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Michael E. Kim

Publications and source records attributed to Michael E. Kim.

At least 19 recordsLinked to original sources

SliceBridge: context-consistent repair of corrupted slice intervals in T1-weighted MRI

Structural magnetic resonance imaging (MRI) images are sometimes corrupted over a contiguous set of slices, where acquisition, motion, hardware, or reconstruction effects leave a single slice or short interval inconsistent with its neighbors while the rest of the image remains usable. Such localized corruption can bias downstream morphometric analysis, yet discarding or reacquiring an otherwise usable image is costly. We formulate this as an image restoration problem: given the location of the affected interval, reconstruct those slices from the surrounding anatomical and imaging context. We propose SliceBridge, a framework for restoring corrupted slice intervals in T1-weighted MRI using rectified flow matching conditioned on the surrounding intact slices and their relative slice positions. Through-plane consistency is encouraged by coupling the slices within the interval through interval-correlated initial noise, a shared flow time, and synchronized sampling. The restored interval is then inserted back, leaving all other slices unchanged. We trained and validated the model on 9,877 T1-weighted brain MRI volumes from four datasets and evaluated it on 581 external subjects using clean interval withholding and controlled corruptions. Compared with a matched model that reconstructed target slices independently, SliceBridge reduced error in slice-to-slice changes within repaired intervals by 32.9%-41.3% across interval lengths and achieved higher SSIM at every interval length. In controlled-corruption cases, SliceBridge reduced the median error in regional brain volume estimates produced by a downstream segmentation model from 1.95% in corrupted volumes to 1.05%.

cs.CV

Quality assurance of the Federal Interagency Traumatic Brain Injury Research (FITBIR) database for multi-site MRI analysis

The Federal Interagency Traumatic Brain Injury Research (FITBIR) database is a centralized data repository for traumatic brain injury (TBI) research. It includes over 45,529 magnetic resonance images (MRI) from 6,211 subjects (9,229 imaging sessions) across 26 studies with heterogeneous organization formats, contrasts, acquisition parameters, and demographics. In this work, we organized and harmonized all available structural and diffusion MRI from FITBIR along with relevant demographic information into the Brain Imaging Data Structure. We analyzed whole-brain mean fractional anisotropy, mean diffusivity, total intracranial volume, and the volumes of 132 regions of interest using UNesT segmentations. There were 4,868 subjects (7,035 sessions) with structural MRI and 2,666 subjects (3,763 sessions) with diffusion MRI following quality assurance and harmonization. We modeled profiles for these metrics across ages with generalized additive models for location, scale, and shape (GAMLSS) and found significant differences in subjects with TBI compared to controls in volumes of 15 regions of the brain (q < 0.05, likelihood ratio test with false discovery rate correction).

eess.IV

Large-Scale Deployment and Analytical Implications of Structured Quality Control in Diffusion Magnetic Resonance Imaging

Purpose: Diffusion MRI (dMRI) provides a diverse set of quantitative measures and derived datatypes to assess white matter microstructure and macrostructure. Coupled with the increasing size of imaging studies using dMRI, the number of downstream outputs requiring quality control (QC) will continue to grow. Previous work has shown that failure modes which are often not evident from aggregate metrics or summary statistics can be identified through structured visual inspection. This work aims to better understand common failure modes and the expected characteristics of valid dMRI processing outputs to ensure the validity and interpretability of quantitative findings. Approach: We deployed a structured QC framework to assess 18,328 dMRI scans across nine datasets, visually evaluating the outputs of seven processing pipelines representative of conventional dMRI analyses. Results: Downstream outputs that pass visual QC may still rely on failed upstream dependencies; such failures may only be visually detectable through systematic inspection of the full pipeline hierarchy. Additionally, appropriate QC granularity is algorithm-specific, as the spatial structure of each algorithm's outputs determines whether failures warrant selective or global exclusion. Conclusion: This work demonstrates the feasibility and analytical value of large-scale, structured QC for dMRI processing pipelines. Our results highlight the need for systematic QC spanning the full processing hierarchy to ensure the validity and interpretability of quantitative findings.

