OSCR

Functional dual-slope frequency-domain near-infrared spectroscopy data interpreted with two- and three-layer models.

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 · 3 of them tie a paragraph to a whole file without given lines: weak matches, whose lines are not tinted
  1. [1] § Methods › Data Collection › In silico simulations of two- and three-layered media ↔ TwoLayerSpectroscopy/R_2L_withPreCom.m, the whole file · a weak match · score 0.67 · angular modulation frequency, absorption coefficient, speed, photons, refractive, Sec · Report a mismatch
  2. [2] § Methods › Data Analysis › Measure of functional brain activation with data type M (maximum at 830 nm) ↔ DualRatio_FluorescenceFlowCytometry/221101Data/NEUprocessed/two_probe__4_pmt_preProc.m, lines 30 to 147 · score 0.61 · standard deviation, fibers, peak, window, threshold, SNR · Report a mismatch
  3. [3] § Methods › Data Collection › In silico simulations of two- and three-layered media ↔ TwoLayerSpectroscopy/R_2L_withPreCom.m, the whole file · a weak match · score 0.59 · reduced scattering coefficient, radius, zero, photons, diffusive, refractive · Report a mismatch
  4. [4] § Biographies ↔ PulseOxSpectralLinewidth/LEDspecColor_forPUB.m, lines 1 to 35 · score 0.58 · Biomedical Optics, Sergio Fantini, Optical · Report a mismatch
  5. [5] § Methods › Data Collection › In silico simulations of two- and three-layered media ↔ TwoLayer/TwoLayerReflectance.m, the whole file · a weak match · score 0.57 · angular modulation frequency, speed, photons, refractive, coefficient, Sec · Report a mismatch
  6. [6] § Methods › Data Analysis › Changes in absorption coefficient ( ) ↔ PulseOxSpectralLinewidth/LEDspecColor_forPUB.m, lines 219 to 246 · score 0.57 · deoxy hemoglobin, Beer, law, wavelengths, concentration, coefficient · Report a mismatch
  7. [7] § Methods › Data Collection › In vivo brain measurements › Equipment and human subjects ↔ PulseOxSpectralLinewidth/LEDspecColor_forPUB.m, lines 37 to 61 · score 0.54 · laser diodes, skin, wavelengths, setup, dual, tissue · Report a mismatch
  8. [8] § Methods › Data Collection › In vivo brain measurements › Equipment and human subjects ↔ DualSlope/DSdmua.m, lines 1 to 115 · score 0.54 · dual slope, human, modulated, Tufts, brain, intensity · Report a mismatch
  9. [9] § Biographies ↔ PulseOxSpectralLinewidth/LEDspecColor_forPUB.m, lines 1 to 35 · score 0.51 · optical measurements, Giles Blaney, optics, Biomedical · Report a mismatch
  10. [10] § Methods › Data Analysis › Changes in absorption coefficient ( ) ↔ CHS/time-domain CHS/Example.m, lines 52 to 110 · score 0.50 · deoxy hemoglobin · Report a mismatch

Paper

Loaded from Europe PMC by your browser; OSCR does not store it: doi.org · Europe PMC

