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Hierarchical Bayesian Modelling Improves Microstructural Parameter Mapping in Diffusion and Exchange MRI Data.

Code ↔ Paper

10 matches between paragraphs of the paper and lines of its authors' code, computed by the harvester (lexical-v1). Click a colored paragraph or line to see its counterpart.

The 10 matches
  1. [1] § Methods › Data › DKI › Human Connectom Project Data ↔ dmipy/data/saved_data.py, lines 58–81 · score 0.93 · WU Minn Consortium, Washington University, Neuroscience Research, NIH Blueprint, McDonnell, U54MH091657
  2. [2] § Methods › Model Fitting › Hierarchical Bayesian Estimation ↔ examples/example_axr_simulated_data.m, lines 1–54 · score 0.69 · BBB FEXI, regional priors, LSQ fit, Matlab, burn, bounds
  3. [3] § Methods › Data › DKI › Human Connectom Project Data ↔ dmipy/tissue_response/white_matter_response.py, lines 79–214 · score 0.68 · MRtrix, selecting voxels, gradient directions, FA, tensor, anisotropy
  4. [4] § Methods › Model Fitting › Hierarchical Bayesian Estimation ↔ examples/example_dki_simulated_data.m, lines 1–56 · score 0.60 · regional priors, LSQ fit, Matlab, DKI, burn, bounds
  5. [5] § Methods › Exemplar Microstructure Models › BBB‐FEXI ↔ fexi_fit.m, lines 36–136 · score 0.57 · encoding block, extravascular, intravascular, FEXI, filter, diffusion
  6. [6] § Methods › Data › BBB‐FEXI › Simulations ↔ examples/example_axr_simulated_data.m, lines 56–97 · score 0.56 · Gaussian noise, complex signal, noisy, gradient directions, zero, Simulations
  7. [7] § Methods › Background: A General Hierarchical Bayesian Microstructure Model ↔ examples/example_axr_simulated_data.m, lines 1–54 · score 0.54 · blood brain barrier, BBB, exchange, FEXI, Bayesian, signal
  8. [8] § Methods › Exemplar Microstructure Models › BBB‐FEXI ↔ fexi_sim.m, lines 30–108 · score 0.54 · diffusion encoding block, FEXI, filter, mixing, weighted, signal
  9. [9] § Full Derivation of the General Hierarchical Bayesian Microstructure Model › Parameter Transforms ↔ fit_bayes.py, lines 379–438 · score 0.53 · Metropolis Hastings, transformed parameter, Gibbs
  10. [10] § Full Derivation of the General Hierarchical Bayesian Microstructure Model › Parameter Transforms ↔ fit_bayes.m, lines 152–213 · score 0.53 · Metropolis Hastings, transformed parameter, Gibbs

