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

Maxwell-compensated Design of Asymmetric Gradient Waveforms for Tensor-valued Diffusion Encoding

Szczepankiewicz F, Westin C-F, Nilsson M. Maxwell-compensated Design of Asymmetric Gradient Waveforms for Tensor-valued Diffusion Encoding. Magn Reson Med. 2019.Abstract
PURPOSE: Diffusion encoding with asymmetric gradient waveforms is appealing because the asymmetry provides superior efficiency. However, concomitant gradients may cause a residual gradient moment at the end of the waveform, which can cause significant signal error and image artifacts. The purpose of this study was to develop an asymmetric waveform designs for tensor-valued diffusion encoding that is not sensitive to concomitant gradients. METHODS: The "Maxwell index" was proposed as a scalar invariant to capture the effect of concomitant gradients. Optimization of "Maxwell-compensated" waveforms was performed in which this index was constrained. Resulting waveforms were compared to waveforms from literature, in terms of the measured and predicted impact of concomitant gradients, by numerical analysis as well as experiments in a phantom and in a healthy human brain. RESULTS: Maxwell-compensated waveforms with Maxwell indices below 100 (mT/m) ms showed negligible signal bias in both numerical analysis and experiments. By contrast, several waveforms from literature showed gross signal bias under the same conditions, leading to a signal bias that was large enough to markedly affect parameter maps. Experimental results were accurately predicted by theory. CONCLUSION: Constraining the Maxwell index in the optimization of asymmetric gradient waveforms yields efficient diffusion encoding that negates the effects of concomitant fields while enabling arbitrary shapes of the b-tensor. This waveform design is especially useful in combination with strong gradients, long encoding times, thick slices, simultaneous multi-slice acquisition, and large FOVs.
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Mapping of apparent susceptibility yields promising diagnostic separation of progressive supranuclear palsy from other causes of parkinsonism

Sjöström H, Surova Y, Nilsson M, Granberg T, Westman E, van Westen D, Svenningsson P, Hansson O. Mapping of apparent susceptibility yields promising diagnostic separation of progressive supranuclear palsy from other causes of parkinsonism. Sci Rep. 2019;9 (1) :6079.Abstract
There is a need for methods that distinguish Parkinson's disease (PD) from progressive supranuclear palsy (PSP) and multiple system atrophy (MSA), which have similar characteristics in the early stages of the disease. In this prospective study, we evaluate mapping of apparent susceptibility based on susceptibility weighted imaging (SWI) for differential diagnosis. We included 134 patients with PD, 11 with PSP, 10 with MSA and 44 healthy controls. SWI data were processed into maps of apparent susceptibility. In PSP, apparent susceptibility was increased in the red nucleus compared to all other groups, and in globus pallidus, putamen, substantia nigra and the dentate nucleus compared to PD and controls. In MSA, putaminal susceptibility was increased compared to PD and controls. Including all studied regions and using discriminant analysis between PSP and PD, 100% sensitivity and 97% specificity was achieved, and 91% sensitivity and 90% specificity in separating PSP from MSA. Correlations between putaminal susceptibility and disease severity in PD could warrant further research into using susceptibility mapping for monitoring disease progression and in clinical trials. Our study indicates that susceptibility in deep nuclei could play a role in the diagnosis of atypical parkinsonism, especially in PSP.
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Detecting microstructural white matter abnormalities of frontal pathways in children with ADHD using advanced diffusion models