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The authors' code

MATLAB · 778 lines · 25 KB · no license · 4 matches

  1. %% Giles Blaney, PhD; Spring 2026
  2. % Please cite
  3. % Giles Blaney, Sergio Fantini "Broad-linewidth sources result in a skin-tone
  4. % bias in noninvasive optical measurement of oxygen saturation,"
  5. % Journal of Biomedical Optics 31(7), 070501 (9 Jul 2026)
  6. % https://doi.org/10.1117/1.JBO.31.7.070501
  7. % for anything regarding this code.
  9. clear; home;
  11. % Nominal RED and IR wavelengths & full width half maxes
  12. lamRED = 660; %nm
  13. lamIR = 880; %nm
  14. LEDfwhm_all = linspace(10,100, 10); %nm
  16. % Melanin volume fractions
  17. Mfrac_all = linspace(0,0.43,10);
  19. % Pulsatile hemoglobin perturbation & arterial oxygen saturation
  20. dTart = 1; %uM
  21. SaO2_all = linspace(0.7,1,100);
  23. % Wavelengths to simulate
  24. lam = (550:1050).'; %nm
  26. % Set if we assume constant epidermis thickness (useMCpathlen=false) or use
  27. % path-lengths from Monte-Carlo (useMCpathlen=true)
  28. useMCpathlen = true;
  30. % Thickness and source detector distance
  31. s = 10; %mm
  32. rho = s; % Detector is directly opposite source
  34. % Number of terms in diffusion theory solution to sum
  35. m_max = 100;
  37. %% ########## Setup #######################################################
  38. % Load results from Monte Carlo based on the model in:
  39. % G. Blaney, J. Frias, F. Tavakoli, A. Sassaroli, and S. Fantini,
  40. % "Dual-ratio approach to pulse oximetry and the effect of skin tone,"
  41. % JBO, vol. 29, no. S3, p. S33311, Oct. 2024,
  42. % doi: 10.1117/1.JBO.29.S3.S33311
  43. if useMCpathlen
  44. MCavg = load('deps/MCout_avg.mat');
  45. end
  47. % Find indexes of the nominal RED and IR wavelengths
  48. [~,iRED] = min(abs(lam-lamRED));
  49. [~,iIR] = min(abs(lam-lamIR));
  51. % Create Laser Diode (LD) emission spectrum
  52. P0red_LD = zeros(size(lam));
  53. P0red_LD(iRED) = 1; %power/nm
  54. P0ir_LD = zeros(size(lam));
  55. P0ir_LD(iIR) = 1; %power/nm
  57. % Generate bulk tissue optical property spectra
  58. [muspTIS, muaTIS, nTIS] = tissueOptProps_func(lam);
  60. % Generate matrix of extinction coefficients for oxy- and deoxy-hemoglobin
  61. E_OD = makeE('OD',lam); %(1/mm)/uM
  63. %% ########## Calculate total path-length in bulk tissue <L> ##############
  64. % Infinitesimal perturbation for numerical derivative
  65. dmua_numDer = 1e-6; %1/mm
  67. % Initialize optical property structure
  68. optProp.nin=[];
  69. optProp.nout=1;
  70. optProp.musp=[]; %1/mm
  71. optProp.mua=[]; %1/mm
  73. % Loop through wavelength and calculate <L> for each
  74. L = NaN(size(lam));
  75. for i = 1:length(lam)
  77. % Set refractive index and reduced scattering coefficient
  78. optProp.nin=nTIS(i);
  79. optProp.musp=muspTIS(i); %1/mm
  81. % Calculate transmittance Green's function with a symmetric
  82. % infinitesimal perturbation
  83. optProp.mua=muaTIS(i)-dmua_numDer/2; %1/mm
  84. Tgrn_0 = Tslab(rho, s, optProp, m_max); %1/mm^2
  85. optProp.mua=muaTIS(i)+dmua_numDer/2; %1/mm
  86. Tgrn_1 = Tslab(rho, s, optProp, m_max); %1/mm^2
  88. % Find <L> via numerical derivative
  89. L(i) = -(log(Tgrn_1)-log(Tgrn_0))/dmua_numDer; %mm
  91. end
  93. %% ########## Loop over all arterial oxygen saturations ###################
  94. % Variable initialization (below)
  96. % Intensity spectra emitted from tissue for illumination from the RED or
  97. % IR LED (wavelength,SaO2,Melanin,FWHM)
  98. IredLED = NaN(length(lam),length(SaO2_all),length(Mfrac_all), ...
  99. length(LEDfwhm_all));
  100. IirLED = NaN(length(lam),length(SaO2_all),length(Mfrac_all), ...
  101. length(LEDfwhm_all));
  103. % Ratio-of-ratios for LDs or LEDs (SaO2,Melanin,FWHM)
  104. RoR_LD = NaN(length(SaO2_all),length(Mfrac_all),length(LEDfwhm_all));
  105. RoR_LED = NaN(length(SaO2_all),length(Mfrac_all),length(LEDfwhm_all));
  107. % Recovered arterial oxygen saturations for LDs, LEDs with nominal
  108. % extinction coefficients, or LEDs with weighted extinction coefficients
  109. % (SaO2,Melanin,FWHM)
  110. sat_LD_rec = NaN(length(SaO2_all),length(Mfrac_all),length(LEDfwhm_all));
  111. sat_LED_rec = NaN(length(SaO2_all),length(Mfrac_all),length(LEDfwhm_all));
  112. satw_LED_rec = NaN(length(SaO2_all),length(Mfrac_all),length(LEDfwhm_all));
  114. % SaO2 loop
  115. for SaO2ind = 1:length(SaO2_all)
  116. % Calculate changes in absorption given total-hemoglobin concentration
  117. % and arterial oxygen saturation
  118. dO = dTart*SaO2_all(SaO2ind); %uM
  119. dD = dTart-dO; %uM
  120. dmua = E_OD*[dO;dD]; %1/mm
  122. %% ########## Transmittance Green's functions #########################
  123. % Loop through wavelength and calculate Green's function during
  124. % systolic and diastolic phases for each wavelength
  125. Tgrn_sys = NaN(size(lam));
  126. Tgrn_dia = NaN(size(lam));
  127. for i = 1:length(lam)
  129. % Set refractive index and reduced scattering coefficient
  130. optProp.nin=nTIS(i);
  131. optProp.musp=muspTIS(i); %1/mm
  133. % Calculate transmittance Green's function with a symmetric
  134. % blood volume perturbation
  135. optProp.mua=muaTIS(i)+dmua(i)/2; %1/mm
  136. Tgrn_sys(i) = Tslab(rho, s, optProp, m_max); %1/mm^2
  137. optProp.mua=muaTIS(i)-dmua(i)/2; %1/mm
  138. Tgrn_dia(i) = Tslab(rho, s, optProp, m_max); %1/mm^2
