Diffusive process under Lifshitz scaling and pandemic scenarios.

We here propose to model active and cumulative cases data from COVID-19 by a continuous effective model based on a modified diffusion equation under Lifshitz scaling with a dynamic diffusion coefficient. The proposed model is rich enough to capture different aspects of a complex virus diffusion as humanity has been recently facing. The model being continuous it is bound to be solved analytically and/or numerically. So, we investigate two possible models where the diffusion coefficient associated with possible types of contamination are captured by some specific profiles. The active cases curves here derived were able to successfully describe the pandemic behavior of Germany and Spain. Moreover, we also predict some scenarios for the evolution of COVID-19 in Brazil. Furthermore, we depicted the cumulative cases curves of COVID-19, reproducing the spreading of the pandemic between the cities of São Paulo and São José dos Campos, Brazil. The scenarios also unveil how the lockdown measures can flatten the contamination curves. We can find the best profile of the diffusion coefficient that better fit the real data of pandemic.

Additive manufacturing models of fetuses built from three-dimensional ultrasound, magnetic resonance imaging and computed tomography scan data.

OBJECTIVE: To generate physical fetal models using images obtained by three-dimensional ultrasonography (3DUS), magnetic resonance imaging (MRI) and computed tomography (CT) to guide additive manufacturing technology. METHODS: Images from 33 fetuses, including three sets of twins, were used. Fifteen fetuses were normal and evaluated only by 3DUS. Eighteen cases had abnormalities such as conjoined twins, tumors, aneuploidy, skeletal abnormalities, central nervous system abnormalities and facial or thoracic defects. Scans were performed using high-resolution 3DUS. In cases of abnormalities, MRI and CT were performed on the same day as 3DUS. The images obtained with 3DUS, CT or MRI were exported to a workstation in DICOM format. A single observer performed slice-by-slice manual segmentation using a digital high-definition screen. Software that converts medical images into numerical models was used to construct virtual 3D models, which were physically realized using additive manufacturing technologies. RESULTS: Physical models based on 3DUS, MRI and CT images either separately or combined were successfully generated. They were remarkably similar to the postnatal appearance of the aborted fetus or newborn baby, especially in cases with pathology. CONCLUSION: The use of 3DUS, MRI and CT may improve our understanding of fetal anatomical characteristics, and these technologies can be used for educational purposes and as a method for parents to visualize their unborn baby. The images can be segmented and applied separately or combined to construct 3D virtual and physical models.