In collaboration with the with Catherine Blish and her lab at Stanford School of Medicine, I am investigating how NK cells can be harnessed for therapeutic purposes. I develop and consult for several projects using RNA-seq, microarrays, and CyTOF data.
In this applied statistics project, I modeled brain connectivity for functional resting-state Magnetic Resonance Imaging (rfMRI) studies using two multivariate heteroscedasticity models. I applied our models to processed brain connectivity data from the Human Connectome Project (HCP) to compare short and conventional sleepers.
In collaboration with Allan L. Reiss and his lab at Stanford School of Medicine, I studied interactions between brain imaging and cognitive data in girls with Turner syndrome. The procedure combines multi-table methods with permutation tests by constructing cluster size test statistics that incorporate spatial dependencies.
In this mathematical statistics project, I estimated running times of Hamiltonian Monte Carlo in high dimensions using Riemannian geometry and coarse Ricci curvature. I proposed a new metric based on the generalization of curvature to Riemannian manifolds, namely sectional curvature. I derived asymptotic sectional curvature for the multivariate normal distribution and showed simulation results for the multivariate t distribution with varying degrees of freedom. My results suggest sectional curvature as a quality control tool during Hamiltonian Monte Carlo simulations.
My first three years as a postdoctoral fellow were funded by the Swiss National Science Foundation for a project on uncertainty quantification in computational anatomy. Most neuroimaging studies (and medical imaging studies in general) require registration of subjects to a template brain. The goal is it estimate non-linear deformations that map subjects to a template brain. Many algorithms are available, but few provide confidence or credible intervals. I addressed this issue in two projects.
First, I used modern Bayesian nonparametrics to find regions of interest in computed tomography images of the human spine:
Second, I built a Bayesian registration model and implemented the Hamiltonian Monte Carlo sampler to draw samples from its posterior distribution:
During my PhD, I introduced a new type of structured medial image registration algorithm that can handle multiscale hierarchical anatomical structures. I applied my new method to mandible imaging data and showed how to design medical implants that fit a large population of people.
I applied my new registration method to a wide range of clinical applications. In collaboration with orthopaedic researchers, I compared the shape symmetry between left and right femur bones. In collaboration with orthopaedic implant designers, I constructed virtual mandible bones for better implant fitting and design. In collaboration with cardiac researchers, I modeled the dynamics of the human heart using ultrasound imaging. In collaboration with an orthopaedic surgeon in Argentina, I developed a bone allograft selection algorithm to pick the optimal bone from a femur bone bank for tumor replacement. In collaboration with mechanical engineers, I constructed statistical shape and appearance models to evaluate the mechanical properties of femur bones.
During my PhD, I classified stem cells during differentiation based on their shape from time-lapse video microscopy. My algorithm was able to distinguish myogenic from osteogenic and adipogenic cells.
For my MSc thesis, I implemented fast GPU code using shader processing to model soft tissue deformations with Markov random fields.