  140. end
  142. %% ########## Loop through melanin concentrations #####################
  143. for melInd = 1:length(Mfrac_all)
  144. % Absorption of epidermis from melanosomes using Equation 8 in:
  145. % S. L. Jacques, "Optical properties of biological tissues: a
  146. % review," PMB, vol. 58, no. 11, pp. R37–R61, May 2013,
  147. % doi: 10.1088/0031-9155/58/11/r37
  148. muaEPI = Mfrac_all(melInd) * 51.9*(lam/500).^-3.5; %1/mm
  150. %% Determine length through epidermal melanin filter
  151. if useMCpathlen
  152. % Find index of closest melanin concentration in Monte Carlo
  153. % data
  154. [~,iM_MC] = min(abs( MCavg.Mfracs - Mfrac_all(melInd) ));
  156. % Map partial path-lengths from Monte Carlo onto the simulated
  157. % wavelengths
  158. tmpLam = movmean(MCavg.lams, 10); %nm
  159. tmpL = movmean(MCavg.l(iM_MC,:,1), 10); %mm
  160. d = interp1(tmpLam, tmpL, lam, ...
  161. 'linear','extrap'); %mm
  162. else
  163. % Assume 0.25 mm thick on each side
  164. d = 0.25*2; %mm
  165. end
  167. %% ########## Loop through FWHM cases #############################
  168. for fwhmInd = 1:length(LEDfwhm_all)
  169. % Generate LED emission spectra
  170. P0red_LED = LEDspec_func(lam, lamRED, LEDfwhm_all(fwhmInd));
  171. P0ir_LED = LEDspec_func(lam, lamIR, LEDfwhm_all(fwhmInd));
  173. %% ########## Model spectra reaching the detector #############
  174. % Spectra for LD and systolic or diastolic cases (will be the
  175. % same for every FWHM loop iteration)
  176. IredLD_sys = P0red_LD .* exp(-muaEPI.*d) .* Tgrn_sys;
  177. IirLD_sys = P0ir_LD .* exp(-muaEPI.*d) .* Tgrn_sys;
  178. IredLD_dia = P0red_LD .* exp(-muaEPI.*d) .* Tgrn_dia;
  179. IirLD_dia = P0ir_LD .* exp(-muaEPI.*d) .* Tgrn_dia;
  181. % Spectra for LED and systolic or diastolic cases (will depend
  182. % on FWHM loop iteration)
  183. IredLED_sys = P0red_LED .* exp(-muaEPI.*d) .* Tgrn_sys;
  184. IirLED_sys = P0ir_LED .* exp(-muaEPI.*d) .* Tgrn_sys;
  185. IredLED_dia = P0red_LED .* exp(-muaEPI.*d) .* Tgrn_dia;
  186. IirLED_dia = P0ir_LED .* exp(-muaEPI.*d) .* Tgrn_dia;
  188. % Find average spectra reaching the detectors for the LED case
  189. IredLED(:,SaO2ind,melInd,fwhmInd) = ...
  190. (IredLED_sys+IredLED_dia)/2;
  191. IirLED(:,SaO2ind,melInd,fwhmInd) = ...
  192. (IirLED_sys+IirLED_dia)/2;
  194. %% ########## Find detected signals ###########################
  195. % Sum spectra reaching the detectors to find detected signal
  196. % for LDs during systolic and diastolic phases (will be the
  197. % same for every FWHM loop iteration)
  198. IredLD_sys_det = sum(IredLD_sys);
  199. IirLD_sys_det = sum(IirLD_sys);
  200. IredLD_dia_det = sum(IredLD_dia);
  201. IirLD_dia_det = sum(IirLD_dia);
  203. % Sum spectra reaching the detectors to find detected signal
  204. % for LEDs during systolic and diastolic phases (will depend
  205. % on FWHM loop iteration)
  206. IredLED_sys_det = sum(IredLED_sys);
  207. IirLED_sys_det = sum(IirLED_sys);
  208. IredLED_dia_det = sum(IredLED_dia);
  209. IirLED_dia_det = sum(IirLED_dia);
  211. %% ########## Calculate ratio-of-ratios #######################
  212. RoR_LD(SaO2ind,melInd,fwhmInd) = ...
  213. ((IredLD_sys_det-IredLD_dia_det)/IredLD_dia_det)/...
  214. ((IirLD_sys_det-IirLD_dia_det)/IirLD_dia_det);
  215. RoR_LED(SaO2ind,melInd,fwhmInd) = ...
  216. ((IredLED_sys_det-IredLED_dia_det)/IredLED_dia_det)/...
  217. ((IirLED_sys_det-IirLED_dia_det)/IirLED_dia_det);
  219. %% ########## Apply modified Beer Lambert law #################
  220. % Generate matrix of extinction coefficients for oxy- and
  221. % deoxy-hemoglobin only at the nominal wavelengths
  222. E_mBLL = makeE('OD', [lamRED,lamIR]);
  224. % Calculate recovered absorption changes for LDs
  225. dmuaRED_LD = -log(IredLD_sys_det/IredLD_dia_det)/L(iRED);
  226. dmuaIR_LD = -log(IirLD_sys_det/IirLD_dia_det)/L(iIR);
  228. % Convert absorption to concentration and calculate recovered
  229. % oxygen saturation for LDs
  230. dC_LD = E_mBLL\[dmuaRED_LD;dmuaIR_LD];
  231. dO_LD_rec = dC_LD(1);
  232. dD_LD_rec = dC_LD(2);
  233. sat_LD_rec(SaO2ind,melInd,fwhmInd) = ...
  234. dO_LD_rec / (dO_LD_rec+dD_LD_rec);
  236. % Calculate recovered absorption changes for LEDs
  237. dmuaRED_LED = -log(IredLED_sys_det/IredLED_dia_det)/L(iRED);
  238. dmuaIR_LED = -log(IirLED_sys_det/IirLED_dia_det)/L(iIR);
  240. % Convert absorption to concentration and calculate recovered
  241. % oxygen saturation for LDs
  242. dC_LED = E_mBLL\[dmuaRED_LED;dmuaIR_LED];
  243. dO_LED_rec = dC_LED(1);
  244. dD_LED_rec = dC_LED(2);
  245. sat_LED_rec(SaO2ind,melInd,fwhmInd) = ...
  246. dO_LED_rec / (dO_LED_rec+dD_LED_rec);
  248. %% ########## Implement weighted extinction coefficients ######
  249. % Generate extinction spectra for oxy- and deoxy-hemoglobin
  250. extO = makeE('O',lam);
  251. extD = makeE('D',lam);
  253. % Weight extinction coefficients by the spectra reaching the
  254. % detectors
  255. Wred = IredLED(:,SaO2ind,melInd,fwhmInd);
  256. Wir = IirLED(:,SaO2ind,melInd,fwhmInd);
  257. extOred = sum(Wred.*extO)/sum(Wred);
  258. extDred = sum(Wred.*extD)/sum(Wred);
  259. extOir = sum(Wir.*extO)/sum(Wir);
  260. extDir = sum(Wir.*extD)/sum(Wir);
  262. % Convert absorption to concentration and calculate recovered
  263. % oxygen saturation considering weighted coefficients for LEDs