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Harmonization mitigates diffusion MRI scanner effects in infancy: insights from the HEALthy Brain and Childhood Development (HBCD) study

The HEALthy Brain and Childhood Development (HBCD) Study is an ongoing longitudinal initiative to understand population-level brain maturation; however, large-scale studies must overcome site-related variance and preserve biologically relevant signal. In addition to diffusion-weighted magnetic resonance imaging images, the HBCD dataset offers analysis-ready derivatives for scientists to conduct their analysis, including scalar diffusion tensor (DTI) metrics in a predetermined set of bundles. The purpose of this study is to characterize HBCD-specific site effects in diffusion MRI data, which have not been systematically reported. In this work, we investigate the sensitivity of HBCD bundle metrics to scanner model-related variance and address these variations with ComBat-GAM harmonization within the current HBCD data release 1.1 across six scanner models. Following ComBat-GAM, we observe zero statistically significant differences between the distributions from any scanner model following FDR correction and reduce Cohen's f effect sizes across all metrics. Our work underscores the importance of rigorous harmonization efforts in large-scale studies, and we encourage future investigations of HBCD data to control for these effects.

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Evaluation of neuroCombat and deep learning harmonization for multi-site magnetic resonance neuroimaging in youth with prenatal alcohol exposure

In cases of prevalent diseases and disorders, such as Prenatal Alcohol Exposure (PAE), multi-site data collection allows for increased study samples. However, multi-site studies introduce additional variability through heterogeneous collection materials, such as scanner and acquisition protocols, which confound with biologically relevant signals. Neuroscientists often utilize statistical methods on image-derived metrics, such as volume of regions of interest, after all image processing to minimize site-related variance. HACA3, a deep learning harmonization method, offers an opportunity to harmonize image signals prior to metric quantification; however, HACA3 has not yet been validated in a pediatric cohort. In this work, we investigate HACA3's ability to remove site-related variance and preserve biologically relevant signal compared to a statistical method, neuroCombat, and pair HACA3 processing with neuroCombat to evaluate the efficacy of multiple harmonization methods in a pediatric (age 7 to 21) population across three unique scanners with controls and cases of PAE with downstream MaCRUISE volume metrics. We find that HACA3 qualitatively improves inter-site contrast variations, but statistical methods reduce greater site-related variance within the MaCRUISE volume metrics following an ANCOVA test, and HACA3 relies on follow-up statistical methods to approach maximal biological preservation in this context.

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Personalized White Matter Bundle Segmentation for Early Childhood

White matter segmentation methods from diffusion magnetic resonance imaging range from streamline clustering-based approaches to bundle mask delineation, but none have proposed a pediatric-specific approach. We hypothesize that a deep learning model with a similar approach to TractSeg will improve similarity between an algorithm-generated mask and an expert-labeled ground truth. Given a cohort of 56 manually labelled white matter bundles, we take inspiration from TractSeg's 2D UNet architecture, and we modify inputs to match bundle definitions as determined by pediatric experts, evaluation to use k fold cross validation, the loss function to masked Dice loss. We evaluate Dice score, volume overlap, and volume overreach of 16 major regions of interest compared to the expert labeled dataset. To test whether our approach offers statistically significant improvements over TractSeg, we compare Dice voxels, volume overlap, and adjacency voxels with a Wilcoxon signed rank test followed by false discovery rate correction. We find statistical significance across all bundles for all metrics with one exception in volume overlap. After we run TractSeg and our model, we combine their output masks into a 60 label atlas to evaluate if TractSeg and our model combined can generate a robust, individualized atlas, and observe smoothed, continuous masks in cases that TractSeg did not produce an anatomically plausible output. With the improvement of white matter pathway segmentation masks, we can further understand neurodevelopment on a population level scale, and we can produce reliable estimates of individualized anatomy in pediatric white matter diseases and disorders.

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MetaVoxel: Joint Diffusion Modeling of Imaging and Clinical Metadata

Modern deep learning methods have achieved impressive results across tasks from disease classification, estimating continuous biomarkers, to generating realistic medical images. Most of these approaches are trained to model conditional distributions defined by a specific predictive direction with a specific set of input variables. We introduce MetaVoxel, a generative joint diffusion modeling framework that models the joint distribution over imaging data and clinical metadata by learning a single diffusion process spanning all variables. By capturing the joint distribution, MetaVoxel unifies tasks that traditionally require separate conditional models and supports flexible zero-shot inference using arbitrary subsets of inputs without task-specific retraining. Using more than 10,000 T1-weighted MRI scans paired with clinical metadata from nine datasets, we show that a single MetaVoxel model can perform image generation, age estimation, and sex prediction, achieving performance comparable to established task-specific baselines. Additional experiments highlight its capabilities for flexible inference. Together, these findings demonstrate that joint multimodal diffusion offers a promising direction for unifying medical AI models and enabling broader clinical applicability.

