A fractal dimension analysis: a new method for evaluating the response of anticancer therapy

The therapeutic effects of various anticancer therapies on malignant tumors are evaluated as objective response (OR) by comparing the tumor size before and after the therapy However, it is difficult to evaluate the OR because malignant tumors frequently have very irregular or stellate shapes. In the present study we investigated a new method for evaluating the response of esophageal cancer to radio-chemotherapy using the fractal dimension (FD).

The changes in tumor size or shape during therapy were recorded in 6 patients with esophageal cancer by esophageal fluoroscopy. The OR was evaluated by WHO standard criteria by calculating the tumor regression rate (TRR), while the FD was calculated by a standard compass-counting method.

All 6 patients complained of dysphagia before therapy, but the food passage improved after therapy in all patients. The TRR after therapy ranged between -90% and 43.4%, and the OR was evaluated as no change (NC) in 5 patients and progressive disease (PD) in one patient. On the other hand, the RD gradually decreased in all 6 patients during the therapy. Furthermore, 5 patients underwent esophagectomy and the histological effect was evaluated as grade-2 response in two patients and grade-1 response in three patients. The decreases in the FD were 0.069 and 0.079 in grade-2 responses and 0.022-0.034 in grade-1 responses. By contrast, 4 NCs included 2 grade-2 responses and 2 grade-1 responses, and PD was evaluated as grade-1 response. These results suggested that the standard criteria for an OR could not accurately evaluate the therapeutic effect in some cases, and the changes in FD correlated with the improvement in the symptoms and histological effect more precisely than the TRR or the OR.

The FD represented the therapeutic effect of radio-chemotherapy well for esophageal cancer, and may be widely applied for evaluating the therapeutic effect of cancer therapy.