What is LMI?
The Laboratory of Mathematics in Imaging (LMI) is focused on the
application of mathematical theory, analysis, modeling, and signal
processing to medical imaging applications. Research projects within
the group cover computational and visual display research, and
research on novel imaging and treatment methods within the BWH
Department of Radiology. Modeling, and the development of novel and
efficient technology based on those models, lie at the heart of our
Members of the LMI collaborate with other departments within Brigham
and Women's Hospital, with other researchers at the Harvard Medical
School, with local universities such as Harvard, MIT, Tufts, and
Northeastern, and with gifted clinicians, researchers, and engineers
throughout the world.
What is our main mission?
Our mission is to improve human health by improving imaging technology used
in diagnosis, analysis, and treatment of disease. Our primary expertise is
in the application of advanced mathematical models to improve visualization
and analysis of raw imaging data. Examples include
- Diffusion MRI
- Image registration
- Data visualization
- Efficient data acquisition
The research at the LMI
The Laboratory of Mathematics in Imaging combines strengths in computer
science and mathematics with radiology and neuroscience. The combination of
theoretical and clinical expertise supports the overall research mission of
the LMI: develop quantitative and visual methods for analyzing medical
imaging data, and then refine and apply these methods to real-life
applications. These applications include, but are not limited to:
- White matter architecture from diffusion MRI in Schizophrenia
- Automated generation of patient-specific vasculature models
- Computer-assisted endovascular navigation for the treatment of brain aneurysms
- Image-data fusion methods for MR-guided Cardiac Ablation
- Automated image analysis tools in Chronic Obstructive Pulmonary Disease (COPD)
Examples of work
Uncertainty in diffusinon MRI tractography
Conventional tractography methods estimate fibers by tracing the direction of maximum water diffusivity. A main limitation of this traditional approach is that it gives an impression of being very precise. However, in practice there are several factors that introduce uncertainty in the tracking procedure. Noise, splitting and crossing fibers, head motion and image artifacts are all examples of factors that cause variability in the estimated fibers. To address this uncertainty we have been working on stochastic tractography methods, which aim to quantify and visualize the uncertainty associated with the estimated fibers. The figure shows, a probability density functions of the underlying fiber orientation for the three different voxels indicated in the FA map to the right.
Diffusion MRI visualization
Another line of work is to extend the widely used tensor model of the local water diffusion profile. Because of the relatively large voxel size in DT-MRI, a voxel may contain two or more fiber bundles with different orientations. The widely used tensor model, which assumes a single bundle in each voxel, is unable to describe such a situation. A model mismatch introduces extra variability in any parameter used for quantifying the anisotropy of the water diffusion, which ultimately leads to a loss of sensitivity when testing hypotheses regarding differences between schizophrenics and normal controls. We have developed a two-tensor model (see initial implementation in Peled et al., 2005), which recently was presented at the ISMRM 2005 conference. The traditional DT-MRI single tensor model is shown to the left, and the extended two-tensor model shown to the right. The two-tensor model allows the modeling of crossing fiber tracts.
Grouping diffusion MRI tractography resutls to white matter bundles
A clustering algorithm takes a number of traced fibers (left), extracts features from these fibers (middle), and produces a segmentation based on the similarity of the fibers (right). Our initial goal was to color fibers in order to enhance visualization and human perception of fiber trace connectivity. In (Brun et al., 2003) we developed a novel method for pseudo-coloring fiber traces, using a recent machine learning technique called Laplacian Eigenmaps, where fiber traces with similar connectivity were assigned similar pseudo-colors. This method is useful mainly in explorative studies.
In the result to the left, showing sagittal and axial views of the white matter fiber tracts demonstrate anatomical connectivity by fibers of similar colors, traces connecting similar areas on the cortical surface were considered more similar than traces connecting different cortical regions. Each fiber is mapped to a 3-dimensional space corresponding to the color components red, green and blue. Hence, color is used here to explain an abstract mapping of each fiber trace onto a three dimensional space using the criteria of similarity.
In more recent work (Brun et al., 2004), we introduced a method that aims to segment fibers into bundles. This method is based on a graph partitioning method called Normalized Cuts. The proposed method recursively divides clusters into two parts until a satisfactory segmentation has been obtained. A segmentation using this method is shown to the right.
This technique allows us to use fibers from multiple brains as input, and thereby obtain a simultaneous clustering and matching of the bundles in all brains. In addition, we automatically obtain correspondence of bundles across brains; by selecting one or several paths of interest in one brain, the most similar paths in all brains are obtained as the nearest points in the high- dimensional space.
Diffusion MRI in schizophrenia
Schizophrenia affects close to 1% of the general population and is often psychologically and financially devastating to patients, their families, and the community. The etiology of schizophrenia is currently unknown, although it is likely that there are several interactive biological factors (e.g., genetic factors, fetal anomalies) and environmental factors (e.g., viral infection, fetal insult) that predispose individuals to schizophrenia. Both post-mortem and neuroimaging studies have contributed significantly to what we know about the brain and schizophrenia.
There is also a growing body of evidence to suggest that a disturbance in connectivity between different brain regions, rather than abnormalities within the separate regions themselves, are responsible for the clinical symptoms and cognitive dysfunctions observed in this disorder. Thus an interest in white matter fiber tracts is emerging, as these structures provide anatomical connections between distant, as well as proximal, brain regions. This interest coincides with the recent advent of Diffusion Tensor Imaging (DTI), which makes it possible to evaluate the organization and coherence of white matter fiber tracts. This is an important advance as conventional MRI in vivo techniques are insensitive to fiber tract direction and organization, and have, in general, not consistently demonstrated white matter abnormalities. While the functional centers of the brain (cortex and nuclei) are easily appreciated with conventional MRI techniques, crucial brain connections (the white matter tracts) are not individually identifiable.
The Psychiatry Neruroscience Laboratory (PNL), headed by Professor Martha Shenton, is working closely with LMI on developing novel technology for comparing DT-MRI scans of patients with schizophrenia to populations of normal controls.
Diffusion MRI in neuro-surgery
In order to achieve its main goal of maximal tumor removal while avoiding
postoperative neurologic deficits, neuro-oncological surgery is strongly
dependent on image guidance. Among all currently available imaging
modalities, MRI provides the best anatomic detail and is highly sensitive
for intracranial pathology. However, conventional MRI does not detect the
exact location of white matter tracts or areas of cortical activation. This
essential in- formation can be obtained non-invasively by means of diffusion
MRI (dMRI) and functional MRI (fMRI) respectively. Here we present
our initial experience with fMRI and DT-MRI for surgical planning and
guidance in ten brain tumor cases.