Teriparatide is a bone-forming therapy for osteoporosis that increases bone quantity and texture, with uncertain action on bone geometry. No data are available regarding its influence on bone strain. To investigate teriparatide action on parameters of bone quantity and quality and on Bone Strain Index (BSI), also derived from DXA lumbar scan, based on the mathematical model finite element method. Forty osteoporotic patients with fractures were studied before and after two years of daily subcutaneous 20 mcg of teriparatide with dual X-ray photon absorptiometry to assess bone mineral density (BMD), hip structural analysis (HSA), trabecular bone score (TBS), BSI. Spine deformity index (SDI) was calculated from spine X-ray. Shapiro-Wilks, Wilcoxon and Student's t test were used for classical statistical analysis. Auto Contractive Map was used for Artificial Neural Network Analysis (ANNs). In the entire population, the ameliorations after therapy regarded BSI (-13.9%), TBS (5.08%), BMD (8.36%). HSA parameters of femoral shaft showed a worsening. Dividing patients into responders (BMD increase >10%) and non-responders, the first presented TBS and BSI ameliorations (11.87% and -25.46%, respectively). Non-responders presented an amelioration of BSI only, but less than in the other subgroup (-6.57%). ANNs maps reflect the mentioned bone quality improvements. Teriparatide appears to ameliorate not only BMD and TBS, but also BSI, suggesting an increase of bone strength that may explain the known reduction in fracture risk, not simply justified by BMD increase. BSI appears to be a sensitive index of TPD effect. ANNs appears to be a valid tool to investigate complex clinical systems.