Al~tract--A T-cell acute lymphoblastic leukemia (T-ALL) patient (female, age 8) was monitored some 500 days, during which period she had two relapses of the disease. Remission induction by chemotherapy was applied three times, starting days 0 (diagnosis), 198 (first relapse) and 365 (second relapse). The first two remission induction therapies were successful and therefore were followed by continuous maintenance therapy. The second relapse did not respond sufficiently to chemotherapy and the patient died.
At diagnosis and during follow-up immunological marker was performed on peripheral blood (PB) and bone marrow (BM) samples. Double immunofluorescence (IF) staining for a T-cell marker and terminal deoxynucleotidyl transferase (TdT) was used as well. This IF assay is a sensitive and specific technique for recognizing low numbers of T-ALL cells (one T-ALL cell among 10,000 normal cells). The analyses of the PB and BM samples resulted in datapoints of T-ALL cells per mm 3 vs time. The PB and BM plots showed similar patterns. The remission periods were characterized by a decline and subsequent regrowth of the T-ALL population.
Based on preclinical studies in a rat model for acute myelocytic leukemia, a mathematical analysis was performed. Log-linear regression of the PB datapoints showed that the population doubling time during regrowth to relapse was approximately constant (6.5 days, influence of the maintenance therapy included). The population half-time during remission induction therapy amounted to 2.8 days. Population dynamics were modeled with an exponential growth curve, therapy influence with an exponential decay of the therapy level as an approximation of the series of instantaneous "log cell kills" caused by the discrete events in the therapy protocol. Curve fitting (standard least squares fitting routine) yielded values for the parameters in the drug influence function for each remission induction therapy. The development of therapy resistance was obvious; equal treatment schedules resulted sequentially in an effective log cell kill of 6, 4 and 1. Area under the therapy level curve, as a measure of therapy efficiency, dropped from 229.34 to 183.61 to 115.27.
These results indicate that mathematical analysis of data obtained by a sensitive method for the detection of low numbers of malignant cells yields valuable information about the growth characteristics of the malignant population, as well as about its therapy sensitivity and the development of therapy resistance.