S14DiffuseOpticalTomography

*EDITOR'S NOTE* When the original page on the UMNWiki had no coherent ordering for the images - they were scattered in the text with no rhyme or reason. As I did the transfer from UMNWiki to Google Sites I just put all the images at the end of the page instead.

-- Main.perri142 - 17 May 2014

Diffuse optical tomography is an imaging method using fluorescence-based methods to create 3-dimensional images of masses in tissue. It can be modeled as a diffusive process through tissue. This model is used to infer localized properties within the medium. Medically, this could be used to find tumors or blood clots in the body. Originally light enters the medium in a continuous wave with a direction, but after scattering begins, it can be modeled as a diffusive process. In this experiment, the process will be modeled by directing a light on an object placed in coffee creamer, which simulates tissue, and measuring the intensity of the scattered light at various positions along the surface of the liquid. Coffee creamer can be used in this case because it is a turbid medium, like human tissue, which means that it contains many suspended particles in the fluid such that light is easily deflected when passing through. When an object is placed in the medium, it will absorb some of the photons. Therefore, the photo-detector will only detect the photons around the object. Based on these measurements, the size, shape, and location of the object can be determined. By testing this measurement process with the light source placed at various distances from the object, the requirements for using this technique to accurately determine the size, shape, and location of the object in the medium can be determined.

Theory for this experiment is a bit extensive. Complicated math analysis and computer coding is required to fully complete the analysis. The radiative transfer equation can mathematically model the transfer of energy as photons move inside a tissue. To solve this equation, a diffusive approximation is assumed that the scattering coefficient is larger than the absorption. When an arbitrary sphere is being measured within the medium, light impacts it from multiple directions. To determine the amount of light that is absorbed at any given point on the sphere, the amount of photons traversing the unit cross-section of this sphere, or the fluence rate, is calculated. Using the diffusion approximation in the radiative transfer equation, photon fluence is represented. To find a realistic model for the photon fluence, the diffusive equation was solved using Green's function. The boundaries of the experiment as needed to solve are assumed that the medium is infinite and homogeneous with an infinte, planar interface between the turbid medium and air. Using the method of images to reproduce the boundary conditions of this problem and assuming that the image source is at position and the detector is at z=0, the fluence equation then becomes:

where is the distance between the detector and the point source in the turbid medium and is the distance between the detector and the image source.

In the case of large source detector separations, with r being the source-detector separation, the fluence rate can be approximated by a linear equation as (3)

This equation implies that the measured intensity is proportional to the fluence. The logarithmic decay of the intensity with increasing source detector separation can be approximated by a line with a slope , the attenuation coefficient. This slope can be fitted and used to characterize the turbid medium, so that a comparison can be made between the amount of light scattered. By determining how light propagates through the uniform medium, the presence and spatial characteristics of a foreign object can be observed through MatLab analysis.

Our setup was basic as required for transfer to classroom usage. We used blue LEDs, glass dishes, a circuit board, resistors, cables, power sources, an x-y plotter, and the computer equipped with a DAQ card. We utilized lab view to run the X-Y plotter consistently. To avoid moving the system 3 LEDs were set up with individual wires running out. A diagram of the setup is as shown

Our anaylsis did not run smoothly, but graphing our raw data in Excel did give us an image of the object which we could find resolution from. Our resolution was of 2mm by 2mm. We could definitely see shapes. An example of this can be seen in our analysis of a tri-bead.

To demonstrate our understanding of the analysis process, an example fluence set was run through our Matlab program. This simple version had only one absorption location, and gave us an image. That we could use to determine the size and other characteristics of our anomaly.