About

The Laboratory of Mathematics in Imaging (LMI) is focused on the application of mathematical theory, analysis, modeling, and signal processing to medical imaging. Research projects within the group cover both novel theoretical contributions and translational clinical efforts. The research team combine strengths in computer science and mathematics with radiology, neuroscience, and novel MRI sequence developmentLearn more

Recent Publications

Patient-Specific Connectomic Models Correlate With, but Do Not Reliably Predict, Outcomes in Deep Brain Stimulation for Obsessive-Compulsive Disorder

Widge AS, Zhang F, Gosai A, Papadimitrou G, Wilson-Braun P, Tsintou M, Palanivelu S, Noecker AM, McIntyre CC, O'Donnell L, et al. Patient-Specific Connectomic Models Correlate With, but Do Not Reliably Predict, Outcomes in Deep Brain Stimulation for Obsessive-Compulsive Disorder. Neuropsychopharmacology. 2021.Abstract
Deep brain stimulation (DBS) of the ventral internal capsule/ventral striatum (VCVS) is an emerging treatment for obsessive-compulsive disorder (OCD). Recently, multiple studies using normative connectomes have correlated DBS outcomes to stimulation of specific white matter tracts. Those studies did not test whether these correlations are clinically predictive, and did not apply cross-validation approaches that are necessary for biomarker development. Further, they did not account for the possibility of systematic differences between DBS patients and the non-diagnosed controls used in normative connectomes. To address these gaps, we performed patient-specific diffusion imaging in 8 patients who underwent VCVS DBS for OCD. We delineated tracts connecting thalamus and subthalamic nucleus (STN) to prefrontal cortex via VCVS. We then calculated which tracts were likely activated by individual patients' DBS settings. We fit multiple statistical models to predict both OCD and depression outcomes from tract activation. We further attempted to predict hypomania, a VCVS DBS complication. We assessed all models' performance on held-out test sets. With this best-practices approach, no model predicted OCD response, depression response, or hypomania above chance. Coefficient inspection partly supported prior reports, in that capture of tracts projecting to cingulate cortex was associated with both YBOCS and MADRS response. In contrast to prior reports, however, tracts connected to STN were not reliably correlated with response. Thus, patient-specific imaging and a guideline-adherent analysis were unable to identify a tractographic target with sufficient effect size to drive clinical decision-making or predict individual outcomes. These findings suggest caution in interpreting the results of normative connectome studies.
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Significant Spirometric Transitions and Preserved Ratio Impaired Spirometry (PRISm) Among Ever-Smokers

Wan ES, Hokanson JE, Regan EA, Young KA, Make BJ, DeMeo DL, Mason SE, Estepar RSJ, Crapo J, Silverman EK. Significant Spirometric Transitions and Preserved Ratio Impaired Spirometry (PRISm) Among Ever-Smokers. Chest. 2021.Abstract
BACKGROUND: Emerging data from longitudinal studies suggest that PRISm, defined by proportionate reductions in FEV1 and FVC, is a heterogeneous population with frequent transitions to other lung function categories relative to individuals with normal and obstructive spirometry. Controversy regarding the clinical significance of these transitions exists (e.g., whether transitions merely reflect measurement variability or "noise"). RESEARCH QUESTION: Are individuals with PRISm enriched for transitions associated with substantial changes in lung function? STUDY DESIGN AND METHODS: Current and former smokers enrolled in COPDGene with spirometry available at Phases 1-3 (enrollment, 5-year, and 10-year follow-up) were analyzed. Post-bronchodilator lung function categories were: PRISm=FEV1<80% predicted with FEV1/FVC ratio≥0.7, GOLD0=FEV1≥80% predicted and FEV1/FVC ≥0.7, and obstruction=FEV1/FVC<0.7. "Significant-transition" status was affirmative if a subject belonged to ≥2 spirometric categories and had >10% change in FEV1% and/or FVC% predicted between consecutive visits. "Ever-PRISm" was present if a subject had PRISm at any visit. Logistic regression examined the association between "significant-transitions" and "ever-PRISm" status, adjusted for age, sex, race, FEV1% predicted, current smoking, pack-years, BMI, and ever-positive bronchodilator response. RESULTS: Among subjects with complete data (n=1,775) over 10.1±0.4 years of follow-up, the prevalence of PRISm remained consistent (10.4%-11.3%) between P1-P3, but nearly half of subjects with PRISm transitioned into or out of PRISm at each visit. 19.7% of subjects had a "significant transition"; "ever-PRISm" was a significant predictor of "significant transitions" (ORunadjusted=10.3, 95%CI=7.9-13.5, ORadjusted=14.9, 95%CI=10.9-20.7). Results were similar with additional adjustment for radiographic emphysema and gas trapping, when lower limit of normal criteria were used to define lung function categories, and when FEV1 alone (regardless of change in FVC%) was used to define "significant transitions" . INTERPRETATION: PRISm is an unstable group, with frequent significant transitions to both obstruction and normal spirometry over time.
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Concentration of 7Be, 210Pb, 40K, 137Cs, 134Cs Radionuclides in the Ground Layer of the Atmosphere in the Polar (Hornsund, Spitsbergen) and Mid-Latitudes (Otwock-Świder, Poland) Regions