cs.CV

Characterizing Continuous and Discrete Hybrid Latent Spaces for Structural Connectomes

Structural connectomes are detailed graphs that map how different brain regions are physically connected, offering critical insight into aging, cognition, and neurodegenerative diseases. However, these connectomes are high-dimensional and densely interconnected, which makes them difficult to interpret and analyze at scale. While low-dimensional spaces like PCA and autoencoders are often used to capture major sources of variation, their latent spaces are generally continuous and cannot fully reflect the mixed nature of variability in connectomes, which include both continuous (e.g., connectivity strength) and discrete factors (e.g., imaging site). Motivated by this, we propose a variational autoencoder (VAE) with a hybrid latent space that jointly models the discrete and continuous components. We analyze a large dataset of 5,761 connectomes from six Alzheimer's disease studies with ten acquisition protocols. Each connectome represents a single scan from a unique subject (3579 females, 2182 males), aged 22 to 102, with 4338 cognitively normal, 809 with mild cognitive impairment (MCI), and 614 with Alzheimer's disease (AD). Each connectome contains 121 brain regions defined by the BrainCOLOR atlas. We train our hybrid VAE in an unsupervised way and characterize what each latent component captures. We find that the discrete space is particularly effective at capturing subtle site-related differences, achieving an Adjusted Rand Index (ARI) of 0.65 with site labels, significantly outperforming PCA and a standard VAE followed by clustering (p < 0.05). These results demonstrate that the hybrid latent space can disentangle distinct sources of variability in connectomes in an unsupervised manner, offering potential for large-scale connectome analysis.

q-bio.NC

Fully Differentiable dMRI Streamline Propagation in PyTorch

Diffusion MRI (dMRI) provides a distinctive means to probe the microstructural architecture of living tissue, facilitating applications such as brain connectivity analysis, modeling across multiple conditions, and the estimation of macrostructural features. Tractography, which emerged in the final years of the 20th century and accelerated in the early 21st century, is a technique for visualizing white matter pathways in the brain using dMRI. Most diffusion tractography methods rely on procedural streamline propagators or global energy minimization methods. Although recent advancements in deep learning have enabled tasks that were previously challenging, existing tractography approaches are often non-differentiable, limiting their integration in end-to-end learning frameworks. While progress has been made in representing streamlines in differentiable frameworks, no existing method offers fully differentiable propagation. In this work, we propose a fully differentiable solution that retains numerical fidelity with a leading streamline algorithm. The key is that our PyTorch-engineered streamline propagator has no components that block gradient flow, making it fully differentiable. We show that our method matches standard propagators while remaining differentiable. By translating streamline propagation into a differentiable PyTorch framework, we enable deeper integration of tractography into deep learning workflows, laying the foundation for a new category of macrostructural reasoning that is not only computationally robust but also scientifically rigorous.

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Phenotype discovery of traumatic brain injury segmentations from heterogeneous multi-site data

Traumatic brain injury (TBI) is intrinsically heterogeneous, and typical clinical outcome measures like the Glasgow Coma Scale complicate this diversity. The large variability in severity and patient outcomes render it difficult to link structural damage to functional deficits. The Federal Interagency Traumatic Brain Injury Research (FITBIR) repository contains large-scale multi-site magnetic resonance imaging data of varying resolutions and acquisition parameters (25 shared studies with 7,693 sessions that have age, sex and TBI status defined - 5,811 TBI and 1,882 controls). To reveal shared pathways of injury of TBI through imaging, we analyzed T1-weighted images from these sessions by first harmonizing to a local dataset and segmenting 132 regions of interest (ROIs) in the brain. After running quality assurance, calculating the volumes of the ROIs, and removing outliers, we calculated the z-scores of volumes for all participants relative to the mean and standard deviation of the controls. We regressed out sex, age, and total brain volume with a multivariate linear regression, and we found significant differences in 37 ROIs between subjects with TBI and controls (p < 0.05 with independent t-tests with false discovery rate correction). We found that differences originated in 1) the brainstem, occipital pole and structures posterior to the orbit, 2) subcortical gray matter and insular cortex, and 3) cerebral and cerebellar white matter using independent component analysis and clustering the component loadings of those with TBI.

