John Bodenschatz

Education

• 2021 - Present      Ph.D. Candidate in Computational Sciences, Marquette University, Milwaukee, WI
• 2021 - 2023          M.S. Applied Statistics, Marquette University, Milwaukee, WI
• 2017 - 2021          B.S. Mathematics, Physics, University of Cincinnati, Cincinnati, OH

Experience

• 08/2024 - Present :   Research Assistant, Department of Mathematical and Statistical Sciences, Marquette University, Milwaukee, WI
• 08/2021 - 05/2024 :  Teaching Assistant, Department of Mathematical and Statistical Sciences, Marquette University, Milwaukee, WI
• Calculus 1
• Calculus 2
• Multivariable Calculus
• Differential Equations
• Elements of Calculus
• Elementary Statistics
• Biostatistical Methods and Models

Research

1. Simulation and Harmonic Analysis of k-Space Readout (SHAKER)

Running fMRI experiments with human subjects is a temporally and financially costly task. Many researchers turn to simulated data to develop and refine models as a result. This aim of this research project was to develop a comprehensive MATLAB package for simulating complex-valued fMRI time series data, which we call SHAKER. SHAKER simulates fMRI data in a physically accurate representation, using steady-state solutions of the Bloch equations to generate k-space measurements. SHAKER allows for users to adjust any relevant MR parameters, including custom pulse sequences and k-space trajectories. Some common statistical analysis tools are also built-in, with templates for custom applications to be inserted as well.

A draft manustript for SHAKER can be found on arXiv. This manuscript is currently under review for a scientific journal. The lateset version of SHAKER can be found on GitHub. If you have any features that you would like to see added, please reach out!

The below picture is a screenshot of the SHAKER GUI. The top left pane is where the phantom can be viewed and a slice can be selected. The bottom left pane is where MR and fMRI xperimental parameters are adjusted. The top right pane is where simulated data can be viewed. The bottom right pane is where some statistical analysis can be conducted on the simulated data.



2. Bayesian Magnitude and Phase Estimation of Non-Cartesian k-Space for FMRI

It is well known in fMRI studies that the first three or so images in a time series have much higher signal than the remainder of the time series. The remaining steady state images hahve singificantly reduced signal. This project aims to use the first three images and known distributions for fMRI k-space data to form posterior estimations of the spatial frequency coefficients. A manuscript of this work is in submission for review for a scientific journal.

The below picture outlines the process of my second project. The first column shows the k-space array and reconstructed image that are formed from the calibration data (the first three images)- this constitutes the prior. The second column shows what the steady state data looks like. It has much weaker signal resulting in a low SNR and CNR. This is the likelihood. The last two columns show the results of the two Bayesian methods to form posterior measurements based on the prior and observed likelihood. Both the MAP and MPM methods perform similarly well, improving both SNR and CNR in the image. The ability to detect task active voxels is not inhibited by this process.



3. Increased Brain Activation Power from A Mathematically Accurate Angular Phase Model

My third project (which I often refer to as "project 2.5") involves using maximum likelihood estimation to detect phase activation in experimental fMRI data. The distribution of an individual voxel's time series of phase measurements is often simplified to be the normal distribution in fMRI. This is only acceptable for voxels in regions of high SNR. A more accurate model uses an unamed distribution from Lathi (1983). This project focuses on task activation in the often ignored phase part of the complex-valued reconstructed images. We use maximum likelihood estimation to perform a hypothesis test on the existance of a linear change in phase that is associated with task. This gives a likelihood ratio statistic comparing the null hypothesis (no change in phase) with the alternative hypothesis (linear change in phase associated with task). The picture below shows maximum likelihook images for the values of baseline phase (theta_0) and task related phase change (theta_1). On the right is the resulting z statistics that commes from the likelihood ratio test. The magenta arrow and circle highlight the detected region of task-related activation in the left momtor cortex, which corresponds to the expected region of activation for the performed right hand finger tapping experiment.

4. Bayesian Estimation and Reconstruction of Subsampled Non-Cartesian k-Space for FMRI

My final and ongoing project aims to significantly reduced dynamic scan times by employing Bayesian methods to non-Cartesian (in particular, radial) trajectories of k-space. This work is in collaboration with Dr. Tugan Muftuler (MCW) whose previous work on Highly Accelerated Projection Imaging (HAPI, 2013) will form the groundwork for this project. The below image depicts the Fourier slice theorem, a clever mathematical theorem and necessary tool for the reconstruction of images when using HAPI.