Wu W, McAnulty G, Hamoda HM, Sarill K, Karmacharya S, Gagoski B, Ning L, Grant EP, Shenton ME, Waber DP, et al. Detecting microstructural white matter abnormalities of frontal pathways in children with ADHD using advanced diffusion models. Brain Imaging Behav. 2019.Abstract
Studies using diffusion tensor imaging (DTI) have documented alterations in the attention and executive system in children and adolescents with attention-deficit/hyperactivity disorder (ADHD). While abnormalities in the frontal lobe have also been reported, the associated white matter fiber bundles have not been investigated comprehensively due to the complexity in tracing them through fiber crossings. Furthermore, most studies have used a non-specific DTI model to understand white matter abnormalities. We present results from a first study that uses a multi-shell diffusion MRI (dMRI) data set coupled with an advanced multi-fiber tractography algorithm to probe microstructural measures related to axonal/cellular density and volume of fronto-striato-thalamic pathways in children with ADHD (N = 30) and healthy controls (N = 28). Head motion was firstly examined as a priority in order to assure that no group difference existed. We investigated 45 different white matter fiber bundles in the brain. After correcting for multiple comparisons, we found lower axonal/cellular packing density and volume in ADHD children in 8 of the 45 fiber bundles, primarily in the right hemisphere as follows: 1) Superior longitudinal fasciculus-II (SLF-II) (right), 2) Thalamus to precentral gyrus (right), 3) Thalamus to superior-frontal gyrus (right), 4) Caudate to medial orbitofrontal gyrus (right), 5) Caudate to precentral gyrus (right), 6) Thalamus to paracentral gyrus (left), 7) Caudate to caudal middlefrontal gyrus (left), and 8) Cingulum (bilateral). Our results demonstrate reduced axonal/cellular density and volume in certain frontal lobe white matter fiber tracts, which sub-serve the attention function and executive control systems. Further, our work shows specific microstructural abnormalities in the striato-thalamo-cortical connections, which have not been previously reported in children with ADHD.
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Harmonization of chest CT scans for different doses and reconstruction methods

Vegas-Sánchez-Ferrero G, Ledesma-Carbayo MJ, Washko GR, San José Estépar R. Harmonization of chest CT scans for different doses and reconstruction methods. Med Phys. 2019.Abstract
PURPOSE: To develop and validate a CT harmonization technique by combining noise-stabilization and autocalibration methodologies to provide reliable densitometry measurements in heterogeneous acquisition protocols. METHODS: We propose to reduce the effects of spatially-variant noise such as non-uniform patterns of noise and biases. The method combines the statistical characterization of the signal-to-noise relationship in the CT image intensities, which allows us to estimate both the signal and spatially-variant variance of noise, with an autocalibration technique that reduces the non-uniform biases caused by noise and reconstruction techniques. The method is firstly validated with anthropomorphic synthetic images that simulate CT acquisitions with variable scanning parameters: different dosage, non-homogeneous variance of noise, and various reconstruction methods. We finally evaluate these effects and the ability of our method to provide consistent densitometric measurements in a cohort of clinical chest CT scans from two vendors (Siemens, n=54 subjects; and GE, n=50 subjects) acquired with several reconstruction algorithms (filtered back-projection and iterative reconstructions) with high-dose and low-dose protocols. RESULTS: The harmonization reduces the effect of non-homogeneous noise without compromising the resolution of the images (25% RMSE reduction in both clinical datasets). An analysis through hierarchical linear models showed that the average biases induced by differences in dosage and reconstruction methods are also reduced up to 74:20%, enabling comparable results between highdose and low-dose reconstructions. We also assessed the statistical similarity between acquisitions obtaining increases of up to 30 percentage points and showing that the low-dose vs. high-dose comparisons of harmonized data obtain similar and even higher similarity than the observed for high-dose vs. high-dose comparisons of non-harmonized data. CONCLUSION: The proposed harmonization technique allows to compare measures of low-dose with high-dose acquisitions without using a specific reconstruction as a reference. Since the harmonization does not require a precalibration with a phantom, it can be applied to retrospective studies. This approach might be suitable for multicenter trials for which a reference reconstruction is not feasible or hard to define due to differences in vendors, models and reconstruction techniques. This article is protected by copyright. All rights reserved.
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Increased Airway Wall Thickness in Interstitial Lung Abnormalities and Idiopathic Pulmonary Fibrosis