q-bio.QM

Pitfalls of defacing whole-head MRI: re-identification risk with diffusion models and compromised research potential

Defacing is often applied to head magnetic resonance image (MRI) datasets prior to public release to address privacy concerns. The alteration of facial and nearby voxels has provoked discussions about the true capability of these techniques to ensure privacy as well as their impact on downstream tasks. With advancements in deep generative models, the extent to which defacing can protect privacy is uncertain. Additionally, while the altered voxels are known to contain valuable anatomical information, their potential to support research beyond the anatomical regions directly affected by defacing remains uncertain. To evaluate these considerations, we develop a refacing pipeline that recovers faces in defaced head MRIs using cascaded diffusion probabilistic models (DPMs). The DPMs are trained on images from 180 subjects and tested on images from 484 unseen subjects, 469 of whom are from a different dataset. To assess whether the altered voxels in defacing contain universally useful information, we also predict computed tomography (CT)-derived skeletal muscle radiodensity from facial voxels in both defaced and original MRIs. The results show that DPMs can generate high-fidelity faces that resemble the original faces from defaced images, with surface distances to the original faces significantly smaller than those of a population average face (p < 0.05). This performance also generalizes well to previously unseen datasets. For skeletal muscle radiodensity predictions, using defaced images results in significantly weaker Spearman's rank correlation coefficients compared to using original images (p < 10-4). For shin muscle, the correlation is statistically significant (p < 0.05) when using original images but not statistically significant (p > 0.05) when any defacing method is applied, suggesting that defacing might not only fail to protect privacy but also eliminate valuable information.

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Brain age identification from diffusion MRI synergistically predicts neurodegenerative disease

Estimated brain age from magnetic resonance image (MRI) and its deviation from chronological age can provide early insights into potential neurodegenerative diseases, supporting early detection and implementation of prevention strategies. Diffusion MRI (dMRI) presents an opportunity to build an earlier biomarker for neurodegenerative disease prediction because it captures subtle microstructural changes that precede more perceptible macrostructural changes. However, the coexistence of macro- and micro-structural information in dMRI raises the question of whether current dMRI-based brain age estimation models are leveraging the intended microstructural information or if they inadvertently rely on the macrostructural information. To develop a microstructure-specific brain age, we propose a method for brain age identification from dMRI that mitigates the model's use of macrostructural information by non-rigidly registering all images to a standard template. Imaging data from 13,398 participants across 12 datasets were used for the training and evaluation. We compare our brain age models, trained with and without macrostructural information mitigated, with an architecturally similar T1-weighted (T1w) MRI-based brain age model and two recent, popular, openly available T1w MRI-based brain age models that primarily use macrostructural information. We observe difference between our dMRI-based brain age and T1w MRI-based brain age across stages of neurodegeneration, with dMRI-based brain age being older than T1w MRI-based brain age in participants transitioning from cognitively normal (CN) to mild cognitive impairment (MCI), but younger in participants already diagnosed with Alzheimer's disease (AD). Furthermore, dMRI-based brain age may offer advantages over T1w MRI-based brain age in predicting the transition from CN to MCI up to five years before diagnosis.

cs.CV

Lifespan Pancreas Morphology for Control vs Type 2 Diabetes using AI on Largescale Clinical Imaging

Purpose: Understanding how the pancreas changes is critical for detecting deviations in type 2 diabetes and other pancreatic disease. We measure pancreas size and shape using morphological measurements from ages 0 to 90. Our goals are to 1) identify reliable clinical imaging modalities for AI-based pancreas measurement, 2) establish normative morphological aging trends, and 3) detect potential deviations in type 2 diabetes. Approach: We analyzed a clinically acquired dataset of 2533 patients imaged with abdominal CT or MRI. We resampled the scans to 3mm isotropic resolution, segmented the pancreas using automated methods, and extracted 13 morphological pancreas features across the lifespan. First, we assessed CT and MRI measurements to determine which modalities provide consistent lifespan trends. Second, we characterized distributions of normative morphological patterns stratified by age group and sex. Third, we used GAMLSS regression to model pancreas morphology trends in 1350 patients matched for age, sex, and type 2 diabetes status to identify any deviations from normative aging associated with type 2 diabetes. Results: When adjusting for confounders, the aging trends for 10 of 13 morphological features were significantly different between patients with type 2 diabetes and non-diabetic controls (p < 0.05 after multiple comparisons corrections). Additionally, MRI appeared to yield different pancreas measurements than CT using our AI-based method. Conclusions: We provide lifespan trends demonstrating that the size and shape of the pancreas is altered in type 2 diabetes using 675 control patients and 675 diabetes patients. Moreover, our findings reinforce that the pancreas is smaller in type 2 diabetes. Additionally, we contribute a reference of lifespan pancreas morphology from a large cohort of non-diabetic control patients in a clinical setting.