Paper

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The authors' code

MATLAB · 270 lines · 12 KB · MIT · 3 matches

  1. %=========================================================================%
  2. %
  3. % Created on Thu, 21 Nov 2024
  4. % author: E Powell
  5. %
  6. % Simulate data (BBB-FEXI [1], AXR model [2])
  7. %
  8. % [1] E Powell, Y Ohene, M Battiston, BR Dickie, LM Parkes, GJM Parker.
  9. % "Blood-brain barrier water exchange measurements using FEXI: Impact
  10. % of modeling paradigm and relaxation time effects". MRM, (2023).
  11. % doi: 10.1002/mrm.29616
  12. %
  13. % [2] S Lasic, M Nilsson, J Latt, F Stahlberg, D Topgaard. "Apparent
  14. % exchange rate mapping with diffusion MRI". MRM. (2011)
  15. % doi: 10.1002/mrm.22782
  16. %
  17. %=========================================================================%
  19. clearvars -except SNR nsteps nroifit; clc; warning('off')
  21. %------------------------ USER DEFINED PARAMETERS ------------------------%
  22. basedir = fullfile('/home','epowell','code','matlab','matlab-bayesian'); % path to matlab-bayesian code directory
  23. % nsteps = 1e5; % no. MCMC steps
  24. burn_in = round(nsteps/2); % no. of steps to discard (burn-in)
  25. nupdates = 100; % how often weights are updated
  26. % nroifit = 2; % no. regional priors
  27. % SNR = 20; % SNR in bf=0, tm=min, be=0 data
  28. nsa = 6; % no. gradient directions + no. signal averages
  29. ninit = 25; % no. initial values for LSQ fit
  30. useparpool = 1; % use Matlab parallel pool for LSQ fit (1 yes; 0 no)
  31. saveflag = 1; % save output (1 yes; 0 no)
  32. plotflag = 0; % plot output (1 yes; 0 no)
  33. %-------------------------------------------------------------------------%
  35. % fitting bounds
  36. lb = [0.1e-9 0 0]; % [D, sigma, AXR] (SI units)
  37. ub = [3.5e-9 1 50]; % [D, sigma, AXR] (SI units)
  39. % load FEXI acqusition scheme (spherical mean scheme)
  40. loadloc = fullfile(basedir,'data');
  41. bf = read_text_files(fullfile(loadloc,'sim_axr.bvalf'));
  42. tm = read_text_files(fullfile(loadloc,'sim_axr.tm'));
  43. be = read_text_files(fullfile(loadloc,'sim_axr.bval'));
  44. bvecs = read_text_files(fullfile(loadloc,'sim_axr.bvec'));
  46. % load test data
  47. load(fullfile(loadloc,'sim_axr_data.mat')) % vars: adc, axr, mask, nvox, nx, ny, rois, sig
  49. if saveflag
  50. saveloc = loadloc;
  51. % savenm = ['sim_axr_fit__',char(datetime('now','Format','yyyy-MM-dd_HH-mm-SS'))];
  52. savenm = ['axr_snr',num2str(SNR),'_nsteps',num2str(nsteps),'_nroi',num2str(nroifit),char(datetime('now','Format','__yyyy-MM-dd_HH-mm-SS'))];
  53. fprintf('Saving to %s\n\n',fullfile(saveloc,savenm))
  54. end
  56. %% generate signals (noise free & noisy)
  57. E_nfree = zeros(nvox,numel(bf),nsa);
  58. E_noisy = zeros(nvox,numel(bf),nsa);
  59. for i = 1:nvox
  60. for j = 1:nsa
  61. E_nfree(i,:,j) = axr_sim(adc(i),sig(i),axr(i),bf(:),be(:),tm(:));
  62. % add Gaussian noise to complex signal (only necessary if min. SNR ~< 2)
  63. re = E_nfree(i,:,j) + (1/SNR)*randn(1,numel(bf));
  64. im = zeros(1,numel(bf)) + (1/SNR)*randn(1,numel(bf));
  65. E_noisy(i,:,j) = abs(re + 1i*im);
  66. % E_noisy(i,:,j) = E_nfree(i,:,j) + (1/SNR).*randn(1,numel(bf));
  67. end
  68. end
  70. fprintf('\n SNR set in 1 b0 = %.0f\n SNR in bf=min,tm=min,b=min = %.0f\n SNR in bf=max,tm=max,b=max = %.0f\n',...
  71. SNR,...
  72. mean(E_noisy(:,bf==min(bf)&tm==min(tm)&be==min(be)),1)/std(E_noisy(:,bf==min(bf)&tm==min(tm)&be==min(be),1)),...
  73. mean(E_noisy(:,bf==max(bf)&tm==max(tm)&be==max(be)),1)/std(E_noisy(:,bf==max(bf)&tm==max(tm)&be==max(be),1)))
  74. % figure, subplot(1,2,1), plot(repmat(be,[1 nsa]),squeeze(E_noisy(1,:,:)),'bo', repmat(be,[1 nsa]),squeeze(E_nfree(1,:,:)),'g*'), axis square, set(findobj(gca,'type','line'),'LineWidth',2,'markersize',8)
  76. % "spherically average" the simulated data
  77. E_nfree = mean(E_nfree,3);
  78. E_noisy = mean(E_noisy,3);
  79. fprintf('\n SNR averaged for %i gradient directions = %.0f\n SNR in bf=min,tm=min,b=min = %.0f\n SNR in bf=max,tm=max,b=max = %.0f\n\n',...
