &
Environmental Chemistry, 37: 207-210.
14. Farooqi,
Z.H. and Zaman,
L., 1994, "Spectral Estimation of Heart Rate
Variability Using An Algorithm for Unequally Spaced Data", COMCON
4 ---
1993, 4th International Conference on Advances in
Communications &
Control; Proceedings,
15. Farooqi,
Z.H. and Aboul-Enein,
H.Y., 1994, "Conformational Energy of Cyclohexylaminoglutethimide:
A Potent Aromatase
Inhibitor. Comparison of the Three Forms", Cancer Letters,
82:
1-5.
16. Farooqi,
Z.H. and Aboul-Enein,
H.Y., 1995, "The Theoretical Structure of
Propranolol and Some
Fluorinated Derivatives," Structural
Chemistry, 6(4/5): 349-355. (Available @ http://www.springerlink.com/content/g0m5468275776073/ or here)
17. Farooqi,
Z.H. and Aboul-Enein,
H.Y., 1996, "The IR and UV/Vis Spectra of
Propranolol and Some
Fluorinated Derivatives:
Comparison of Experimental and Calculated Values," Biospectroscopy,
2: 131-141. (http://www3.interscience.wiley.com/cgi-bin/fulltext/73162/PDFSTART)
18. Farooqi,
Z.H. and AliNiazee,
M.T., 1997, "Insect Phenology
Models: Theoretical Basis ", Trends in Entomology, 1.
31-47.
19. Farooqi,
Z.H. and Aboul-Enein,
H.Y., 1999, "The Theoretical Study on the
Structure of Cyclohexylaminoglutethimide:
A Potent Aromatase
Inhibitor. Comparison of the
Three Configurations of the Cyclohexyl
Moiety," Archive
der Pharmazie, 332.81-84.
20. Farooqi,
Z.H., 1999,
"Performance Evaluation of Lomb-Scargle
Algorithm For Spectral Analysis of Unequally-Spaced Data", (Submitted).
IEEE Control System Society, Member;
IEEE Engineering in Medicine and Biology Society, Member;
IEEE Signal Processing Society, Member;
IEEE Computer Society, Member; and
IEEE Standards Association, Member;
WideBand Gigabit Networking
ii)
Annals of Saudi Medicine; and
iii)
Analytical Letters. (From
1990 -- 1995)
iv) Computer
Based Medical Systems (Conferences), 2006, 2007
v) OATYC
2007
vi) ASEE
2008 Conference and
the IJME 2008 Conference
vi) Have
reviewed several books in the
prepublication stage.