De geometria Dei

Invocatio: D.D.

Hyperbolinen ja kvasihyperbolinen geometria

Tämä Pro gradu -tutkielma käsittelee hyperbolista ja kvasihyperbolista geometriaa. Tutkielmassa tarkasteellaan hyperbolista geometriaa ylemmässä puolitasossa ja yksikkökiekossa. Sovelluksena tarjotaan kaava hyperbolisen geodeesin hyperboliselle keskipisteelle. Kvasihyperbolista geometriaa tutkitaan tasovyössä. Erityisesti selvitetään millaisia ovat tasovyön kvasihyperboliset geodeesit.

Nuclear morphometry, apoptotic and mitotic indices, and tubular differentiation in Libyan breast cancer

Aims of this study were to evaluate the relations of nuclear morphometry, mitotic and apoptotic indices, and tubular differentiation with clinicopathological features and survival rate in Libyan women. The data were compared with corresponding results on Finnish, and Nigerian female breast cancer patients. Histological samples of breast cancer (BC) from 131 patients were retrospectively studied. Mitotic activity indices (MAI and SMI), apoptotic index (AI), and fraction of fields with tubular differentiation (FTD) were estimated. Samples were also studied by computerized nuclear morphometry, such as mean nuclear area (MNA). Demographic and clinicopathological features were analyzed from 234 patients. The Libyan BC was dominantly premenopausal, and aggressive in behavior. There were statistically significant correlations between the mean nuclear area, fraction of fields with tubular differentiation, apoptotic index and proliferative indices, and most clinicopathological features. The highest significances were shown between lymph node status and the proliferative and apoptotic indices (p=0.003 with SMI, and p=0.005 with AI). There were significant associations between clinical stage and SMI and AI (p=0.002 and 0.009, respectively). The most significant associations with grade were observed with MNA and FTD (p<0.0001 and 0.001, respectively). The proliferative differences between Libyan, Nigerian and Finnish populations were prominent. These indices in Libyan were lower than in Nigerian, but higher than in Finnish patients. The Libyan patients’ AI is slightly higher than in Nigeria, but much higher than in Finland. The differences between countries may be associated with the known variation in the distribution of genetic markers in these populations. The results also indicated that morphometric factors can be reliable prognostic indicators in Libyan BC patients.