  80. nsa,...
  81. SNR*sqrt(nsa),...
  82. mean(E_noisy(:,bf==min(bf)&tm==min(tm)&be==min(be)))/std(E_noisy(:,bf==min(bf)&tm==min(tm)&be==min(be))),...
  83. mean(E_noisy(:,bf==max(bf)&tm==max(tm)&be==max(be)))/std(E_noisy(:,bf==max(bf)&tm==max(tm)&be==max(be))))
  84. % subplot(1,2,2), plot(be,E_noisy(1,:),'bo', be,E_nfree(1,:),'g*'), axis square, set(findobj(gca,'type','line'),'LineWidth',2,'markersize',8)
  87. %{
  88. test_SNR=10; test_nsa=1;
  89. n = 1e6;
  90. test_nfree = ones(1,n);
  91. re = test_nfree + (1/(test_SNR*sqrt(test_nsa)))*randn(1,n);
  92. im = zeros(1,n) + (1/(test_SNR*sqrt(test_nsa)))*randn(1,n);
  93. test_noisy = abs(re + 1i*im);
  94. [SNR*sqrt(nsa) mean(test_noisy)/std(test_noisy)]
  95. % figure, axis square, hold on
  96. histogram(test_noisy,100)
  97. %}
  99. %% LSQ fitting
  101. % use "ninit" initialisations for LSQ fit
  102. lsq_fit = struct;
  103. lsq_fit.adc = zeros(nvox,1);
  104. lsq_fit.sigma = zeros(nvox,1);
  105. lsq_fit.axr = zeros(nvox,1);
  106. init = [linspace(lb(1),ub(1),round(ninit^(1/3)))',...
  107. linspace(lb(2),ub(2),round(ninit^(1/3)))',...
  108. linspace(lb(3),ub(3),round(ninit^(1/3)))']; % D, sigma, AXR
  109. init = combvec(init(:,1)',init(:,2)',init(:,3)')';
  110. tic
  111. if useparpool, mypool = parpool(4); end
  112. for i = 1:nvox
  113. display_progress(i,nvox,i==1)
  114. if mask(i)
  115. [lsq_fit.adc(i), lsq_fit.sigma(i), lsq_fit.axr(i)] ...
  116. = axr_fit(bf(:), be(:), tm(:), E_noisy(i,:), init, lb, ub, useparpool);
  117. end
  118. end
  119. if useparpool, delete(mypool), end
  120. t_lsq = toc;
  121. fprintf('Time for LSQ fit: %.2f min\n',t_lsq/60)
  123. % predict signals from LSQ fit
  124. E_fit_lsq = zeros(nvox,numel(bf));
  125. for i = 1:nvox
  126. E_fit_lsq(i,:) = axr_sim(lsq_fit.adc(i),lsq_fit.sigma(i),lsq_fit.axr(i),bf(:),be(:),tm(:));
  127. end
  129. %% HBM fitting
  131. t = tic;
  133. % setup model (dmipy-style)
  134. model = [];
  135. model.partial_volume_names = {};
  136. model.parameter_cardinality.adc = 1;
  137. model.parameter_cardinality.sigma = 1;
  138. model.parameter_cardinality.axr = 1;
  139. model.parameter_names = {'adc','sigma','axr'};
  140. model.parameter_ranges.adc = [lb(1) ub(1)]*1e9;
  141. model.parameter_ranges.sigma = [lb(2) ub(2)];
  142. model.parameter_ranges.axr = [lb(3) ub(3)];
  143. model.parameter_scales.adc = 1e-9;
  144. model.parameter_scales.sigma = 1;
  145. model.parameter_scales.axr = 1;
  146. model.parameter_fixed.adc = 0;
  147. model.parameter_fixed.sigma = 0;
  148. model.parameter_fixed.axr = 0;
  150. model.simulate_signal = @(scheme,pvec) arrayfun(@(i) axr_sim(pvec.adc(i),pvec.sigma(i),pvec.axr(i),scheme.bf(:),scheme.bvalues(:),scheme.tm(:)), 1:numel(pvec.adc), 'UniformOutput',false);
  152. % setup acquisition scheme (dmipy-style)
  153. acq_scheme = struct;
  154. acq_scheme.bf = bf;
  155. acq_scheme.tm = tm;
  156. acq_scheme.bvalues = be;
  157. acq_scheme.gradient_directions = bvecs;
  159. % setup parameter vector (dmipy-style)
  160. parameter_vector_init = struct;
  161. parameter_vector_init.adc = lsq_fit.adc*1e9;
  162. parameter_vector_init.sigma = lsq_fit.sigma;
  163. parameter_vector_init.axr = lsq_fit.axr;
  165. if nroifit == 1
  166. rois = logical(rois);
  167. else
  168. % do nothing: rois = rois.
  169. end
  171. % run Bayesian fitting
  172. [params_all, ~, ~, stats_posterior, stats_prior] ...
  173. = fit_bayes(model, acq_scheme, E_noisy, parameter_vector_init, [], rois, nsteps, burn_in, nupdates, 0);
  174. t_hbm = toc(t);
  175. fprintf('Time for HBM fit: %.2f min\n',t_hbm/60)
  177. % NOTE: stats_posterior.(param).mn and params_all.(param) may be slightly
  178. % different (<0.1%) as params_all calculated over all MCMC steps post
  179. % burn-in, but stats_posterior calculated over a subsampled set of steps
  180. % post burn-in (for memory reasons)
  182. % predict signals from Bayesian fit
  183. E_fit_bayes = cell2mat(model.simulate_signal(acq_scheme, params_all))';
  185. % save
  186. if saveflag
  187. fprintf('Saving...')