  264. Ew_mBLL = [
  265. extOred, extDred;
  266. extOir, extDir
  267. ];
  268. dCw_LED = Ew_mBLL\[dmuaRED_LED;dmuaIR_LED];
  269. dOw_LED_rec = dCw_LED(1);
  270. dDw_LED_rec = dCw_LED(2);
  271. satw_LED_rec(SaO2ind,melInd,fwhmInd) = ...
  272. dOw_LED_rec / (dOw_LED_rec+dDw_LED_rec);
  273. end
  274. end
  275. end
  277. %% ########## Plot -- Modeled Spectra #####################################
  278. cols = lines(7);
  279. Mind = length(Mfrac_all);
  281. [~,satInd] = min(abs(SaO2_all-0.95));
  282. [~,fwhmInd] = min(abs(LEDfwhm_all-50));
  286. figure(101); clf;
  288. % -------------------------------------------------------------------------
  289. subplot(2,1,1); hold on;
  290. plot(lam, LEDspec_func(lam, lamRED, LEDfwhm_all(fwhmInd)), '-',...
  291. 'Color',cols(7,:));
  292. xlim([-100,100]+lamRED);
  293. ylim([0,1]);
  294. ylabel('$P/P_{max}$');
  295. xlabel('Wavelength (nm)');
  296. title('Red LED');
  298. pos = get(gca,"Position");
  299. legend( ...
  300. 'Source Emission', ...
  301. 'Orientation','horizontal', ...
  302. 'Location','northoutside');
  303. set(gca, "Position",pos);
  305. % -------------------------------------------------------------------------
  306. subplot(2,1,2); hold on;
  307. plot(lam, LEDspec_func(lam, lamRED, LEDfwhm_all(fwhmInd)), '--',...
  308. 'Color',cols(7,:));
  309. tmp = IredLED(:,satInd,Mind,fwhmInd);
  310. plot(lam, tmp/max(tmp), '-',...
  311. 'Color',cols(7,:));
  312. xlim([-100,100]+lamRED);
  313. ylim([0,1]);
  314. ylabel('$I/I_{max}$');
  315. xlabel('Wavelength (nm)');
  316. title('Red LED');
  318. pos = get(gca,"Position");
  319. legend( ...
  320. 'Source Emission', ...
  321. 'Detected Spectrum', ...
  322. 'Orientation','vertical', ...
  323. 'Location','northoutside');
  324. set(gca, "Position",pos);
  328. % -------------------------------------------------------------------------
  329. % Absorption of epidermis from melanosomes using Equation 8 in:
  330. % S. L. Jacques, "Optical properties of biological tissues: a
  331. % review," PMB, vol. 58, no. 11, pp. R37–R61, May 2013,
  332. % doi: 10.1088/0031-9155/58/11/r37
  333. muaEPI = Mfrac_all(Mind) * 51.9*(lam/500).^-3.5; %1/mm
  335. [~,iM_MC] = min(abs( MCavg.Mfracs - Mfrac_all(Mind) ));
  336. tmpLam = movmean(MCavg.lams, 10);
  337. tmpL = movmean(MCavg.l(iM_MC,:,1), 10);
  338. d = interp1(tmpLam, tmpL, lam, ...
  339. 'linear','extrap');
  341. figure(102); clf;
  342. yyaxis left;
  343. plot(lam, muaEPI);
  344. ylabel('$\mu_a$ (mm$^{-1}$)');
  346. yyaxis right;
  347. plot(lam, d);
  348. ylabel('$\langle \ell \rangle$ (mm)', ...
  349. 'Interpreter','latex');
  351. xlim(lam([1,end]));
  352. xlabel('Wavelength (nm)');
  354. title('Epidermis Properties');
  358. % -------------------------------------------------------------------------
  359. figure(103); clf;
  361. yyaxis left;
  362. plot(lam, muaTIS);
  363. ylabel('$\mu_a$ (mm$^{-1}$)');
  365. yyaxis right;
  366. plot(lam, L);
  367. ylabel('$\langle L \rangle$ (mm)');
  369. xlim(lam([1,end]));
  370. xlabel('Wavelength (nm)');
  372. title('Bulk Tissue Properties');
  374. %% ########## Plot -- SaO2 vs. RoR ########################################
  376. colsM=flipud(copper(length(Mfrac_all)));
  378. [~,fwhmInd] = min(abs(LEDfwhm_all-50));
  382. figure(200); clf;
  383. % -------------------------------------------------------------------------
  384. ax1 = subplot(2,2,1);
  385. slp_LD = NaN(size(Mfrac_all));
  386. for i = 1:length(Mfrac_all)
  387. plot(RoR_LD(:,i,fwhmInd), SaO2_all,'-',...
  388. 'Color',colsM(i,:));
  389. hold on;
  391. p = polyfit(RoR_LD(:,i,fwhmInd),SaO2_all,1);
  392. slp_LD(i) = p(1);
  393. end
  394. xlabel('Recovered Ratio-of-Ratios');
  395. ylabel('Modeled SaO$_2$');
  396. title('(a) LDs');
  398. % -------------------------------------------------------------------------
  399. ax2 = subplot(2,2,2);
  400. slp_LED = NaN(size(Mfrac_all));
  401. for i = 1:length(Mfrac_all)
  402. plot(RoR_LED(:,i,fwhmInd), SaO2_all,'-',...
  403. 'Color',colsM(i,:));
  404. hold on;
  406. p = polyfit(RoR_LED(:,i,fwhmInd),SaO2_all,1);
  407. slp_LED(i) = p(1);
  408. end
  409. xlabel('Recovered Ratio-of-Ratios');
  410. ylabel('Modeled SaO$_2$');
  411. title('(b) LEDs');
  413. linkaxes([ax1,ax2], 'xy');
  414. xlim([0.3,1.3]);
  416. % -------------------------------------------------------------------------
  417. ax3 = subplot(2,2,3);
  418. plot(Mfrac_all,slp_LD, '-k'); hold on;
  419. for i = 1:length(Mfrac_all)
  420. plot(Mfrac_all(i),slp_LD(i), 'o', 'Color',colsM(i,:));
  421. end
  422. xlabel('Melanin Volume Fraction');
  423. ylabel('Slope of (a)');
  424. title('(c) LDs');
  426. % -------------------------------------------------------------------------
  427. ax4 = subplot(2,2,4);
  428. plot(Mfrac_all,slp_LED, '-k'); hold on;
  429. for i = 1:length(Mfrac_all)
  430. plot(Mfrac_all(i),slp_LED(i), 'o', 'Color',colsM(i,:));
  431. end
  432. xlabel('Melanin Volume Fraction');
  433. ylabel('Slope of (b)');
  434. title('(d) LEDs');
  436. linkaxes([ax3,ax4], 'xy');
  437. ylim([-0.38,-0.3]);
  439. %% ########## Plot -- Application of weighted extinction coefficients #####
  441. colsM = flipud(copper(length(Mfrac_all)));
  443. [~,fwhmInd] = min(abs(LEDfwhm_all-50));
  447. figure(300); clf;
