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A stochastic model for metabolizing systems with computer simulation (1973)

Milton, J. Susan ; Tsokos, Chris P. ; Hardiman, S. T.

Springer

Journal of statistical physics 8 (1973), S. 79-101

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ISSN: 1572-9613

Keywords: Stochastic integral equation ; metabolizing system ; multicompartment model ; chemotherapy ; lymphatics ; diffusion processes ; Volterra ; random solution ; Lebesgue space ; probability measure space ; Banach space ; Banach's fixed-point theorem ; linear operator

Source: Springer Online Journal Archives 1860-2000

Topics: Physics

Notes: Abstract A stochastic model for a first-order metabolizing system which was studied in the deterministic sense by Branson and others is formulated and a detailed study of the random integral equation arising in the probabilistic model is presented. The equation is used to describe the evolution in time of the amount of metabolite present in the system. Specifically we present a study of the random integral equation of the Volterra type given by $$M\left( {t; \omega } \right) = M\left( {0; \omega } \right)e^{ - et} + \int_0^t {R\left( {\tau ; \omega } \right) e^{ - e\left( {t - \tau } \right)} d\tau , } t \geqslant 0$$ whereM(t; ω) is an unknown random function giving the amount of metabolite in the system at time t ≥ 0. This equation can be expressed in the general form $$x\left( {t; \omega } \right) = h\left( {t; \omega } \right) + \int_0^t {k\left( {t, \tau ; \omega } \right) f\left( {\tau , x\left( {\tau ; \omega } \right)} \right) d\tau } t \geqslant 0$$ which is of a type whose theoretical aspects have recently been studied by the present authors using as a basis the techniques of probabilistic functional analysis. Conditions are derived under which there exists a unique random solution to the above equation. The usefulness of the model is illustrated using computer simulation by considering a one-organ model, an organ-heart model, and a multicompartment model.

Type of Medium: Electronic Resource

URL: http://dx.doi.org/10.1007/BF01008443

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Zur Sensibilitätstestung maligner menschlicher Tumoren gegenüber Cytostatica. II (1972)

Mattern, J. ; Kaufmann, M. ; Volm, M. ; [et al.]

Springer

Journal of molecular medicine 50 (1972), S. 196-198

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ISSN: 1432-1440

Keywords: Screening ; chemotherapy ; tumour ; DNA ; Sensibilitätstestung ; Chemotherapie ; Tumor ; DNA

Source: Springer Online Journal Archives 1860-2000

Topics: Medicine

Description / Table of Contents: Zusammenfassung Mit einer früher beschriebenen Methode zur Sensibilitätstestung (3H-Thymidineinbau, Flüssigkeitsscintillationsmessung) haben wir 30 menschliche Adenocarcinome (10 Rectum-Sigma-Carcinome, 10 Magen-Carcinome, 30 Mamma-Carcinome) gegenüber Trenimon®, Methotrexat® und Natulan® getestet und statistisch ausgewertet. Die in unserer früheren Untersuchung vermutete Individualität der Tumoren konnte bestätigt werden.

Notes: Summary Using a sensibility testing method previously described by the authors (3H-thymidine incorporation, liquid scintillation counting), the sensitivity of 30 human tumours (10 recto-sigmoid carcinomas, 10 gastric carcinomas, 10 carcinomas of the breast) was tested in vitro against Trenimon®, Methotrexat® and Natulan®. The results obtained were evaluated statistically. Each tumour proved to react specifically to the agents.