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

Characterization of Spatial Dynamics of Fmri Data in White Matter Using Diffusion-Informed White Matter Harmonics

Behjat H, Aganj I, Abramian D, Eklund A, Westin C-F. Characterization of Spatial Dynamics of Fmri Data in White Matter Using Diffusion-Informed White Matter Harmonics. Proc IEEE Int Symp Biomed Imaging. 2021;2021 :1586-90.Abstract
In this work, we leverage the Laplacian eigenbasis of voxel-wise white matter (WM) graphs derived from diffusion-weighted MRI data, dubbed WM harmonics, to characterize the spatial structure of WM fMRI data. Our motivation for such a characterization is based on studies that show WM fMRI data exhibit a spatial correlational anisotropy that coincides with underlying fiber patterns. By quantifying the energy content of WM fMRI data associated with subsets of WM harmonics across multiple spectral bands, we show that the data exhibits notable subtle spatial modulations under functional load that are not manifested during rest. WM harmonics provide a novel means to study the spatial dynamics of WM fMRI data, in such way that the analysis is informed by the underlying anatomical structure.
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Mapping Prostatic Microscopic Anisotropy Using Linear and Spherical B-Tensor Encoding: A Preliminary Study

Nilsson M, Eklund G, Szczepankiewicz F, Skorpil M, Bryskhe K, Westin C-F, Lindh C, Blomqvist L, Jäderling F. Mapping Prostatic Microscopic Anisotropy Using Linear and Spherical B-Tensor Encoding: A Preliminary Study. Magn Reson Med. 2021.Abstract
PURPOSE: Tensor-valued diffusion encoding provides more specific information than conventional diffusion-weighted imaging (DWI), but has mainly been applied in neuroimaging studies. This study aimed to assess its potential for the imaging of prostate cancer (PCa). METHODS: Seventeen patients with histologically proven PCa were enrolled. DWI of the prostate was performed with linear and spherical tensor encoding using a maximal b-value of 1.5 ms/µm2 and a voxel size of 3 × 3 × 4 mm3 . The gamma-distribution model was used to estimate the mean diffusivity (MD), the isotropic kurtosis (MKI ), and the anisotropic kurtosis (MKA ). Regions of interest were placed in MR-defined cancerous tissues, as well as in apparently healthy tissues in the peripheral and transitional zones (PZs and TZs). RESULTS: DWI with linear and spherical encoding yielded different image contrasts at high b-values, which enabled the estimation of MKA and MKI . Compared with healthy tissue (PZs and TZs combined) the cancers displayed a significantly lower MD (P < .05), higher MKI (P < 10-5 ), and lower MKA (P < .05). Compared with the TZ, tissue in the PZ showed lower MD (P < 10-3 ) and higher MKA (P < 10-3 ). No significant differences were found between cancers of different Gleason scores, possibly because of the limited sample size. CONCLUSION: Tensor-valued diffusion encoding enabled mapping of MKA and MKI in the prostate. The elevated MKI in PCa compared with normal tissues suggests an elevated heterogeneity in the cancers. Increased in-plane resolution could improve tumor delineation in future studies.
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Cross-term-compensated gradient waveform design for tensor-valued diffusion MRI

Szczepankiewicz F, Sjölund J. Cross-term-compensated gradient waveform design for tensor-valued diffusion MRI. J Magn Reson. 2021;328 :106991.Abstract
Diffusion MRI uses magnetic field gradients to sensitize the signal to the random motion of spins. In addition to the prescribed gradient waveforms, background field gradients contribute to the diffusion weighting and thereby cause an error in the measured signal and consequent parameterization. The most prominent contribution to the error comes from so-called 'cross-terms.' In this work we present a novel gradient waveform design that enables diffusion encoding that cancels such cross-terms and yields a more accurate measurement. This is achieved by numerical optimization that maximizes encoding efficiency with a simultaneous constraint on the 'cross-term sensitivity' (c = 0). We found that the optimized cross-term-compensated waveforms were superior to previous cross-term-compensated designs for a wide range of waveform types that yield linear, planar, and spherical b-tensor encoding. The efficacy of the proposed design was also demonstrated in practical experiments using a clinical MRI system. The sensitivity to cross-terms was evaluated in a water phantom with a folded surface which provoked strong internal field gradients. In every comparison, the cross-term-compensated waveforms were robust to the effects of background gradients, whereas conventional designs were not. We also propose a method to measure background gradients from diffusion-weighted data, and show that cross-term-compensated waveforms produce parameters that are markedly less dependent on the background compared to non-compensated designs. Finally, we also used simulations to show that the proposed cross-term compensation was robust to background gradients in the interval 0 to 3 mT/m, whereas non-compensated designs were impacted in terms of a severe signal and parameter bias. In conclusion, we have proposed and demonstrated a waveform design that yields efficient cross-term compensation and facilitates accurate diffusion MRI in the presence of static background gradients regardless of their amplitude and direction. The optimization framework is compatible with arbitrary spin-echo sequence timing and RF events, b-tensor shapes, suppression of concomitant gradient effects and motion encoding, and is shared in open source.
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Smaller subcortical volumes and enlarged lateral ventricles are associated with higher global functioning in young adults with 22q11.2 deletion syndrome with prodromal symptoms of schizophrenia