  448. % -------------------------------------------------------------------------
  449. ax1 = subplot(2,2,1);
  450. for i = 1:length(Mfrac_all)
  451. plot(SaO2_all, sat_LD_rec(:,i,fwhmInd)-SaO2_all.', '-', ...
  452. 'Color',colsM(i,:)); hold on;
  453. end
  454. xlabel('Modeled SaO$_2$');
  455. ylabel('SaO$_{2,recovered}$ $-$ SaO$_{2,modeled}$');
  456. title('(a) LDs with Assumed $\epsilon$s');
  458. % -------------------------------------------------------------------------
  459. ax2 = subplot(2,2,2);
  460. for i = 1:length(Mfrac_all)
  461. plot(SaO2_all, sat_LED_rec(:,i,fwhmInd)-SaO2_all.', '-', ...
  462. 'Color',colsM(i,:)); hold on;
  463. end
  464. xlabel('Modeled SaO$_2$');
  465. ylabel('SaO$_{2,recovered}$ $-$ SaO$_{2,modeled}$');
  466. title('(b) LEDs with Assumed $\epsilon$s');
  468. % -------------------------------------------------------------------------
  469. subplot(2,2,3);
  470. cb = colorbar;
  471. cb.Limits = Mfrac_all([1,end]);
  472. cb.Ticks = round(Mfrac_all,2);
  473. cb.Label.String = 'Melanin Volume Fraction';
  474. cb.Position = cb.Position + [-0.1, 0, 0.01, 0];
  475. clim(Mfrac_all([1,end]));
  476. colormap(colsM);
  477. axis off;
  479. % -------------------------------------------------------------------------
  480. ax4 = subplot(2,2,4);
  481. for i = 1:length(Mfrac_all)
  482. plot(SaO2_all, satw_LED_rec(:,i,fwhmInd)-SaO2_all.', '-', ...
  483. 'Color',colsM(i,:)); hold on;
  484. end
  485. xlabel('Modeled SaO$_2$');
  486. ylabel('SaO$_{2,recovered}$ $-$ SaO$_{2,modeled}$');
  487. title('(c) LEDs with Weighted $\epsilon$s');
  489. linkaxes([ax1,ax2,ax4], 'xy');
  491. %% ########## Plot -- Dependance on LED FWHM ##############################
  493. colsM = flipud(copper(length(Mfrac_all)));
  497. figure(400); clf;
  498. % -------------------------------------------------------------------------
  499. ax1 = subplot(1,2,1);
  500. for i = 1:length(Mfrac_all)
  501. plot([0,LEDfwhm_all], ...
  502. [squeeze(rms(sat_LD_rec(:,i,1) - SaO2_all.'));...
  503. squeeze(rms(sat_LED_rec(:,i,:) - SaO2_all.'))], '-', ...
  504. 'Color',colsM(i,:)); hold on;
  505. end
  506. xlabel('Source FWHM (nm)');
  507. ylabel('SaO$_2$ RMS Error');
  509. title('(a) Assumed $\epsilon$s');
  511. % -------------------------------------------------------------------------
  512. ax2 = subplot(1,2,2);
  513. for i = 1:length(Mfrac_all)
  514. plot([0,LEDfwhm_all], ...
  515. [squeeze(rms(sat_LD_rec(:,i,1) - SaO2_all.'));...
  516. squeeze(rms(satw_LED_rec(:,i,:) - SaO2_all.'))], '-', ...
  517. 'Color',colsM(i,:)); hold on;
  518. end
  519. xlabel('Source FWHM (nm)');
  520. ylabel('SaO$_2$ RMS Error');
  521. title('(b) Weighted $\epsilon$s');
  523. pos = get(gca,'Position');
  524. cb = colorbar;
  525. cb.Limits = Mfrac_all([1,end]);
  526. cb.Ticks = round(Mfrac_all,2);
  527. cb.Label.String = 'Melanin Volume Fraction';
  528. clim(Mfrac_all([1,end]));
  529. colormap(colsM);
  530. set(gca,'Position',pos);
  532. linkaxes([ax1,ax2],'xy');
  536. %% ########################################################################
  537. %% ########## Functions ###################################################
  538. %% ########################################################################
  540. % =============== LED Spectra =============================================
  541. function [P0_LED] = LEDspec_func(lam, lamPK, lamFWHM)
  543. % Generate Gaussian and normalize
  544. P0_LED = normpdf(lam, ...
  545. lamPK, lamFWHM/(2*sqrt(2*log(2))));
  546. P0_LED = P0_LED/max(P0_LED);
  548. end
  550. % =============== Tissue Optical Properties ===============================
  551. function [muspTIS, muaTIS, nTIS] = tissueOptProps_func(lam, NVA)
  552. % Tissue optical properties based on:
  553. % S. L. Jacques, "Optical properties of biological tissues: a
  554. % review," PMB, vol. 58, no. 11, pp. R37–R61, May 2013,
  555. % doi: 10.1088/0031-9155/58/11/r37
  557. % By default use relative tissue volumes from model in:
  558. % G. Blaney, J. Frias, F. Tavakoli, A. Sassaroli, and S. Fantini,
  559. % "Dual-ratio approach to pulse oximetry and the effect of skin tone,"
  560. % JBO, vol. 29, no. S3, p. S33311, Oct. 2024,
  561. % doi: 10.1117/1.JBO.29.S3.S33311
  562. % Thus V_tisTyp/V_tot,noEpi are:
  563. % Bone = 0.119
  564. % Muscle = 0.457
  565. % Fat = 0.228
  566. % Dermis = 0.196
  567. arguments
  568. lam (:,1) double; %nm
  570. NVA.T (1,1) double = ...
  571. 69.8*0.119 + 117*0.457 + 12.5*0.228 + 4.70*0.196; %uM
  572. NVA.S (1,1) double = ...
  573. 0.875*0.119 + 0.641*0.457 + 0.760*0.228 + 0.390*0.196;
  574. NVA.W (1,1) double = ...
  575. 0.318*0.119 + 0.795*0.457 + 0.110*0.228 + 0.650*0.196;
  576. NVA.L (1,1) double = ...
  577. 0.00*0.119 + 0.00*0.457 + 0.69*0.228 + 0.00*0.196;
  579. NVA.ap (1,1) double = ...
  580. 15.3*0.119 + 13.0*0.457 + 34.2*0.228 + 43.6*0.196; %1/cm
  581. NVA.fray (1,1) double = ...
  582. 0.022*0.119 + 0.000*0.457 + 0.260*0.228 + 0.410*0.196;
  583. NVA.bMie (1,1) double = ...
  584. 0.326*0.119 + 0.926*0.457 + 0.567*0.228 + 0.562*0.196;
  585. end
  587. %% musp
  588. ap = NVA.ap; % 1/cm
  589. fRay = NVA.fray;
  590. bMie = NVA.bMie;
  591. % Combination of Rayleigh and Mie scattering
  592. muspTIS = ap*0.1*(fRay*(lam/500).^-4 ...
  593. + (1-fRay)*(lam/500).^-bMie); %1/mm
  595. %% mua
  596. T = NVA.T; % uM
  597. S = NVA.S;
