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

Suprathreshold fiber cluster statistics: Leveraging white matter geometry to enhance tractography statistical analysis

Zhang F, Wu W, Ning L, McAnulty G, Waber D, Gagoski B, Sarill K, Hamoda HM, Song Y, Cai W, et al. Suprathreshold fiber cluster statistics: Leveraging white matter geometry to enhance tractography statistical analysis. Neuroimage. 2018;171 :341-354.Abstract
This work presents a suprathreshold fiber cluster (STFC) method that leverages the whole brain fiber geometry to enhance statistical group difference analyses. The proposed method consists of 1) a well-established study-specific data-driven tractography parcellation to obtain white matter tract parcels and 2) a newly proposed nonparametric, permutation-test-based STFC method to identify significant differences between study populations. The basic idea of our method is that a white matter parcel's neighborhood (nearby parcels with similar white matter anatomy) can support the parcel's statistical significance when correcting for multiple comparisons. We propose an adaptive parcel neighborhood strategy to allow suprathreshold fiber cluster formation that is robust to anatomically varying inter-parcel distances. The method is demonstrated by application to a multi-shell diffusion MRI dataset from 59 individuals, including 30 attention deficit hyperactivity disorder patients and 29 healthy controls. Evaluations are conducted using both synthetic and in-vivo data. The results indicate that the STFC method gives greater sensitivity in finding group differences in white matter tract parcels compared to several traditional multiple comparison correction methods.
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Exposure to Traffic Emissions and Fine Particulate Matter and Computed Tomography Measures of the Lung and Airways

Rice MB, Li W, Dorans KS, Wilker EH, Ljungman P, Gold DR, Schwartz J, Koutrakis P, Kloog I, Araki T, et al. Exposure to Traffic Emissions and Fine Particulate Matter and Computed Tomography Measures of the Lung and Airways. Epidemiology. 2018;29 (3) :333-341.Abstract
BACKGROUND: Exposure to ambient air pollution has been associated with lower lung function in adults, but few studies have investigated associations with radiographic lung and airway measures. METHODS: We ascertained lung volume, mass, density, visual emphysema, airway size, and airway wall area by computed tomography (CT) among 2,545 nonsmoking Framingham CT substudy participants. We examined associations of home distance to major road and PM2.5 (2008 average from a spatiotemporal model using satellite data) with these outcomes using linear and logistic regression models adjusted for age, sex, height, weight, census tract median household value and population density, education, pack-years of smoking, household tobacco exposure, cohort, and date. We tested for differential susceptibility by sex, smoking status (former vs. never), and cohort. RESULTS: The mean participant age was 60.1 years (standard deviation 11.9 years). Median PM2.5 level was 9.7 µg/m (interquartile range, 1.6). Living <100 m from a major road was associated with a 108 ml (95% CI = 8, 207) higher lung volume compared with ≥400 m away. There was also a log-linear association between proximity to road and higher lung volume. There were no convincing associations of proximity to major road or PM2.5 with the other pulmonary CT measures. In subgroup analyses, road proximity was associated with lower lung density among men and higher odds of emphysema among former smokers. CONCLUSIONS: Living near a major road was associated with higher average lung volume, but otherwise, we found no association between ambient pollution and radiographic measures of emphysema or airway disease.
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Bayesian uncertainty quantification in linear models for diffusion MRI

Sjölund J, Eklund A, Özarslan E, Herberthson M, Bånkestad M, Knutsson H. Bayesian uncertainty quantification in linear models for diffusion MRI. Neuroimage. 2018.Abstract
Diffusion MRI (dMRI) is a valuable tool in the assessment of tissue microstructure. By fitting a model to the dMRI signal it is possible to derive various quantitative features. Several of the most popular dMRI signal models are expansions in an appropriately chosen basis, where the coefficients are determined using some variation of least-squares. However, such approaches lack any notion of uncertainty, which could be valuable in e.g. group analyses. In this work, we use a probabilistic interpretation of linear least-squares methods to recast popular dMRI models as Bayesian ones. This makes it possible to quantify the uncertainty of any derived quantity. In particular, for quantities that are affine functions of the coefficients, the posterior distribution can be expressed in closed-form. We simulated measurements from single- and double-tensor models where the correct values of several quantities are known, to validate that the theoretically derived quantiles agree with those observed empirically. We included results from residual bootstrap for comparison and found good agreement. The validation employed several different models: Diffusion Tensor Imaging (DTI), Mean Apparent Propagator MRI (MAP-MRI) and Constrained Spherical Deconvolution (CSD). We also used in vivo data to visualize maps of quantitative features and corresponding uncertainties, and to show how our approach can be used in a group analysis to downweight subjects with high uncertainty. In summary, we convert successful linear models for dMRI signal estimation to probabilistic models, capable of accurate uncertainty quantification.
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Asymmetric Orientation Distribution Functions (AODFs) revealing intravoxel geometry in diffusion MRI

