Six patients with bronchogenic carcinomas presenting as solitary nodules had from seven to nine serial chest roentgenograms which permitted measurement of tumor diameters in the absence of definitive therapy. Growth curves were plotted simultaneously on semilogarithmic and arithmetic coordinates to determine whe.ther growth rates were constant. The findings suggested exponential growth in three of the six cancers, but the curves for the other three cases did not provide evidence for constancy of growth rate. The sparse data in this series and in the literature are insufficient to permit generalization on the shape of growth curves for bronchogenic carcinoma.
ANCER IS CHARACTERIZED BY GROWTH, BUT,
C in clinical practice, there has been no quantitative method for describing it until recently. In 1956, Collins et al.3 developed a simple exponential model of cancer growth in which one malignant cell divides to become two, two become four, four become eight, etc. If the rate of growth is constant it can be described in terms of doubling time, i.e., the time required for the tumor to double its number of cells or volume.
If the average cancer cell is 10 p, in diameter, and, if cancer growth is exponential, then 20 doublings produce a nodule 1 mm in diameter, 30 doublings a nodule 1 cm in diameter, and 40 doublings a mass 10 cm in diameter.3 A few more doublings produce a volume of tumor tissue incompatible with life. A model of this sort, if valid, makes extrapolation simple. Several measurements of tumor diameter at appropriate intervals establish the growth curve which is a straight line when diameter is plotted against time on semilogarithmic paper. Extrapolation backward permits an estimate of the duration of the cancer and the point in time of its inception. Extrapolation forward provides, in the absence of effective therapy, a prediction of the time of death. It follows that if under treatment the patient's survival exceeds the predicted period, then therapy has been effective.
Collins et al.3 estimated the doubling time
From the Hahnemann Medical College Section of the Pulmonary Disease Service, Philadelphia General Hospital, Philadelphia, Pa. Professor of Medicine.