A mathematical model of double minute (dm) population dynamics has been developed based upon current concepts of the saltatory replication, random partitioning, nuclear exclusion and loss, and cellular growth inhibition of these extrachromosomal elements. A highly accurate approximate analytical solution has been obtained for the dm frequency distribution at steady state and preliminary analysis of transient states has been performed. The steady state solution has been fit to experimental frequency data of the SW527N carcinoma line, the excellent goodness of fit (X2 = 2.6, d.f. = 29) providing preliminary evidence for the consistency of this set of mechanisms. Two special cases are examined in which extrareplicative dms are produced on both the chromosome and existing dms at equal rates or on the chromosome alone. The model predicts that the population--average rate of extrareplicative dm production is 0.039 +/- S.E. 0.009 dms/hr/cell in the first case and is tenfold higher than when such replication occurs on the chromosome alone (0.0043 +/- S.E. 0.0004 dms/hr/cell). Allowable ranges of the extent of dm-related growth inhibition and dm loss are determined for the SW527N cell line. It is found that dm-related growth inhibition can be nearly as high as that observed for the S180 sarcoma lines (on the order of 0.5% per dm lengthening of the doubling time) or as low as zero.

A simplified mathematical model is proposed for describing steady-state hematologic compensation in the presence of altered red cell properties. The unique pattern of renal oxygen consumption, related to sodium reabsorption and consequently linear in blood flow, is the basis for the simplicity of the model. The model is then applied to the prediction of improvement in the chronic anemia of sickle-cell disease, when red cell life span and oxygen affinity are modified as a result of carbamylation therapy. On this basis, it is predicted that a straight-line relationship exists between hemoglobin concentration and red cell lifetime, and that the reduction in oxygen P-50, as a result of carbamylation, is secondary to red cell lifetime as a factor in determining the reduction in anemia. The predictions are compared with the limited information available from the sodium cyanate clinical trails, and the qualitative agreement between predicted and measured mean values is satisfactory.

The methotrexate (MTX)-plasma concentrations of 172 high-dose infusions over the range of 50-200 mg/kg were measured over the 72-hour period following the beginning of infusion. Pharmacokinetic analysis shows that a biexponential function adequately describes the plasma decay for all doses. The distribution of plasma clearances over the patient population at a given dose has been characterized by a biexponential clearance function and associated time-dependent variance. It is found that when each of the plasma clearance functions are scaled by their respective dose, the 1 SD bands about the resulting unit dose curves overlap throughout their time ranges and are therefore insignificantly different from one another. Thus, the plasma clearance over the 50-200-mg/kg range may be represented by a single dose-scalable biexponential model with half-lives of 1.8 +/- 0.1 and 8.4 +/- 0.5 hours. For a given maximum allowable plasma-MTX level (eg, 10(-5) M at 24 hours), the variance of the clearance distribution is shown to predict the expected fraction of patients who will require intensified rescue. Urinary clearance has been determined at 104 +/- 8 ml/minute over the dose range of 50-300 mg/kg and only 60% of the MTX was excreted in the urine by 72 hours.

Computer tools for data analysis such as CLINFO can be combined with modern laboratory measurement techniques to provide quantitative practical rules for therapeutic decision-making in cancer chemotherapy. The analysis of extensive data on the clearance of methotrexate from the blood following a high-dose (50–200 mg/kg) methotrexate infusion on a fixed protocol provides a decision rule for increasing citrovorum rescue to prevent toxicity. This example demonstrates a computer-based approach to improve the reliability of chemotherapeutic pharmacology.Des outils informatiques tels que CLINFO peuvent ětre associés à des techniques de mesures très modernes. Cette association permet d'élaborer des règles quantitatives pratiques de décision dons la chimiothérapie des cancers. L'analyse de la clearance sanguine du methotrexate, à la suite de la perfusion d'une forte dose de 50 a 200 mg/kg, donne une règle de décision pour ajuster la quantité de citrovum à visée antitoxique. Cet exemple apporte la preuve qu'un support informatique est capable d'améliorer la sécurité et la fiabilite d'une chimiothérapie.

A computer-based model of the pharmacokinetics of cytosine arabinoside (ara-C) and its active metabolite, ara-CTP, has been developed. This model, which is an intracellular extension of the Bischoff-Dedrick model of multi-organ pharmcokinetics gives predictions which are in agreement with the recent measurements of Chou et al on tissue concentrations of ara-CTP and Borsa et al on blood levels of ara-C. It is shown that the ara-CTP halving time in tissue is much greater than the ara-C halving time in blood because of low tissue levels of phosphatase. For a single dose at the LD10 level in mice, significant splenic DNA inhibition is calculated to occur for 26 hours, while the ara-C levels are negligible in 6 hours. The calculated duration of cytostatic effect at lower dosages (2.5 mg/kg) is 10 or 12 hours, while ara-C blood levels are negligible within 3 hours. Implications for cell kinetics and scheduling studies are also briefly described.