Cetin Karayumak S, Özarslan E, Unal G. Asymmetric Orientation Distribution Functions (AODFs) revealing intravoxel geometry in diffusion MRI. Magn Reson Imaging. 2018;49 :145-158.Abstract
Characterization of anisotropy via diffusion MRI reveals fiber crossings in a substantial portion of voxels within the white-matter (WM) regions of the human brain. A considerable number of such voxels could exhibit asymmetric features such as bends and junctions. However, widely employed reconstruction methods yield symmetric Orientation Distribution Functions (ODFs) even when the underlying geometry is asymmetric. In this paper, we employ inter-voxel directional filtering approaches through a cone model to reveal more information regarding the cytoarchitectural organization within the voxel. The cone model facilitates a sharpening of the ODFs in some directions while suppressing peaks in other directions, thus yielding an Asymmetric ODF (AODF) field. We also show that a scalar measure of AODF asymmetry can be employed to obtain new contrast within the human brain. The feasibility of the technique is demonstrated on in vivo data obtained from the MGH-USC Human Connectome Project (HCP) and Parkinson's Progression Markers Initiative (PPMI) Project database. Characterizing asymmetry in neural tissue cytoarchitecture could be important for localizing and quantitatively assessing specific neuronal pathways.
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Alteration of putaminal fractional anisotropy in Parkinson's disease: a longitudinal diffusion kurtosis imaging study

Surova Y, Nilsson M, Lampinen B, Lätt J, Hall S, Widner H, van Westen D, Hansson O. Alteration of putaminal fractional anisotropy in Parkinson's disease: a longitudinal diffusion kurtosis imaging study. Neuroradiology. 2018;60 (3) :247-254.Abstract
PURPOSE: In Parkinson's disease (PD), pathological microstructural changes occur that may be detected using diffusion magnetic resonance imaging (dMRI). However, there are few longitudinal studies that explore the effect of disease progression on diffusion indices. METHODS: We prospectively included 76 patients with PD and 38 healthy controls (HC), all of whom underwent diffusion kurtosis imaging (DKI) as part of the prospective Swedish BioFINDER study at baseline and 2 years later. Annualized rates of change in DKI parameters, including fractional anisotropy (FA), mean diffusivity (MD), and mean kurtosis (MK), were estimated in the gray matter (GM) by placing regions of interest (ROIs) in the basal ganglia and the thalamus, and in the white matter (WM) by tract-based spatial statistics (TBSS) analysis. RESULTS: When adjusting for potential confounding factors (age, gender, baseline-follow-up interval, and software upgrade of MRI scanner), only a decrease in FA in the putamen of PD patients (β = - 0.248, P < .01) over 2 years was significantly different from the changes observed in HC over the same time period. This 2-year decrease in FA in the putamen in PD correlated with higher L-dopa equivalent dose at baseline (Spearman's rho = .399, P < .0001). CONCLUSION: The study indicates that in PD microstructural changes in the putamen occur selectively over a 2-year period and can be detected with DKI.
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Respiratory Symptoms in Young Adults and Future Lung Disease: The CARDIA Lung Study

Kalhan R, Dransfield MT, Colangelo LA, Cuttica MJ, Jacobs DR, Thyagarajan B, Estepar RSJ, Harmouche R, Onieva Onieva J, Ash SY, et al. Respiratory Symptoms in Young Adults and Future Lung Disease: The CARDIA Lung Study. Am J Respir Crit Care Med. 2018.Abstract
RATIONALE: There are limited data on factors in young adulthood that predict future lung disease. OBJECTIVE: To determine the relationship between respiratory symptoms, loss of lung health, and incident respiratory disease in a population-based study of young adults. METHODS: Prospective data from 2749 participants in the Coronary Artery Risk Development in Young Adults (CARDIA) study who completed respiratory symptom questionnaires at baseline and 2 years later and repeated spirometry measurements over 30 years. MEASUREMENTS AND MAIN RESULTS: Cough or phlegm, episodes of bronchitis, wheeze, shortness of breath, and chest illnesses at both baseline and year 2 were the main predictor variables in models assessing decline in forced expiratory volume in 1 second (FEV1) and forced vital capacity (FVC) from year 5 to year 30, incident obstructive and restrictive lung physiology, and visual emphysema on thoracic CT. After adjustment for covariates including body mass index (BMI), asthma, and smoking, report of any symptom was associated with -2.71 mL/year excess decline in FEV1 (p<0.001) and -2.18 in FVC (P<0.001) as well as greater odds of incident (pre-bronchodilator) obstructive (odds ratio (OR) 1.63, 95% CI 1.24, 2.14) and restrictive (OR 1.40, 95% CI 1.09, 1.80) physiology. Cough-related symptoms (OR 1.56, 95% CI 1.13, 2.16) were associated with greater odds of future emphysema. CONCLUSIONS: Persistent respiratory symptoms in young adults are associated with accelerated decline in lung function, incident obstructive and restrictive physiology, and greater odds of future radiographic emphysema.
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