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

Free-Water Diffusion MRI Detects Structural Alterations Surrounding White Matter Hyperintensities in the Early Stage of Cerebral Small Vessel Disease

Mayer C, Nägele FL, Petersen M, Frey BM, Hanning U, Pasternak O, Petersen E, Gerloff C, Thomalla G, Cheng B. Free-Water Diffusion MRI Detects Structural Alterations Surrounding White Matter Hyperintensities in the Early Stage of Cerebral Small Vessel Disease. J Cereb Blood Flow Metab. 2022 :271678X221093579.Abstract
In cerebral small vessel disease (CSVD), both white matter hyperintensities (WMH) of presumed vascular origin and the normal-appearing white matter (NAWM) contain microstructural brain alterations on diffusion-weighted MRI (DWI). Contamination of DWI-derived metrics by extracellular free-water can be corrected with free-water (FW) imaging. We investigated the alterations in FW and FW-corrected fractional anisotropy (FA-t) in WMH and surrounding tissue and their association with cerebrovascular risk factors. We analysed 1,000 MRI datasets from the Hamburg City Health Study. DWI was used to generate FW and FA-t maps. WMH masks were segmented on FLAIR and T1-weighted MRI and dilated repeatedly to create 8 NAWM masks representing increasing distance from WMH. Linear models were applied to compare FW and FA-t across WMH and NAWM masks and in association with cerebrovascular risk. Median age was 64 ± 14 years. FW and FA-t were altered 8 mm and 12 mm beyond WMH, respectively. Smoking was significantly associated with FW in NAWM (p = 0.008) and FA-t in WMH (p = 0.008) and in NAWM (p = 0.003) while diabetes and hypertension were not. Further research is necessary to examine whether FW and FA-t alterations in NAWM are predictors for developing WMH.
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Deep Brain Stimulation: Emerging Tools for Simulation, Data Analysis, and Visualization

Wårdell K, Nordin T, Vogel D, Zsigmond P, Westin C-F, Hariz M, Hemm S. Deep Brain Stimulation: Emerging Tools for Simulation, Data Analysis, and Visualization. Front Neurosci. 2022;16 :834026.Abstract
Deep brain stimulation (DBS) is a well-established neurosurgical procedure for movement disorders that is also being explored for treatment-resistant psychiatric conditions. This review highlights important consideration for DBS simulation and data analysis. The literature on DBS has expanded considerably in recent years, and this article aims to identify important trends in the field. During DBS planning, surgery, and follow up sessions, several large data sets are created for each patient, and it becomes clear that any group analysis of such data is a big data analysis problem and has to be handled with care. The aim of this review is to provide an update and overview from a neuroengineering perspective of the current DBS techniques, technical aids, and emerging tools with the focus on patient-specific electric field (EF) simulations, group analysis, and visualization in the DBS domain. Examples are given from the state-of-the-art literature including our own research. This work reviews different analysis methods for EF simulations, tractography, deep brain anatomical templates, and group analysis. Our analysis highlights that group analysis in DBS is a complex multi-level problem and selected parameters will highly influence the result. DBS analysis can only provide clinically relevant information if the EF simulations, tractography results, and derived brain atlases are based on as much patient-specific data as possible. A trend in DBS research is creation of more advanced and intuitive visualization of the complex analysis results suitable for the clinical environment.
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Left Atrial Contractile Strain Predicts Recurrence of Aatrial Tachyarrhythmia After Catheter Ablation

Nielsen AB, Skaarup KG, Djernæs K, Hauser R, San José Estépar R, Sørensen SK, Ruwald MH, Hansen ML, Worck RH, Johannessen A, et al. Left Atrial Contractile Strain Predicts Recurrence of Aatrial Tachyarrhythmia After Catheter Ablation. Int J Cardiol. 2022.Abstract
BACKGROUND: Despite improvement in treatment strategies of atrial fibrillation (AF), a considerable number of patients still experience recurrence of atrial tachyarrhythmia (ATA) following catheter ablation (CA). This study aimed to investigate the prognostic value of left atrial (LA) deformation analysis in a large group of patients undergoing CA for AF. METHODS: This study included 678 patients with AF. Echocardiography including two-dimensional speckle tracking echocardiography (2DSTE) was performed in all patients prior to CA. Logistic regression analysis was used to assess the association between ATA recurrence and LA strain during reservoir phase (LASr), LA strain during contraction phase (LASct), and LA strain during conduit phase (LAScd). RESULTS: During one-year follow-up, 274 (40%) experienced ATA recurrence. Median age of the included study population was 63.2 years (IQR: 55.5, 69.5) and 485 (72%) were male. Patients with recurrence had lower LASr (22.6% vs. 25.1%, p = 0.001) and LASct (10.7% vs. 12.4%, p < 0.001). No difference in LAScd was observed. After adjusting for potential clinical and echocardiographic confounders LASr (OR = 1.04, CI95% [1.01; 1.07], p = 0.015, per 1% decrease) and LASct (OR = 1.06, CI95% [1.02; 1.11], p = 0.007, per 1% decrease) remained independent predictors of recurrence. However, in patients with a normal-sized LA (LA volume index<34 mL/m2), only LASct remained an independent predictor of recurrence (OR = 1.07, CI95% [1.01; 1.12], p = 0.012, per 1% decrease). CONCLUSION: In patients undergoing CA for AF, LA deformation analysis by 2DSTE could be of use in risk stratification in clinical practice regarding ATA recurrence, even in patients with a normal-sized LA.
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Lung Tissue Shows Divergent Gene Expression Between Chronic Obstructive Pulmonary Disease and Idiopathic Pulmonary Fibrosis