  188. save(fullfile(saveloc,[savenm,'.mat']),'-v7.3')
  189. fprintf('Done.\n\n')
  190. end
  192. %% plotting
  194. if plotflag
  195. % plot parameter maps
  196. figure
  197. nr = 3; nc = 3;
  199. col_adc = autumn;
  200. col_sig = hot;
  201. col_axr = parula;
  203. lb_plot = lb; ub_plot = ub;
  205. % plot GT
  206. tmp = reshape(adc*1e9,[nx,ny]); h = subplot(nr,nc,1); imagesc(tmp) % plot fitted D
  207. clim([lb_plot(1) ub_plot(1)]*1e9), colorbar, colormap(h,col_adc)
  208. title('D (GT)'), set(get(colorbar,'label'),'string','[um^2/mm]'), axis image off
  209. tmp = reshape(sig,[nx,ny]); h = subplot(nr,nc,2); imagesc(tmp) % plot fitted sigma
  210. clim([lb_plot(2) ub_plot(2)]), colorbar, colormap(h,col_sig)
  211. title('\sigma (GT)'), set(get(colorbar,'label'),'string','[a.u.]'), axis image off
  212. tmp = reshape(axr,[nx,ny]); h = subplot(nr,nc,3); imagesc(tmp) % plot fitted AXR
  213. clim([lb_plot(3) ub_plot(3)]), colorbar, colormap(h,col_axr)
  214. title('AXR (GT)'), set(get(colorbar,'label'),'string','[s^{-1}]'), axis image off
  216. % plot LSQ fit
  217. tmp = reshape(lsq_fit.adc*1e9,[nx,ny]); h = subplot(nr,nc,4); imagesc(tmp) % plot fitted D
  218. clim([lb_plot(1) ub_plot(1)]*1e9), colorbar, colormap(h,col_adc)
  219. title('D (LSQ)'), set(get(colorbar,'label'),'string','[um^2/mm]'), axis image off
  220. tmp = reshape(lsq_fit.sigma,[nx,ny]); h = subplot(nr,nc,5); imagesc(tmp) % plot fitted sigma
  221. clim([lb_plot(2) ub_plot(2)]), colorbar, colormap(h,col_sig)
  222. title('\sigma (LSQ)'), set(get(colorbar,'label'),'string','[a.u.]'), axis image off
  223. tmp = reshape(lsq_fit.axr,[nx,ny]); h = subplot(nr,nc,6); imagesc(tmp) % plot fitted AXR
  224. clim([lb_plot(3) ub_plot(3)]), colorbar, colormap(h,col_axr)
  225. title('AXR (LSQ)'), set(get(colorbar,'label'),'string','[s^{-1}]'), axis image off
  227. % plot Bayesian fit
  228. tmp = reshape(params_all.adc*1e9,[nx,ny]); h = subplot(nr,nc,7); imagesc(tmp) % plot fitted D
  229. clim([lb_plot(1) ub_plot(1)]*1e9), colorbar, colormap(h,col_adc)
  230. title('D (HBM)'), set(get(colorbar,'label'),'string','[um^2/mm]'), axis image off
  231. tmp = reshape(params_all.sigma,[nx,ny]); h = subplot(nr,nc,8); imagesc(tmp) % plot fitted sigma
  232. clim([lb_plot(2) ub_plot(2)]), colorbar, colormap(h,col_sig)
  233. title('\sigma (HBM)'), set(get(colorbar,'label'),'string','[a.u.]'), axis image off
  234. tmp = reshape(params_all.axr,[nx,ny]); h = subplot(nr,nc,9); imagesc(tmp) % plot fitted AXR
  235. clim([lb_plot(3) ub_plot(3)]), colorbar, colormap(h,col_axr)
  236. title('AXR (HBM)'), set(get(colorbar,'label'),'string','[s^{-1}]'), axis image off
  240. % plot correlations with GT
  241. figure
  242. nr = 1; nc = 3;
  244. col_lsq = 'r';
  245. col_hbm = 'b';
  247. % D
  248. subplot(nr,nc,1), hold on
  249. plot(adc(:)*1e9,lsq_fit.adc(:)*1e9,'o','color',col_lsq) % plot LSQ fit
  250. plot(adc(:)*1e9,params_all.adc(:)*1e9,'o','color',col_hbm) % plot HBM fit
  251. plot([lb_plot(1) ub_plot(1)]*1e9, [lb_plot(1) ub_plot(1)]*1e9, 'k--') % identity line
  252. xlim([.7 1.6]), ylim([.7 1.6]), axis square
  253. legend('LSQ','HBM'), xlabel('D_{gt} [um^2/mm]'), ylabel('D_{fit} [um^2/mm]')
  254. % sigma
  255. subplot(nr,nc,2), hold on
  256. plot(sig(:),lsq_fit.sigma(:),'o','color',col_lsq) % plot LSQ fit
  257. plot(sig(:),params_all.sigma(:),'o','color',col_hbm) % plot HBM fit
  258. plot([lb_plot(2) ub_plot(2)], [lb_plot(2) ub_plot(2)], 'k--') % identity line
  259. xlim([0.05 .3]), ylim([0.05 .3]), axis square
  260. legend('LSQ','HBM'), xlabel('\sigma_{gt} [a.u.]'), ylabel('\sigma_{fit} [a.u.]')
  261. % AXR
  262. subplot(nr,nc,3), hold on
  263. plot(axr(:),lsq_fit.axr(:),'o','color',col_lsq), hold on % plot LSQ fit
  264. plot(axr(:),params_all.axr(:),'o','color',col_hbm) % plot HBM fit
  265. plot([lb_plot(3) ub_plot(3)], [lb_plot(3) ub_plot(3)], 'k--') % identity line
  266. xlim([0 4]), ylim([lb_plot(3) ub_plot(3)]), axis square
  267. legend('LSQ','HBM'), xlabel('AXR_{gt} [s^{-1}]'), ylabel('AXR_{fit} [s^{-1}]')
  269. end

