Doubling time (DT) is widely used for quantification of tumor growth rate. DT is usually determined from two volume estimations with measurement time intervals comparable with or shorter than DT. Clinical data show that the frequency distribution of DT in patients is positively skewed, with some very long DT values compared with the average DT. Growth rate can also be quantified using specific growth rate (SGR; %/d), equal to ln2/DT. The aim of this work was to compare DT and SGR as growth rate variables. Growth rate calculations were computer simulated for a tumor with DT of 100 days, measurement time interval of 1 to 200 days, and volume estimation uncertainty of 5% to 20%. Growth rate variables were determined and compared for previously published clinical data. The study showed that DT is not a suitable variable for tumor growth rate because (a) for short measurement time intervals, or high volume uncertainties, mean DT can either overestimate or underestimate the average growth rate; (b) DT is not defined if the consecutively estimated volumes are equal; and (c) the asymmetrical frequency distribution of DT makes it unsuitable for common statistical testing. In contrast, mean SGR and its equivalent DT give the correct values for average growth rate, SGR is defined for all tumor volume changes, and it has a symmetrical frequency distribution. SGR is also more accurate to use when discussing, for example, growth fraction, cell loss rate, and growth rate heterogeneities within the tumor. SGR should thus be used, instead of DT, to quantify tumor growth rate. [Cancer Res 2007;67(8):3970-5]

The growth rate of tumor volume should be expressed by SGR, or percentage increase per unit time, regardless of the level of the uncertainty of growth rate estimation. This conclusion is also valid for changes in tumor marker level, whether it is correlated with the growth rate of tumor volume or not.

Background:Current standards for assessment of tumour response to therapy (a) categorise therapeutic efficacy values, inappropriate for patient-specific and deterministic studies, (b) neglect the natural growth characteristics of tumours, (c) are based on tumour shrinkage, inappropriate for cytostatic therapies, and (d) do not accommodate integration of functional/biological means of therapeutic efficacy assessed with, for example, positron emission tomography or magnetic resonance imaging, with data from anatomical changes in tumour.Methods:A quantity for tumour response was formulated assuming that an effective treatment may decrease the cell proliferation rate (cytostatic) and/or increase the cell loss rate (cytotoxic) of the tumour. Tumour response values were analysed for 11 non-Hodgkin's lymphoma patients treated with 131I-labelled anti-B1 antibody and 12 prostate cancer patients treated with a nutritional supplement.Results:Tumour response was found to be equal to the logarithm of the ratio of post-treatment tumour volume to the volume of corresponding untreated tumour. Neglecting the natural growth characteristics of tumours results in underestimation of treatment effectiveness based on currently used methods. The model also facilitates the integration of data from tumour volume changes, with data from functional imaging.Conclusion:Tumour response to therapy can be assessed with a continuous dimensionless quantity for both cytotoxic and cytostatic treatments.

PurposeKnowledge of natural tumour growth is valuable for understanding tumour biology, optimising screening programs, prognostication, optimal scheduling of chemotherapy, and assessing tumour spread. However, mathematical modelling in individuals is hampered by the limited data available. We aimed to develop a method to estimate parameters of the growth model and formation rate of metastases in individual patients.Materials and methodsData from one patient with liver metastases from a primary ileum carcinoid and one patient with lung metastases from a primary renal cell carcinoma were used to demonstrate this new method. Metastatic growth models were estimated by direct curve fitting, as well as with the new proposed method based on the relationship between tumour growth rate and tumour volume. The new model was derived from the Gompertzian growth model by eliminating the time factor (age of metastases), which made it possible to perform the calculations using data from all metastases in each patient. Finally, the formation time of each metastasis and, consecutively, the formation rate of metastases in each patient were estimated.ResultsWith limited measurements in clinical studies, fitting different growth curves was insufficient to estimate true tumour growth, even if patients were followed for several years. Growth of liver metastases was well described with a general growth model for all metastases. However, the lung metastases from renal cell carcinoma were better described by heterogeneous exponential growth with various growth rates.ConclusionAnalysis of the regression of tumour growth rate with the logarithm of tumour volume can be used to estimate parameters of the tumour growth model and metastasis formation rates, and therefore the number and size distribution of metastases in individuals.