Miller ER, Putman RK, Diaz AA, Xu H, San José Estépar R, Araki T, Nishino M, Poli de Frías S, Hida T, Ross J, et al. Increased Airway Wall Thickness in Interstitial Lung Abnormalities and Idiopathic Pulmonary Fibrosis. Ann Am Thorac Soc. 2019;16 (4) :447-454.Abstract
RATIONALE: There is increasing evidence that aberrant processes occurring in the airways may precede the development of idiopathic pulmonary fibrosis (IPF); however, there has been no prior confirmatory data derived from imaging studies. OBJECTIVES: To assess quantitative measures of airway wall thickness (AWT) in populations characterized for interstitial lung abnormalities (ILA) and for IPF. METHODS: Computed tomographic imaging of the chest and measures of AWT were available for 6,073, 615, 1,167, and 38 participants from COPDGene (Genetic Epidemiology of COPD study), ECLIPSE (Evaluation of COPD Longitudinally to Identify Predictive Surrogate Endpoints study), and the Framingham Heart Study (FHS) and in patients with IPF from the Brigham and Women's Hospital Herlihy Registry, respectively. To evaluate these associations, we used multivariable linear regression to compare a standardized measure of AWT (the square root of AWT for airways with an internal perimeter of 10 mm [Pi10]) and characterizations of ILA and IPF by computed tomographic imaging of the chest. RESULTS: In COPDGene, ECLIPSE, and FHS, research participants with ILA had increased measures of Pi10 compared with those without ILA. Patients with IPF had mean measures of Pi10 that were even greater than those noted in research participants with ILA. After adjustment for important covariates (e.g., age, sex, race, body mass index, smoking behavior, and chronic obstructive pulmonary disease severity when appropriate), research participants with ILA had increased measures of Pi10 compared with those without ILA (0.03 mm in COPDGene, 95% confidence interval [CI], 0.02-0.03; P < 0.001; 0.02 mm in ECLIPSE, 95% CI, 0.005-0.04; P = 0.01; 0.07 mm in FHS, 95% CI, 0.01-0.1; P = 0.01). Compared with COPDGene participants without ILA older than 60 years of age, patients with IPF were also noted to have increased measures of Pi10 (2.0 mm, 95% CI, 2.0-2.1; P < 0.001). Among research participants with ILA, increases in Pi10 were correlated with reductions in lung volumes in some but not all populations. CONCLUSIONS: These results demonstrate that measurable increases in AWT are consistently noted in research participants with ILA and in patients with IPF. These findings suggest that abnormalities of the airways may play a role in, or be correlated with, early pathogenesis of pulmonary fibrosis.
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Integrative Genomics Analysis Identifies ACVR1B as a Candidate Causal Gene of Emphysema Distribution

Boueiz A, Pham B, Chase R, Lamb A, Lee S, Naing ZZC, Cho MH, Parker MM, Sakornsakolpat P, Hersh CP, et al. Integrative Genomics Analysis Identifies ACVR1B as a Candidate Causal Gene of Emphysema Distribution. Am J Respir Cell Mol Biol. 2019;60 (4) :388-398.Abstract
Genome-wide association studies (GWAS) have identified multiple associations with emphysema apicobasal distribution (EABD), but the biological functions of these variants are unknown. To characterize the functions of EABD-associated variants, we integrated GWAS results with 1) expression quantitative trait loci (eQTL) from the Genotype Tissue Expression (GTEx) project and subjects in the COPDGene (Genetic Epidemiology of COPD) study and 2) cell type epigenomic marks from the Roadmap Epigenomics project. On the basis of these analyses, we selected a variant near ACVR1B (activin A receptor type 1B) for functional validation. SNPs from 168 loci with P values less than 5 × 10 in the largest GWAS meta-analysis of EABD were analyzed. Eighty-four loci overlapped eQTL, with 12 of these loci showing greater than 80% likelihood of harboring a single, shared GWAS and eQTL causal variant. Seventeen cell types were enriched for overlap between EABD loci and Roadmap Epigenomics marks (permutation P < 0.05), with the strongest enrichment observed in CD4, CD8, and regulatory T cells. We selected a putative causal variant, rs7962469, associated with ACVR1B expression in lung tissue for additional functional investigation, and reporter assays confirmed allele-specific regulatory activity for this variant in human bronchial epithelial and Jurkat immune cell lines. ACVR1B expression levels exhibit a nominally significant association with emphysema distribution. EABD-associated loci are preferentially enriched in regulatory elements of multiple cell types, most notably T-cell subsets. Multiple EABD loci colocalize to regulatory elements that are active across multiple tissues and cell types, and functional analyses confirm the presence of an EABD-associated functional variant that regulates ACVR1B expression, indicating that transforming growth factor-β signaling plays a role in the EABD phenotype. Clinical trial registered with www.clinicaltrials.gov (NCT00608764).
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