Khairy Lab

One common method is surface tessellation. Although able to capture complex shapes, it includes many parameters, only encodes local information and remains a highly approximate method for calculations requiring surface derivatives. In addition, such shape representations do not convey biological meaning in their shape descriptors.  We circumvent all of the above drawbacks and apply a concept from Fourier series expansion approximations by making use of the spherical harmonics basis functions and shape parameterization. The parametric application of spherical harmonics, with its global descriptors, has tremendous potential for biology. For example, we can create an equation that models the mechanics of cellular membranes to predict the biconcave disc structure of circulating red blood cells. Careful alterations to equation parameters that reflect and match real-life perturbations occurring in mechanical properties of these cells in certain disease states, produces predicted shapes that match those observed in pathological conditions. 

Developing this method and applying it to imagery-derived biological morphology across scales is a focus of our research. We are also interested in enhancing the images themselves using state-of-the-art deep learning methodology for image restoration, registration, segmentation and mixed-modality data fusion. Applications of advanced image analysis and three-dimensional Fourier parameterization in our group range from modeling the nuclear envelope, and cataloguing other subcellular structures, to precise morphological quantification of tumors and whole brain regions. The wealth of high-resolution and high-information-content multi-dimensional data that modern imaging technology provides continues to fuel all our efforts.