Models and Software

  1. Image Processing and Analysis

    Description: We are developing new methods of using MRI and CT to measure, infer, and estimate three-dimensional maps of important physiological parameters. These include extracellular diffusivity, hydraulic conductivity, extracellular volume fraction, capillary permeability, and elasticity, required as input by our computational models. Our maps of these physiological states may be used in diagnosing and monitoring disease progression.

    Therapy Monitoring

    infusate concentration

    Figure 1. Infusate concentration.
    We can make quantitative maps of the concentration of tracers

    Quantitative parameter

    Quantitative parameter

    Figure 2. Quantitative parameter maps.
    We have new algorithms that allow us to infer physiological parameters, not directly contained in magnetic resonance signals from those such as diffusivity, which are. The above figures show a calculation of extracellular volume fraction and interstitial pressure from diffusivity and other MR images.

    Brain surface segmentation

    Figure 3. Brain surface segmentation.
    We have automatic methods of segmentation that are already the best available. Improvements are under way.

  2. Model and simulations

    Description: Therataxis has developed fast stochastic simulation algorithms for transport in a strongly anisotropic, inhomogenous medium, implemented in a comprehensive C++ library designed for efficient prototyping of different mathematical models. For example, we can compute the concentration of a drug infused into brain tissue for individuals. Below we show some coarse (low resolution) inputs which is sometimes all that is available clinically. The figures show maps of several parameters in a planar section of a pig’s brain.

    fig. 4a Fig 4a. CSF Segmentation

    fig. 4b Fig 4b. Trace of Diffusion Tensor

    fig. 4c Fig 4c. Fractional Anisotropy of Diffusion Tensor

    fig. 4d Fig 4d. Extracellular Volume Fraction Estimation

    From the above images we compute the concentration of infusate. The figures below show the actual measured concentrations of a contrast agent (top row) at several different times during the infusion and the computed or simulated concentrations (bottom row). It should be noted that the concentration data are at higher resolution than the inputs needed to simulate these. Thus the remaining discrepancies may well be the result of the low resolution inputs to the calculation.

    figure 5 figure 5 figure 5 figure 5

    Figures 5. The measured concentrations at different times.

    figure 6 figure 6 figure 6 figure 6

    Figures 6. The computed concentrations to be compared with the figures in 5.

    Other applications can include: (i) electric fields in tissue for planning stimulation in diseases including epilepsy; (ii) temperature fields in tissue for calculating the spread of heat; (iii) chemotactic spread of cells, (iv) acoustic waveforms during speech production, and so on.

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