Using concise morphological representations for computational modeling of the physics and mechanics of biological structures across scales
Morphology is a fundamental observable feature in biology and often the main product of microscopy-based anatomical studies. Our lab is interested in developing mathematical models and precise language that enable the interpretation of biological data, and automatic measurement of differences in biological shape. This allows us to relate complex biological shapes to the physics and mechanics underlying biological structures including cells and whole organisms. We generate shape libraries encompassing a wide range of biological structures and construct a vocabulary specific to biological morphology. Deciphering morphological features has the potential to further our understanding of normal and disease states, create models to predict disease progression, and build a bridge connecting biology and physics.
Biological shape is closely related to a set of underlying mechanical structures, often under direct physiological control at the cell level. A detailed understanding of how biological shape-outlines, as observed by microscopy for example, relate to mechanical load-bearing elements and the biological processes that influence them, can provide important insights across biology. Physical and mechanical computational models can already take into account a large range of morphogenetic factors. However, shape complexity, and our inability to capture it mathematically in a concise manner, is often a limiting factor of computations. Such computations often avoid morphologies more complex than simple spheres and ellipsoids or are inherently limited to specific symmetries.
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.