Heller C, Weiss T, Del Re EC, Swago S, Coman IL, Antshel KM, Fremont W, Bouix S, Kates WR, Kubicki MR, et al. Smaller subcortical volumes and enlarged lateral ventricles are associated with higher global functioning in young adults with 22q11.2 deletion syndrome with prodromal symptoms of schizophrenia. Psychiatry Res. 2021;301 :113979.Abstract
The 22q11.2 deletion syndrome (22q11DS) is a developmental genetic syndrome associated with a 30% risk for developing schizophrenia. Lateral ventricles and subcortical structures are abnormal in this syndrome as well as in schizophrenia. Here, we investigated whether these structures are related in young adults with 22q11DS with and without prodromal symptoms (PS) for schizophrenia and whether abnormalities in volumes are associated with global functioning. MR images were acquired on a 3T scanner from 51 individuals with 22q11DS and 30 healthy controls (mean age: 21±2 years). Correlations were performed to evaluate the relationship between ventricular and subcortical volumes, with Global Assessment of Functioning (GAF) and Premorbid Adjustment Scale (PAS) in each group. Lateral ventricular volumes correlated negatively with subcortical volumes in individuals with 22q11DS. In individuals with 22q11DS with PS only, GAF correlated positively with volumes of the lateral ventricles and negatively with subcortical volumes. PAS correlated negatively with lateral ventricle volumes, and positively with volumes of subcortical structures. The results suggest a common neurodevelopmental mechanism related to the growth of these brain structures. Further, the ratio between the volumes and clinical measures could potentially be used to characterize individuals with 22q11DS and those from the general population for the risk of the development of schizophrenia.
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A Pilot Study of Multidimensional Diffusion MRI for Assessment of Tissue Heterogeneity in Prostate Cancer

Langbein BJ, Szczepankiewicz F, Westin C-F, Bay C, Maier SE, Kibel AS, Tempany CM, Fennessy FM. A Pilot Study of Multidimensional Diffusion MRI for Assessment of Tissue Heterogeneity in Prostate Cancer. Invest Radiol. 2021.Abstract
OBJECTIVES: The objectives of this exploratory study were to investigate the feasibility of multidimensional diffusion magnetic resonance imaging (MddMRI) in assessing diffusion heterogeneity at both a macroscopic and microscopic level in prostate cancer (PCa). MATERIALS AND METHODS: Informed consent was obtained from 46 subjects who underwent 3.0-T prostate multiparametric MRI, complemented with a prototype spin echo-based MddMRI sequence in this institutional review board-approved study. Prostate cancer tumors and comparative normal tissue from each patient were contoured on both apparent diffusion coefficient and MddMRI-derived mean diffusivity (MD) maps (from which microscopic diffusion heterogeneity [MKi] and microscopic diffusion anisotropy were derived) using 3D Slicer. The discriminative ability of MddMRI-derived parameters to differentiate PCa from normal tissue was determined using the Friedman test. To determine if tumor diffusion heterogeneity is similar on macroscopic and microscopic scales, the linear association between SD of MD and mean MKi was estimated using robust regression (bisquare weighting). Hypothesis testing was 2 tailed; P values less than 0.05 were considered statistically significant. RESULTS: All MddMRI-derived parameters could distinguish tumor from normal tissue in the fixed-effects analysis (P < 0.0001). Tumor MKi was higher (P < 0.05) compared with normal tissue (median, 0.40; interquartile range, 0.29-0.52 vs 0.20-0.18; 0.25), as was tumor microscopic diffusion anisotropy (0.55; 0.36-0.81 vs 0.20-0.15; 0.28). The MKi could not be predicted (no significant association) by SD of MD. There was a significant correlation between tumor volume and SD of MD (R2 = 0.50, slope = 0.008 μm2/ms per millimeter, P < 0.001) but not between tumor volume and MKi. CONCLUSIONS: This explorative study demonstrates that MddMRI provides novel information on MKi and microscopic anisotropy, which differ from measures at the macroscopic level. MddMRI has the potential to characterize tumor tissue heterogeneity at different spatial scales.
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White matter changes in psychosis risk relate to development and are not impacted by the transition to psychosis

Di Biase MA, Cetin-Karayumak S, Lyall AE, Zalesky A, Cho KIK, Zhang F, Kubicki M, Rathi Y, Lyons MG, Bouix S, et al. White matter changes in psychosis risk relate to development and are not impacted by the transition to psychosis. Mol Psychiatry. 2021.Abstract
Subtle alterations in white matter microstructure are observed in youth at clinical high risk (CHR) for psychosis. However, the timing of these changes and their relationships to the emergence of psychosis remain unclear. Here, we track the evolution of white matter abnormalities in a large, longitudinal cohort of CHR individuals comprising the North American Prodrome Longitudinal Study (NAPLS-3). Multi-shell diffusion magnetic resonance imaging data were collected across multiple timepoints (1-5 over 1 year) in 286 subjects (aged 12-32 years): 25 CHR individuals who transitioned to psychosis (CHR-P; 61 scans), 205 CHR subjects with unknown transition outcome after the 1-year follow-up period (CHR-U; 596 scans), and 56 healthy controls (195 scans). Linear mixed effects models were fitted to infer the impact of age and illness-onset on variation in the fractional anisotropy of cellular tissue (FAT) and the volume fraction of extracellular free water (FW). Baseline measures of white matter microstructure did not differentiate between HC, CHR-U and CHR-P individuals. However, age trajectories differed between the three groups in line with a developmental effect: CHR-P and CHR-U groups displayed higher FAT in adolescence, and 4% lower FAT by 30 years of age compared to controls. Furthermore, older CHR-P subjects (20+ years) displayed 4% higher FW in the forceps major (p < 0.05). Prospective analysis in CHR-P did not reveal a significant impact of illness onset on regional FAT or FW, suggesting that transition to psychosis is not marked by dramatic change in white matter microstructure. Instead, clinical high risk for psychosis-regardless of transition outcome-is characterized by subtle age-related white matter changes that occur in tandem with development.
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