Can You Hear the Shape of a Drum?

If you had perfect pitch and listened to a recording of the sounds a drum made when struck, could you determine the shape of the drum? This question is an example of an inverse problem; inverse problems arise in medical imaging, oil prospecting, spectroscopy, and many other fields. We’ll first discuss the analogous question in the simpler setting of plucking a string. Then we’ll tackle the problem for drums and see that there are some surprises. Finally, I will give a brief indication of how this problem relates to some of my recent research. The emphasis will be on the ideas rather than on the technical details, so there will be pretty pictures instead of equations.

Interhemispheric connections shape subjective experience of bistable motion

The right and left visual hemifields are represented in different cerebral hemispheres and are bound together by connections through the corpus callosum. Much has been learned on the functions of these connections from split-brain patients [1-4], but little is known about their contribution to conscious visual perception in healthy humans. We used diffusion tensor imaging and functional magnetic resonance imaging to investigate which callosal connections contribute to the subjective experience of a visual motion stimulus that requires interhemispheric integration. The "motion quartet" is an ambiguous version of apparent motion that leads to perceptions of either horizontal or vertical motion [5]. Interestingly, observers are more likely to perceive vertical than horizontal motion when the stimulus is presented centrally in the visual field [6]. This asymmetry has been attributed to the fact that, with central fixation, perception of horizontal motion requires integration across hemispheres whereas perception of vertical motion requires only intrahemispheric processing [7]. We are able to show that the microstructure of individually tracked callosal segments connecting motion-sensitive areas of the human MT/V5 complex (hMT/V5+; [8]) can predict the conscious perception of observers. Neither connections between primary visual cortex (V1) nor other surrounding callosal regions exhibit a similar relationship.

Time-lapse microscopy and classification of 2D human mesenchymal stem cells based on cell shape picks up myogenic from osteogenic and adipogenic differentiation

Current methods to characterize mesenchymal stem cells (MSCs) are limited to CD marker expression, plastic adherence and their ability to differentiate into adipogenic, osteogenic and chondrogenic precursors. It seems evident that stem cells undergoing differentiation should differ in many aspects, such as morphology and possibly also behaviour; however, such a correlation has not yet been exploited for fate prediction of MSCs. Primary human MSCs from bone marrow were expanded and pelleted to form high-density cultures and were then randomly divided into four groups to differentiate into adipogenic, osteogenic chondrogenic and myogenic progenitor cells. The cells were expanded as heterogeneous and tracked with time-lapse microscopy to record cell shape, using phase-contrast microscopy. The cells were segmented using a custom-made image-processing pipeline. Seven morphological features were extracted for each of the segmented cells. Statistical analysis was performed on the seven-dimensional feature vectors, using a tree-like classification method. Differentiation of cells was monitored with key marker genes and histology. Cells in differentiation media were expressing the key genes for each of the three pathways after 21 days, i.e. adipogenic, osteogenic and chondrogenic, which was also confirmed by histological staining. Time-lapse microscopy data were obtained and contained new evidence that two cell shape features, eccentricity and filopodia (= 'fingers') are highly informative to classify myogenic differentiation from all others. However, no robust classifiers could be identified for the other cell differentiation paths. The results suggest that non-invasive automated time-lapse microscopy could potentially be used to predict the stem cell fate of hMSCs for clinical application, based on morphology for earlier time-points. The classification is challenged by cell density, proliferation and possible unknown donor-specific factors, which affect the performance of morphology-based approaches. Copyright © 2012 John Wiley & Sons, Ltd.

Pathology hinting as the combination of automatic segmentation with a statistical shape model

With improvements in acquisition speed and quality, the amount of medical image data to be screened by clinicians is starting to become challenging in the daily clinical practice. To quickly visualize and find abnormalities in medical images, we propose a new method combining segmentation algorithms with statistical shape models. A statistical shape model built from a healthy population will have a close fit in healthy regions. The model will however not fit to morphological abnormalities often present in the areas of pathologies. Using the residual fitting error of the statistical shape model, pathologies can be visualized very quickly. This idea is applied to finding drusen in the retinal pigment epithelium (RPE) of optical coherence tomography (OCT) volumes. A segmentation technique able to accurately segment drusen in patients with age-related macular degeneration (AMD) is applied. The segmentation is then analyzed with a statistical shape model to visualize potentially pathological areas. An extensive evaluation is performed to validate the segmentation algorithm, as well as the quality and sensitivity of the hinting system. Most of the drusen with a height of 85.5 microm were detected, and all drusen at least 93.6 microm high were detected.

Validation of a statistical shape model-based 2D/3D reconstruction method for determination of cup orientation after THA

The aim of this study was to validate the accuracy and reproducibility of a statistical shape model-based 2D/3D reconstruction method for determining cup orientation after total hip arthroplasty. With a statistical shape model, this method allows reconstructing a patient-specific 3D-model of the pelvis from a standard AP X-ray radiograph. Cup orientation (inclination and anteversion) is then calculated with respect to the anterior pelvic plane that is derived from the reconstructed model.

Age, microbiota, and T cells shape diverse individual IgA repertoires in the intestine

Intestinal immunoglobulin A (IgA) ensures host defense and symbiosis with our commensal microbiota. Yet previous studies hint at a surprisingly low diversity of intestinal IgA, and it is unknown to what extent the diverse Ig arsenal generated by somatic recombination and diversification is actually used. In this study, we analyze more than one million mouse IgA sequences to describe the shaping of the intestinal IgA repertoire, its determinants, and stability over time. We show that expanded and infrequent clones combine to form highly diverse polyclonal IgA repertoires with very little overlap between individual mice. Selective homing allows expanded clones to evenly seed the small but not large intestine. Repertoire diversity increases during aging in a dual process. On the one hand, microbiota-, T cell-, and transcription factor RORγt-dependent but Peyer's patch-independent somatic mutations drive the diversification of expanded clones, and on the other hand, new clones are introduced into the repertoire of aged mice. An individual's IgA repertoire is stable and recalled after plasma cell depletion, which is indicative of functional memory. These data provide a conceptual framework to understand the dynamic changes in the IgA repertoires to match environmental and intrinsic stimuli.