cs.CV

Data-Driven Abdominal Phenotypes of Type 2 Diabetes in Lean, Overweight, and Obese Cohorts

Purpose: Although elevated BMI is a well-known risk factor for type 2 diabetes, the disease's presence in some lean adults and absence in others with obesity suggests that detailed body composition may uncover abdominal phenotypes of type 2 diabetes. With AI, we can now extract detailed measurements of size, shape, and fat content from abdominal structures in 3D clinical imaging at scale. This creates an opportunity to empirically define body composition signatures linked to type 2 diabetes risk and protection using large-scale clinical data. Approach: To uncover BMI-specific diabetic abdominal patterns from clinical CT, we applied our design four times: once on the full cohort (n = 1,728) and once on lean (n = 497), overweight (n = 611), and obese (n = 620) subgroups separately. Briefly, our experimental design transforms abdominal scans into collections of explainable measurements through segmentation, classifies type 2 diabetes through a cross-validated random forest, measures how features contribute to model-estimated risk or protection through SHAP analysis, groups scans by shared model decision patterns (clustering from SHAP) and links back to anatomical differences (classification). Results: The random-forests achieved mean AUCs of 0.72-0.74. There were shared type 2 diabetes signatures in each group; fatty skeletal muscle, older age, greater visceral and subcutaneous fat, and a smaller or fat-laden pancreas. Univariate logistic regression confirmed the direction of 14-18 of the top 20 predictors within each subgroup (p < 0.05). Conclusions: Our findings suggest that abdominal drivers of type 2 diabetes may be consistent across weight classes.

cs.CV

Multi-Modality Conditioned Variational U-Net for Field-of-View Extension in Brain Diffusion MRI

An incomplete field-of-view (FOV) in diffusion magnetic resonance imaging (dMRI) can severely hinder the volumetric and bundle analyses of whole-brain white matter connectivity. Although existing works have investigated imputing the missing regions using deep generative models, it remains unclear how to specifically utilize additional information from paired multi-modality data and whether this can enhance the imputation quality and be useful for downstream tractography. To fill this gap, we propose a novel framework for imputing dMRI scans in the incomplete part of the FOV by integrating the learned diffusion features in the acquired part of the FOV to the complete brain anatomical structure. We hypothesize that by this design the proposed framework can enhance the imputation performance of the dMRI scans and therefore be useful for repairing whole-brain tractography in corrupted dMRI scans with incomplete FOV. We tested our framework on two cohorts from different sites with a total of 96 subjects and compared it with a baseline imputation method that treats the information from T1w and dMRI scans equally. The proposed framework achieved significant improvements in imputation performance, as demonstrated by angular correlation coefficient (p < 1E-5), and in downstream tractography accuracy, as demonstrated by Dice score (p < 0.01). Results suggest that the proposed framework improved imputation performance in dMRI scans by specifically utilizing additional information from paired multi-modality data, compared with the baseline method. The imputation achieved by the proposed framework enhances whole brain tractography, and therefore reduces the uncertainty when analyzing bundles associated with neurodegenerative.

cs.CV

Multipath cycleGAN for harmonization of paired and unpaired low-dose lung computed tomography reconstruction kernels