  598. W = NVA.W;
  599. L = NVA.L;
  601. % Beer's law
  602. E_ODWL = makeE('ODWL', lam);
  603. muaTIS = E_ODWL * [T*S; T*(1-S); W; L];
  605. %% n
  606. % https://www.engineersedge.com/physics/refraction_for_water__15690.htm
  607. % at 40 deg C
  608. n_waterRef=[...
  609. 226.50, 361.05, 404.41, 589.00, 632.80, 1013.98;
  610. 1.39046, 1.34540, 1.34065, 1.33095, 1.32972, 1.32296].';
  611. n_water=interp1(n_waterRef(:, 1), n_waterRef(:, 2), lam, ...
  612. 'linear', 'extrap');
  614. % Equation 3 in:
  615. % S. L. Jacques, "Optical properties of biological tissues: a
  616. % review," PMB, vol. 58, no. 11, pp. R37–R61, May 2013,
  617. % doi: 10.1088/0031-9155/58/11/r37
  618. n_dry = 1.514;
  619. nTIS = n_dry - (n_dry - n_water) * W;
  621. end
  623. % =============== Transmittance Green's Function ==========================
  624. function T = Tslab(rho, s, optProp, m_max)
  625. % Transmitance for a slab with extrapolated boundary
  626. % Equation 4.35 in:
  627. % F. Martelli, S. Del Bianco, A. Ismaelli, and G. Zaccanti, Light
  628. % Propagation through Biological Tissue and Other Diffusive Media.
  629. % 1000 20th Street, Bellingham, WA 98227-0010 USA: SPIE, 2010.
  630. % doi: 10.1117/3.824746
  631. arguments (Input)
  632. rho (1,1) double; %mm -- Source detector distance
  633. s (1,1) double; %mm -- Slab thickness
  635. optProp struct = [];
  636. m_max (1,1) double = 100;
  637. end
  638. arguments (Output)
  639. T (1,1) double; %1/mm^2 -- Transmittance Green's function
  640. end
  642. % Set default optical properties if input not given
  643. if isempty(optProp)
  644. clear optProp;
  646. optProp.nin=1.4;
  647. optProp.nout=1;
  648. optProp.musp=1.1; %1/mm
  649. optProp.mua=0.011; %1/mm
  651. warning('Default optical properties used');
  652. end
  654. mua = optProp.mua; %1/mm
  655. D = 1/(3*optProp.musp); %mm
  657. zs = 1/optProp.musp; %mm
  658. A = n2A(optProp.nin,optProp.nout);
  659. ze = 2*A*D; %mm
  661. m = (-m_max:m_max).';
  662. z1m = (1-2*m)*s - 4*m*ze - zs; %mm
  663. z2m = (1-2*m)*s - (4*m-2)*ze + zs; %mm
  665. T = (1/(4*pi)) * sum( ...
  666. z1m.*(rho^2+z1m.^2).^(-3/2) .* ...
  667. (1+(mua*(rho^2+z1m.^2)/D).^(1/2)) .* ...
  668. exp(-(mua*(rho^2+z1m.^2)/D).^(1/2)) - ...
  669. z2m.*(rho^2+z2m.^2).^(-3/2) .* ...
  670. (1+(mua*(rho^2+z2m.^2)/D).^(1/2)) .* ...
  671. exp(-(mua*(rho^2+z2m.^2)/D).^(1/2)) ...
  672. ); %1/mm^2
  674. end
  676. % =============== Reflection Parameter ====================================
  677. function A = n2A(nin, nout)
  678. % Based on:
  679. % R. Aronson, "Boundary conditions for diffusion of light," JOSA A,
  680. % vol. 12, no. 11, pp. 2532–2539, Nov. 1995, doi: 10/dff63n.
  682. % A = n2A(nin,nout)
  683. % Inputs:
  684. % nin - Index of refraction inside medium
  685. % nout - Index of refraction outside medium
  686. % Output:
  687. % A - Index of refraction mismatch parameter
  689. if nargin==0
  690. dan12=1.4;
  691. else
  692. dan12=nin/nout;
  693. end
  695. if dan12>1
  696. A=504.332889-2641.00214*dan12+...
  697. 5923.699064*dan12.^2-7376.355814*dan12^3+...
  698. 5507.53041*dan12^4-2463.357945*dan12^5+...
  699. 610.956547*dan12^6-64.8047*dan12^7;
  700. elseif dan12<1
  701. A=3.084635-6.531194*dan12+...
  702. 8.357854*dan12^2-5.082751*dan12^3+1.171382*dan12^4;
  703. else
  704. A=1;
  705. end
  707. end
  709. % =============== Extinction Coefficients ===============
  710. function E = makeE(chroms, lambda)
  711. % E = makeE(chroms, lambda)
  712. % Giles Blaney Spring 2021
  713. %
  714. % Inputs: - chroms: String of chromophores to include in E.
  715. % Available chromophores:
  716. % - O: Oxyhemoglobin
  717. % - D: Deoxyhemoglobin
  718. % - W: Water
  719. % - L: Lipid
  720. % (Default: 'OD')
  721. % Spaces are ignored.
  722. % - lambda: Vectors of wavelengths (nm).
  723. % (Default: [830, 690])
  724. %
  725. % Output: - E: Extinction coefficient matrix.
  726. % Units: 1/(mm uM) for O, D, CCOo, and CCOr
  727. % 1/mm for W, L, and C
  728. % size(E)=[length(lambda), length(chroms)];
  729. % Defined as mua=E*C
  730. % Order of C is defined by order in chroms input
  732. % Relevant references in .mat files for each chromophore
  734. if nargin<=0
  735. chroms='OD';
  736. end
  737. if nargin<=1
  738. lambda=[830, 690]; %nm
  739. end
  740. if size(lambda, 1)==1
  741. lambda=lambda';
  742. end
  744. chroms=chroms(~isspace(chroms));
  746. E=[];
  747. while ~isempty(chroms)
  748. switch chroms(1)
  749. case 'O' %Oxy
  750. blood=load('Bext.mat');
  751. Oext=interp1(blood.Blambda, blood.Oext, lambda,...
  752. 'linear', 'extrap');
  753. Oext(Oext<0)=0;
  754. E=[E, Oext];
  755. case 'D' %Deoxy
  756. blood=load('Bext.mat');
  757. Dext=interp1(blood.Blambda, blood.Dext, lambda,...
  758. 'linear', 'extrap');
  759. Dext(Dext<0)=0;
  760. E=[E, Dext];
  761. case 'W' %Water
  762. water=load('Wext.mat');
  763. Wext=interp1(water.Wlambda, water.Wmua, lambda,...
  764. 'linear', 'extrap');
  765. Wext(Wext<0)=0;
  766. E=[E, Wext];
  767. case 'L' %Lipid
  768. lipid=load('Lext.mat');
  769. Lext=interp1(lipid.Llambda, lipid.Lmua, lambda,...
  770. 'linear', 'extrap');
  771. Lext(Lext<0)=0;
  772. E=[E, Lext];
  773. otherwise
  774. warning(['Unknown chromophore' chroms(1) ', ignored']);
  775. end
  776. chroms(1)=[];
  777. end
  778. end

