My published research revolves around two main themes:
Motion Estimation: The ability to measure the way an organ move noninvasively
Soft-tissue Mechanics: Understanding the relationship between motion and its causes.
More information below.
Structure of the Tongue
This study consisted of constructing and testing a model of the structure of the tongue. In particular, we modeled the direction of muscle fibers. This information will be used to better understand how the tongue moves while we speak. More information can be found in the journal article.
Tracts of the genioglossus muscle
The tracts capture the approximate direction of muscle fibers. These results were obtained using diffusion-tensor magnetic resonance imaging (DT-MRI)
FE model superimposed on the tongue
The FE model surface (gray-blue), has a similar shape to the native tongue.
The model is used to determine the approximate direction of fibers.
Measurement of Brain Motion
Part of my research deals with measuring brain motion. Certain types of sudden brain deformation result in traumatic brain injury (TBI). Understanding how TBI occurs can help us prevent it.
Direct observation of the brain during an brain injury would yield useful information to better understand TBI, but there are great challenges for obtaining such observations. Alternatively, we can approximate how the brain deforms during an injurious impact using simulations. Although some of these approximations will be wrong at first, experimental observations of brain motion during a safe activity (which is the focus of this research) could be used to improve the accuracy of simulations. Also, the methods developed to make these initial observations could be the starting point for observations in experimental models during high-acceleration impact.
A manuscript with a detailed description of this research is currently undergoing peer review.
Brain motion estimation starts with the acquisition of tagged MRI. The patterns (grids or lines), which are referred as "tags" are not quite part of the anatomy, but arise from spatial modulation of magnetization. The tags move with the tissue; thus, by tracking tag motion, we can measure how the underlying tissue moves. My collaborators have designed custom equipment and techniques to acquire tagged MRI while a volunteer moves their head.
There are different ways to track MRI tags across a sequence of time frames. One of the things that I do is design and evaluate these techniques. Not long ago, we developed a method to track tagged MRI using finite-element models, which enables motion estimation in 4D (volume and time). The goal now is to measure brain motion during different types of controlled motion.
After tracking, we can measure displacement (a vector field), or deformation (which is measured using strain,--a tensor field). Since MRI allows anatomical characterization, motion can be associated with distinct features, such as anatomical structures or fiber orientation.
HARP-FE stands for HARmonic Phase analysis with Finite Elements. The publication associated with this project can be found here. The idea in HARP is basically to follow (or track) points in space that the same harmonic phase values. What is harmonic phase? It is a quantity derived from MRIs with tag lines, which are shown below. One of the problems with regular HARP is that some points are affected by noise, resulting in tracking errors. What makes HARP-FE special is that it uses a finite-element model of the object to be tracked--the model helps to filter out the noise and makes it so that the output behaves as a simulated physical object.
Experimentally Driven Finite-Element Model
Traditionally finite-element models are used to simulate motion by solving a boundary value problem. In HARP-FE imaging information is transformed into a pseudo force field which generates motion. For this reason, the result is more of a measurement as opposed to a simulation.
Here are two MRIs of a gelatin phantom. In traditional MRIs the cylindrical phantom will appear as white circles. In tagged MRI, we see a grid pattern (the tags), which moves with the object. If we compared two images acquired before and after motion has occurred, we can estimate displacement by following the point as it deforms.
Extraction of Harmonic Images
We can extract harmonic phase images for HARP-FE by applying a multiplicative Fourier filter that extracts part of the spectrum of an MRI image. The output is complex, having a harmonic phase as well as a harmonic magnitude.
A neat feature of combining imaging information and mechanical models is that we can measure values beyond just motion. If we have a good idea of the material behavior of the object, we can estimate stress, which are related to the internal forces that keep particles together.
Applications of MRI-Based Motion Tracking
Motion is very important to study many organs that depend on motion to function, such as the heart and tongue. In other cases, like in the brain, motion can drastically affect function.
Structure of the Right Ventricle
This was a numerical study on the effects of right-ventricular fiber orientation during pressure overload. The study is studied in detail here. In short, we build computational models of the heart to see how fiber orientation affects cardiac output measured by ejection fraction. We were particularly interested in right-ventricular pressure overload, so the challenge was to construct models that were representative of abnormal hearts. We approached this challenge by controlling for modeling variables that have been known to change during pressure overload.
Modeled Fiber Distribution
Virtual fibers can help us visualize the direction of cardiac fibers in the model. As the image shows, these fibers change direction from the inside to the outside of the heart. A the direction of the fibers can be measured by their helix angle (with respect to the equator). In this study we varied this direction to assess the effect of changes in helix angle on cardiac ejection fraction.
Finite-Element of the Heart
These kinds of models are relatively common. The anatomy of the heart (geometry) is constructed tetrahedral elements. These elements are also used to enforce material behavior and boundary interactions.
Finite-Element Extrapolation of Diffusion MRI
This study shows how to use finite-element models to approximate what happens "in between frames" of a diffusion MRI time sequence. The publication associated with this project can be found here. On a personal note, this project helped me show how medical imaging and mechanics can work together: Imaging by itself was accurate, but not have sufficient resolution. Modeling by itself had arbitrary resolution, but was not very accurate. If we combine them, we can get at the best of both worlds :)
Moving Virtual Fibers
This image shows virtual fibers (from diffusion MRI) that move according to a mechanical model of the left ventricle.
Animation of Left-Ventricular Fiber Directions
Each cylinder represents the local fiber direction. Cardiac fiber orientations are rather complex, but this is an approximation of the main direction as it changes across the cardiac cycle.
Measurement of Cardiac Motion
This study focuses on motion estimation of cardiac tissue. What is interesting about this method, in my opinion, is the length scale of the motion involved; we used rats--so everything is tiny. These type of analysis is important because many promising cures for heart disease are tested in rats, and being able to see what happens can bring key clues about how these cures perform. The publication associated with this project can be found here.
This image shows how different parts of the left ventricle move from diastole to systole.
Length Scale Comparison
Here's the image above at about the same scale as a US quarter.
Measurement of Vascular Motion
Changes in vein stiffness are associated to problems in fistulas for dialysis. The gist of this study was to be able to measure deformation in veins subjected to a controlled load. By knowing the load and the amount of motion, we can estimate the relative stiffness of the tissue. Details about this project can be found here.
Samples, Images, and Models
The sample above was imaged using a CT scanner while being pressurized across different loads. We used images to calculate the mount of motion resulting from loading. Then, we constructed a model of the vein, and used it to "guess" its relative stiffness across the same loads used in read life--If the guess of stiffness was too low, then motion was too high (and viceversa). In actuality, we used numerical optimization to get at the best estimate of stiffness.
CT Scans at Different Pressures
CT scans produce 3D images, which allows us to see the vein from different perspectives. In this axial image, we can see how pressure moves the walls of the vein radially.
This is the specimen after optimization. The best stiffness values resulted in simulated motion that was similar to what we observed using the images.