Burakowska A, Kubicki M, Mysłek-Laurikainen B, Piotrowski M, Trzaskowska H, Sosnowiec R. Concentration of 7Be, 210Pb, 40K, 137Cs, 134Cs Radionuclides in the Ground Layer of the Atmosphere in the Polar (Hornsund, Spitsbergen) and Mid-Latitudes (Otwock-Świder, Poland) Regions. J Environ Radioact. 2021;240 :106739.Abstract
This paper presents results of measurements of selected gamma-radioactive radionuclide concentrations (7Be, 210Pb, 40K, 137Cs, 134Cs) in atmospheric aerosols registered in 2002-2017 at the Polish Polar Station of the Institute of Geophysics Polish Academy of Science in Hornsund and in the S. Kalinowski's Geophysical Observatory Institute of Geophysics Polish Academy of Science in Świder. The above measurements and tests are used to control and track long-term concentrations of radionuclides depending on the geometeorological conditions prevailing in the vicinity of the station. Collecting radiological data from polar regions and comparing them with data from medium latitudes leads to a better understanding of the mechanisms of creation and propagation of radionuclides in the air. Hornsund station is one of the northernmost measuring site for continuous airborne radionuclide monitoring in the Spitsbergen archipelago. It also allows the analysis of the relationship of radionuclides to the Earth's magnetic field.
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Time-Efficient Three-Dimensional Transmural Scar Assessment Provides Relevant Substrate Characterization for Ventricular Tachycardia Features and Long-Term Recurrences in Ischemic Cardiomyopathy

Merino-Caviedes S, Gutierrez LK, Alfonso-Almazán JM, Sanz-Estébanez S, Cordero-Grande L, Quintanilla JG, Sánchez-González J, Marina-Breysse M, Galán-Arriola C, Enríquez-Vázquez D, et al. Time-Efficient Three-Dimensional Transmural Scar Assessment Provides Relevant Substrate Characterization for Ventricular Tachycardia Features and Long-Term Recurrences in Ischemic Cardiomyopathy. Sci Rep. 2021;11 (1) :18722.Abstract
Delayed gadolinium-enhanced cardiac magnetic resonance (LGE-CMR) imaging requires novel and time-efficient approaches to characterize the myocardial substrate associated with ventricular arrhythmia in patients with ischemic cardiomyopathy. Using a translational approach in pigs and patients with established myocardial infarction, we tested and validated a novel 3D methodology to assess ventricular scar using custom transmural criteria and a semiautomatic approach to obtain transmural scar maps in ventricular models reconstructed from both 3D-acquired and 3D-upsampled-2D-acquired LGE-CMR images. The results showed that 3D-upsampled models from 2D LGE-CMR images provided a time-efficient alternative to 3D-acquired sequences to assess the myocardial substrate associated with ischemic cardiomyopathy. Scar assessment from 2D-LGE-CMR sequences using 3D-upsampled models was superior to conventional 2D assessment to identify scar sizes associated with the cycle length of spontaneous ventricular tachycardia episodes and long-term ventricular tachycardia recurrences after catheter ablation. This novel methodology may represent an efficient approach in clinical practice after manual or automatic segmentation of myocardial borders in a small number of conventional 2D LGE-CMR slices and automatic scar detection.
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Neural Networks for Parameter Estimation in Microstructural MRI: Application to a Diffusion-Relaxation Model of White Matter

de Almeida Martins JP, Nilsson M, Lampinen B, Palombo M, While PT, Westin C-F, Szczepankiewicz F. Neural Networks for Parameter Estimation in Microstructural MRI: Application to a Diffusion-Relaxation Model of White Matter. Neuroimage. 2021 :118601.Abstract
Specific features of white matter microstructure can be investigated by using biophysical models to interpret relaxation-diffusion MRI brain data. Although more intricate models have the potential to reveal more details of the tissue, they also incur time-consuming parameter estimation that may converge to inaccurate solutions due to a prevalence of local minima in a degenerate fitting landscape. Machine-learning fitting algorithms have been proposed to accelerate the parameter estimation and increase the robustness of the attained estimates. So far, learning-based fitting approaches have been restricted to microstructural models with a reduced number of independent model parameters where dense sets of training data are easy to generate. Moreover, the degree to which machine learning can alleviate the degeneracy problem is poorly understood. For conventional least-squares solvers, it has been shown that degeneracy can be avoided by acquisition with optimized relaxation-diffusion-correlation protocols that include tensor-valued diffusion encoding. Whether machine-learning techniques can offset these acquisition requirements remains to be tested. In this work, we employ artificial neural networks to vastly accelerate the parameter estimation for a recently introduced relaxation-diffusion model of white matter microstructure. We also develop strategies for assessing the accuracy and sensitivity of function fitting networks and use those strategies to explore the impact of the acquisition protocol. The developed learning-based fitting pipelines were tested on relaxation-diffusion data acquired with optimal and sub-optimal acquisition protocols. Networks trained with an optimized protocol were observed to provide accurate parameter estimates within short computational times. Comparing neural networks and least-squares solvers, we found the performance of the former to be less affected by sub-optimal protocols; however, model fitting networks were still susceptible to degeneracy issues and their use could not fully replace a careful design of the acquisition protocol.
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