LEDspecColor_forPUB.m at commit 24e6c13, no license · at the source

Overview

Authors: Jodee Frias1, Giles Blaney1, Angelo Sassaroli1, Sergio Fantini1
ORCID iDs: Jodee Frias, Giles Blaney, Angelo Sassaroli, Sergio Fantini
  1. Tufts University, Department of Biomedical Engineering, Medford, Massachusetts, United States
Institutions: Tufts University (United States)
Journal: Biophotonics discovery, volume 3, issue 2, article 025003
Dates: received 5 December 2025; accepted 25 February 2026; published online 24 March 2026
Type: Research article · Language: English
License: CC BY
Identifiers: DOI 10.1117/1.bios.3.2.025003 · PMID 42038099 · PMCID PMC13107251 · OpenAlex W4417143741
Open access: hybrid, a free copy (OpenAlex)
Preprint: arxiv:2512.05877
Status: code verified (how the code is found and verified)
Categories: fNIRS (modality), human (organism), computational (subfield)
Methods: Graphs, fMRI & imaging, Smoothing, state filtering, decompositions
Keywords: functional near-infrared spectroscopy, diffuse optics, dual-slope, frequency-domain near-infrared spectroscopy, multi-layer model, Monte Carlo simulations
Topic: Optical Imaging and Spectroscopy Techniques (Radiology, Nuclear Medicine and Imaging, Medicine), according to OpenAlex
Funding: NHLBI NIH HHS (K99 HL181290)
Citations: not cited yet (Europe PMC); 41 references in the paper

Abstract

Significance: Functional near-infrared spectroscopy (fNIRS) is impacted by signal contamination from superficial hemodynamics. It is important to develop methods that account for such contamination and provide accurate measurements of cerebral hemodynamics.