example_axr_simulated_data.m at commit 743ae00, under MIT · at the source

Overview

Authors: Elizabeth Powell1, Mark Maskery2,3, Hedley C A Emsley2,3, Laura M Parkes4,5, Geoff J M Parker1,6, Paddy J Slator7,8
ORCID iDs: Elizabeth Powell, Mark Maskery, Hedley C A Emsley, Laura M Parkes, Geoff J M Parker, Paddy J Slator
  1. Department of Medical Physics and Biomedical Engineering, University College London, London, UK
  2. Lancaster Medical School, Lancaster University, Lancaster, UK
  3. Department of Neurology, Lancashire Teaching Hospitals NHS Foundation Trust, Preston, UK
  4. Division of Psychology, Communication and Human Neuroscience, School of Health Sciences, Faculty of Biology, Medicine and Health, University of Manchester, Manchester, UK
  5. Geoffrey Jefferson Brain Research Centre, Faculty of Biology, Medicine and Health, University of Manchester, Manchester, UK
  6. Bioxydyn Limited, Manchester, UK
  7. Cardiff University Brain Research Imaging Centre, School of Psychology, Cardiff University, Cardiff, UK
  8. School of Computer Science and Informatics, Cardiff University, Cardiff, UK
Institutions: University College London (United Kingdom); Lancashire Teaching Hospitals NHS Foundation Trust (United Kingdom); Lancaster University (United Kingdom); University of Manchester (United Kingdom); Cardiff University (United Kingdom)
Journal: NMR in biomedicine, volume 39, issue 6, article e70277
Dates: received 2 June 2025; accepted 10 February 2026; published online 11 May 2026; in print June 2026
Type: Research article · Language: English
License: CC BY
Identifiers: DOI 10.1002/nbm.70277 · PMID 42115150 · PMCID PMC13160881 · OpenAlex W4414048604
Open access: hybrid, a free copy (OpenAlex)
Preprint: doi:10.1101/2025.09.04.674046
Status: code verified
Categories: structural MRI / diffusion (modality), human (organism), computational (subfield)
Methods: fMRI & imaging, Physiology & signal measures
Keywords: Bayesian modelling, blood–brain barrier, diffusion MRI, filter exchange imaging (FEXI), kurtosis, microstructure, water exchange
MeSH: Brain*, Diffusion Magnetic Resonance Imaging*, Image Interpretation, Computer-Assisted*, Algorithms, Bayes Theorem, Computer Simulation, Humans, Reproducibility of Results, Signal-To-Noise Ratio (* major topic)
Topic: Advanced Neuroimaging Techniques and Applications (Radiology, Nuclear Medicine and Imaging, Medicine), according to OpenAlex
Funding: Engineering and Physical Sciences Research Council (EP/M020533/1, EP/S031510/1); EPSRC (EP/S031510/1, EP/M020533/1); Alzheimer's Society (577); Alzheimer's Society Heather Corrie Impact Fund (577[AS-PG-21-045])
Citations: not cited yet (Europe PMC); 54 references in the paper