Ghosh AJ, Hobbs BD, Yun JH, Saferali A, Moll M, Xu Z, Chase RP, Morrow J, Ziniti J, Sciurba F, et al. Lung Tissue Shows Divergent Gene Expression Between Chronic Obstructive Pulmonary Disease and Idiopathic Pulmonary Fibrosis. Respir Res. 2022;23 (1) :97.Abstract
BACKGROUND: Chronic obstructive pulmonary disease (COPD) and idiopathic pulmonary fibrosis (IPF) are characterized by shared exposures and clinical features, but distinct genetic and pathologic features exist. These features have not been well-studied using large-scale gene expression datasets. We hypothesized that there are divergent gene, pathway, and cellular signatures between COPD and IPF. METHODS: We performed RNA-sequencing on lung tissues from individuals with IPF (n = 231) and COPD (n = 377) compared to control (n = 267), defined as individuals with normal spirometry. We grouped the overlapping differential expression gene sets based on direction of expression and examined the resultant sets for genes of interest, pathway enrichment, and cell composition. Using gene set variation analysis, we validated the overlap group gene sets in independent COPD and IPF data sets. RESULTS: We found 5010 genes differentially expressed between COPD and control, and 11,454 genes differentially expressed between IPF and control (1% false discovery rate). 3846 genes overlapped between IPF and COPD. Several pathways were enriched for genes upregulated in COPD and downregulated in IPF; however, no pathways were enriched for genes downregulated in COPD and upregulated in IPF. There were many myeloid cell genes with increased expression in COPD but decreased in IPF. We found that the genes upregulated in COPD but downregulated in IPF were associated with lower lung function in the independent validation cohorts. CONCLUSIONS: We identified a divergent gene expression signature between COPD and IPF, with increased expression in COPD and decreased in IPF. This signature is associated with worse lung function in both COPD and IPF.
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DSNet: A Dual-Stream Framework for Weakly-Supervised Gigapixel Pathology Image Analysis

Xiang T, Song Y, Zhang C, Liu D, Chen M, Zhang F, Huang H, O'Donnell L, Cai W. DSNet: A Dual-Stream Framework for Weakly-Supervised Gigapixel Pathology Image Analysis. IEEE Trans Med Imaging. 2022;PP.Abstract
We present a novel weakly-supervised framework for classifying whole slide images (WSIs). WSIs, due to their gigapixel resolution, are commonly processed by patch-wise classification with patch-level labels. However, patch-level labels require precise annotations, which is expensive and usually unavailable on clinical data. With image-level labels only, patch-wise classification would be sub-optimal due to inconsistency between the patch appearance and image-level label. To address this issue, we posit that WSI analysis can be effectively conducted by integrating information at both high magnification (local) and low magnification (regional) levels. We auto-encode the visual signals in each patch into a latent embedding vector representing local information, and down-sample the raw WSI to hardware-acceptable thumbnails representing regional information. The WSI label is then predicted with a Dual-Stream Network (DSNet), which takes the transformed local patch embeddings and multi-scale thumbnail images as inputs and can be trained by the image-level label only. Experiments conducted on three large-scale public datasets demonstrate that our method outperforms all recent state-of-the-art weakly-supervised WSI classification methods.
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Case Report: The Imperfect Association Between Craniofacial Lesion Burden and Pain in Fibrous Dysplasia

Golden E, Zhang F, Selen DJ, Ebb D, Romo L, Drubach LA, Shah N, O'Donnell LJ, Lemme JD, Myers R, et al. Case Report: The Imperfect Association Between Craniofacial Lesion Burden and Pain in Fibrous Dysplasia. Front Neurol. 2022;13 :855157.Abstract
Patients with fibrous dysplasia (FD) often present with craniofacial lesions that affect the trigeminal nerve system. Debilitating pain, headache, and migraine are frequently experienced by FD patients with poor prognosis, while some individuals with similar bone lesions are asymptomatic. The clinical and biological factors that contribute to the etiopathogenesis of pain in craniofacial FD are largely unknown. We present two adult females with comparable craniofacial FD lesion size and location, as measured by 18F-sodium fluoride positron emission tomography/computed tomography (PET/CT), yet their respective pain phenotypes differed significantly. Over 4 weeks, the average pain reported by Patient A was 0.4/0-10 scale. Patient B reported average pain of 7.8/0-10 scale distributed across the entire skull and left facial region. Patient B did not experience pain relief from analgesics or more aggressive treatments (denosumab). In both patients, evaluation of trigeminal nerve divisions (V1, V2, and V3) with CT and magnetic resonance imaging (MRI) revealed nerve compression and displacement with more involvement of the left trigeminal branches relative to the right. First-time employment of diffusion MRI and tractography suggested reduced apparent fiber density within the cisternal segment of the trigeminal nerve, particularly for Patient B and in the left hemisphere. These cases highlight heterogeneous clinical presentation and neurobiological properties in craniofacial FD and also, the disconnect between peripheral pathology and pain severity. We hypothesize that a detailed phenotypic characterization of patients that incorporates an advanced imaging approach probing the trigeminal system may provide enhanced insights into the variable experiences with pain in craniofacial FD.
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