Reconstruction kernels in computed tomography (CT) affect spatial resolution and noise characteristics, introducing systematic variability in quantitative imaging measurements such as emphysema quantification. Choosing an appropriate kernel is therefore essential for consistent quantitative analysis. We propose a multipath cycleGAN model for CT kernel harmonization, trained on a mixture of paired and unpaired data from a low-dose lung cancer screening cohort. The model features domain-specific encoders and decoders with a shared latent space and uses discriminators tailored for each domain.We train the model on 42 kernel combinations using 100 scans each from seven representative kernels in the National Lung Screening Trial (NLST) dataset. To evaluate performance, 240 scans from each kernel are harmonized to a reference soft kernel, and emphysema is quantified before and after harmonization. A general linear model assesses the impact of age, sex, smoking status, and kernel on emphysema. We also evaluate harmonization from soft kernels to a reference hard kernel. To assess anatomical consistency, we compare segmentations of lung vessels, muscle, and subcutaneous adipose tissue generated by TotalSegmentator between harmonized and original images. Our model is benchmarked against traditional and switchable cycleGANs. For paired kernels, our approach reduces bias in emphysema scores, as seen in Bland-Altman plots (p<0.05). For unpaired kernels, harmonization eliminates confounding differences in emphysema (p>0.05). High Dice scores confirm preservation of muscle and fat anatomy, while lung vessel overlap remains reasonable. Overall, our shared latent space multipath cycleGAN enables robust harmonization across paired and unpaired CT kernels, improving emphysema quantification and preserving anatomical fidelity.

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Investigating the impact of kernel harmonization and deformable registration on inspiratory and expiratory chest CT images for people with COPD

Paired inspiratory-expiratory CT scans enable the quantification of gas trapping due to small airway disease and emphysema by analyzing lung tissue motion in COPD patients. Deformable image registration of these scans assesses regional lung volumetric changes. However, variations in reconstruction kernels between paired scans introduce errors in quantitative analysis. This work proposes a two-stage pipeline to harmonize reconstruction kernels and perform deformable image registration using data acquired from the COPDGene study. We use a cycle generative adversarial network (GAN) to harmonize inspiratory scans reconstructed with a hard kernel (BONE) to match expiratory scans reconstructed with a soft kernel (STANDARD). We then deformably register the expiratory scans to inspiratory scans. We validate harmonization by measuring emphysema using a publicly available segmentation algorithm before and after harmonization. Results show harmonization significantly reduces emphysema measurement inconsistencies, decreasing median emphysema scores from 10.479% to 3.039%, with a reference median score of 1.305% from the STANDARD kernel as the target. Registration accuracy is evaluated via Dice overlap between emphysema regions on inspiratory, expiratory, and deformed images. The Dice coefficient between inspiratory emphysema masks and deformably registered emphysema masks increases significantly across registration stages (p<0.001). Additionally, we demonstrate that deformable registration is robust to kernel variations.

eess.IV

Comparison and calibration of MP2RAGE quantitative T1 values to multi-TI inversion recovery T1 values

While typical qualitative T1-weighted magnetic resonance images reflect scanner and protocol differences, quantitative T1 mapping aims to measure T1 independent of these effects. Changes in T1 in the brain reflect structural changes in brain tissue. Magnetization-prepared two rapid acquisition gradient echo (MP2RAGE) is an acquisition protocol that allows for efficient T1 mapping with a much lower scan time per slab compared to multi-TI inversion recovery (IR) protocols. We collect and register B1-corrected MP2RAGE acquisitions with an additional inversion time (MP3RAGE) alongside multi-TI selective inversion recovery acquisitions for four subjects. We use a maximum a posteriori (MAP) T1 estimation method for both MP2RAGE and compare to typical point estimate MP2RAGE T1 mapping, finding no bias from MAP MP2RAGE but a sensitivity to B1 inhomogeneities with MAP MP3RAGE. We demonstrate a tissue-dependent bias between MAP MP2RAGE T1 estimates and the multi-TI inversion recovery T1 values. To correct this bias, we train a patch-based ResNet-18 to calibrate the MAP MP2RAGE T1 estimates to the multi-TI IR T1 values. Across four folds, our network reduces the RMSE significantly (white matter: from 0.30 +/- 0.01 seconds to 0.11 +/- 0.02 seconds, subcortical gray matter: from 0.26 +/- 0.02 seconds to 0.10 +/- 0.02 seconds, cortical gray matter: from 0.36 +/- 0.02 seconds to 0.17 +/- 0.03 seconds). Using limited paired training data from both sequences, we can reduce the error between quantitative imaging methods and calibrate to one of the protocols with a neural network.

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