Abstract

Microstructure modelling quantifies subvoxel tissue features by combining an MRI acquisition with a mathematical model, which is typically fitted voxel‐by‐voxel with least‐squares (LSQ) minimisation to give voxelwise maps of microstructural quantities such as diffusivity and compartmental fractions. Such approaches are susceptible to voxelwise noise, which can lead to erroneous values in parameter maps. Hierarchical Bayesian modelling (HBM) can address this limitation but has only been demonstrated for simple models. We previously derived an HBM approach for an arbitrary microstructure model with flexible parameter constraints, utilising a Markov chain Monte Carlo algorithm for parameter estimation; here, the method is demonstrated and evaluated using simulated and human data for two previously unexplored diffusion MRI techniques, namely, diffusion kurtosis imaging and blood–brain barrier filter exchange imaging. When compared with LSQ minimisation, HBM increased the accuracy, precision, contrast‐to‐noise ratio and parameter map quality in both simulated and human data. HBM was also able to resolve local parameter variations associated with white matter lesions in a small sample of cerebral small vessel disease subjects, which were obscured by high noise levels in the LSQ‐derived parameter maps. Finally, a noise sensitivity assessment in simulations showed that HBM improved the contrast‐to‐noise ratio and parameter map quality even at low signal‐to‐noise ratios. This generalised HBM framework can improve parameter estimation for more complex diffusion MRI microstructural models that extend beyond linear combinations of exponentials.

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e-powell/hbm-matlab

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At the source: github.com/e-powell/hbm-dmipy

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Data Availability Statement

The data that support the findings of this study are available on request from the corresponding author. The data are not publicly available due to privacy or ethical restrictions.

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Recorded: type, language, journal, volume, issue, pages, dates, 6 authors, 7 keywords, 9 MeSH terms, 4 funders, 54 references.

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Powell, E., Maskery, M., Emsley, H. C. A., Parkes, L. M., Parker, G. J. M., & Slator, P. J. (2026). Hierarchical Bayesian Modelling Improves Microstructural Parameter Mapping in Diffusion and Exchange MRI Data. NMR in biomedicine, 39(6), e70277. https://doi.org/10.1002/nbm.70277

BibTeX

@article{powell2026hierarchical,
author = {Powell, Elizabeth and Maskery, Mark and Emsley, Hedley C A and Parkes, Laura M and Parker, Geoff J M and Slator, Paddy J},
title = {{Hierarchical Bayesian Modelling Improves Microstructural Parameter Mapping in Diffusion and Exchange MRI Data}},
journal = {NMR in biomedicine},
year = {2026},
month = jun,
volume = {39},
number = {6},
pages = {e70277},
publisher = {Wiley},
issn = {0952-3480},
doi = {10.1002/nbm.70277},
url = {https://doi.org/10.1002/nbm.70277},
pmid = {42115150},
pmcid = {PMC13160881}
}

RIS

TY - JOUR
AU - Powell, Elizabeth
AU - Maskery, Mark
AU - Emsley, Hedley C A
AU - Parkes, Laura M
AU - Parker, Geoff J M
AU - Slator, Paddy J
TI - Hierarchical Bayesian Modelling Improves Microstructural Parameter Mapping in Diffusion and Exchange MRI Data
T2 - NMR in biomedicine
J2 - NMR Biomed
PY - 2026
DA - 2026/06/01
VL - 39
IS - 6
SP - e70277
SN - 0952-3480
PB - Wiley
DO - 10.1002/nbm.70277
UR - https://doi.org/10.1002/nbm.70277
LA - en
ER -

CSL-JSON

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"author": [
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"container-title-short": "NMR Biomed",
"volume": "39",
"issue": "6",
"page": "e70277",
"DOI": "10.1002/nbm.70277",
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"URL": "https://doi.org/10.1002/nbm.70277",
"language": "en",
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2026,
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