The growth dynamics of multicell tumour spheroids (MTS) were analysed by means of mathematical techniques derived from signal processing theory. Volume vs. time trajectories of individual spheroids were fitted with the Gompertz growth equation and the residuals (i.e. experimental volume determinations minus calculated values by fitting) were analysed by fast fourier transform and power spectrum. Residuals were not randomly distributed around calculated growth trajectories demonstrating that the Gompertz model partially approximates the growth kinetics of three-dimensional tumour cell aggregates. Power spectra decreased with increasing frequency following a 1/f(delta) power-law. Our findings suggest the existence of a source of 'internal' variability driving the time-evolution of MTS growth. Based on these observations, a new stochastic Gompertzian-like mathematical model was developed which allowed us to forecast the growth of MTS. In this model, white noise is additively superimposed to the trend described by the Gompertz growth equation and integrated to mimic the observed intrinsic variability of MTS growth. A correlation was found between the intensity of the added noise and the particular upper limit of volume size reached by each spheroid within two MTS populations obtained with two different cell lines. The dynamic forces generating the growth variability of three-dimensional tumour cell aggregates also determine the fate of spheroid growth with a strong predictive significance. These findings suggest a new approach to measure tumour growth potential.

No abstract

For the follow-up periods in our series (median, >4 yr), GK radiosurgery seems to be both safe (permanent morbidity rate, 1%) and effective (97% neurological improvement/stability, 97.5% overall TGC, and 96.5% actuarial TGC at 5 yr). GK radiosurgery might be considered a first-choice treatment for selected patients with cavernous sinus meningiomas.

The excellent results obtained for TGC with minimal associated side effects suggest that GK is an effective therapeutic tool also for treatment of PCF meningiomas.

Object. The aim of this retrospective study was to assess the role of gamma knife radiosurgery (GKS) as a primary treatment for brain metastases by evaluating the results in particularly difficult cases such as oncotypes—which are unresponsive to radiation—cystic lesions, and highly critical locations such as the brainstem. Methods. Treatment of 804 patients with 1307 solitary (29%), single (26%), and multiple (45%) brain metastases was evaluated. Treatment planning parameters were as follows: mean tumor volume 4.8 cm3 (range 0.01–21.5 cm3), mean prescription dose 20.6 Gy (range 12–29 Gy), and mean number of isocenters 6.5 (one–19). In unresponsive oncotypes such as melanoma and renal cell carcinoma, the mean target dosages were higher. Cystic metastatic lesions were initially stereotactically evacuated and then GKS was performed. Patients with brainstem metastases were treated with lower doses. Conventional radiotherapy was used in only a minority (14%) of selected cases. The overall median patient survival time was 13.5 months, and the 1-year actuarial local progression-free survival rate was 94%, with a mean palliation index and functional independence index of 53.8 and 52.5 weeks, respectively. The local tumor control rate was 93%, with a mean follow-up period of 14 months. In the overall series, and especially in the unresponsive oncotypes, systemic disease progression was the main limiting factor with regard to patient life expectancy. Conclusions. Gamma knife radiosurgery seems to be the primary treatment option for patients harboring small-tomedium size (≤ 20-cm3) brain metastases with reasonable life expectancy and no impending intracranial hypertension. Results are better than with those obtained using whole-brain radiotherapy and comparable to the best selected surgery—radiation series, even in oncotypes unresponsive to therapeutic radiation, cystic tumors, and tumors located in the brain stem.