Aim: We aim to investigate whether simulated data with two- or three-layer tissue models are able to reproduce in vivo data collected with dual-slope (DS) frequency-domain (FD) near-infrared spectroscopy (NIRS) on human subjects during brain activation.

Approach: We performed Monte Carlo simulations to generate DS FD-NIRS data from two- and three-layer media with a range of layer thicknesses and optical properties. We collected in vivo data with DS FD-NIRS (source-detector distances: 25 and 37 mm, wavelengths: 690 and 830 nm, and modulation frequency: 140 MHz) over the occipital lobe of human subjects during visual stimulation. Simulated and in vivo data were analyzed with diffusion theory for a homogeneous medium, and results were compared for each DS FD-NIRS data type.

Results: We found that the main qualitative features of in vivo data could be reproduced by simulated data from a three-layer medium, with a second layer (representing the cerebrospinal fluid in the subarachnoid space) that is less absorbing and less scattering than the other two layers, and with a top layer thickness that represents the combined scalp and skull thickness.

Conclusions: A three-layer model is a viable improvement over a homogeneous model to analyze DS FD-NIRS data (or any other fNIRS data) to generate more accurate measurements of cerebral hemodynamic changes without a need for large datasets for tomographic reconstructions.

Reproduced under the paper's license (CC BY), from the paper cited above.

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doit-lab/doit-public

License: none: the authors keep all their rights
State: the link answers, verified on 6 November 2026
Evidence: files inventoried
Commit: 24e6c13b4eb47ca4ae5188eabad86c7bbdb4c059, 9 July 2026
Languages: MATLAB (199)
Size: 438 files, 199 scripts
Software Heritage: not archived
Found in: “Code and Data Availability”
Not found: README, license file, CITATION.cff, environment file, tests, continuous integration, documentation
Tools: Statistics and Machine Learning Toolbox (6 files), Optimization Toolbox (5 files), CircStat (4 files), Parallel Computing Toolbox (2 files), Wavelet Toolbox (2 files), Signal Processing Toolbox (1 file)
Availability: 2 checks, the latest on 6 November 2026: the link answers
  • 6 November 2026: the link answers
  • 30 September 2026: the link answers
199 files
At the source: github.com/DOIT-Lab/DOIT-Public/tree/master/ThreeLayer_BiophotonicsDiscovery

The paper's code and data availability statement is in the Data section.

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Code and Data Availability

Data and code will be made available at the following repository: https://github.com/DOIT-Lab/DOIT-Public/tree/master/ThreeLayer_BiophotonicsDiscovery.

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Version 1, 30 September 2026: the first record

Recorded: type, language, journal, volume, issue, pages, dates, 4 authors, 6 keywords, 1 funder, 40 references.

Cite

This paper

Frias, J., Blaney, G., Sassaroli, A., & Fantini, S. (2026). Functional dual-slope frequency-domain near-infrared spectroscopy data interpreted with two- and three-layer models. Biophotonics discovery, 3(2), 025003. https://doi.org/10.1117/1.bios.3.2.025003

BibTeX

@article{frias2026functional,
author = {Frias, Jodee and Blaney, Giles and Sassaroli, Angelo and Fantini, Sergio},
title = {{Functional dual-slope frequency-domain near-infrared spectroscopy data interpreted with two- and three-layer models}},
journal = {Biophotonics discovery},
year = {2026},
month = mar,
volume = {3},
number = {2},
pages = {025003},
publisher = {Society of Photo-Optical Instrumentation Engineers},
issn = {3005-4745},
doi = {10.1117/1.bios.3.2.025003},
url = {https://doi.org/10.1117/1.bios.3.2.025003},
pmid = {42038099},
pmcid = {PMC13107251}
}

RIS

TY - JOUR
AU - Frias, Jodee
AU - Blaney, Giles
AU - Sassaroli, Angelo
AU - Fantini, Sergio
TI - Functional dual-slope frequency-domain near-infrared spectroscopy data interpreted with two- and three-layer models
T2 - Biophotonics discovery
J2 - Biophotonics Discov
PY - 2026
DA - 2026/03/24
VL - 3
IS - 2
SP - 025003
SN - 3005-4745
PB - Society of Photo-Optical Instrumentation Engineers
DO - 10.1117/1.bios.3.2.025003
UR - https://doi.org/10.1117/1.bios.3.2.025003
LA - en
ER -

CSL-JSON

{
"id": "10.1117/1.bios.3.2.025003",
"type": "article-journal",
"title": "Functional dual-slope frequency-domain near-infrared spectroscopy data interpreted with two- and three-layer models",
"container-title": "Biophotonics discovery",
"author": [
{
"family": "Frias",
"given": "Jodee"
},
{
"family": "Blaney",
"given": "Giles"
},
{
"family": "Sassaroli",
"given": "Angelo"
},
{
"family": "Fantini",
"given": "Sergio"
}
],
"container-title-short": "Biophotonics Discov",
"volume": "3",
"issue": "2",
"page": "025003",
"DOI": "10.1117/1.bios.3.2.025003",
"PMID": "42038099",
"PMCID": "PMC13107251",
"ISSN": "3005-4745",
"publisher": "Society of Photo-Optical Instrumentation Engineers",
"URL": "https://doi.org/10.1117/1.bios.3.2.025003",
"language": "en",
"issued": {
"date-parts": [
[
2026,
3,
24
]
]
}
}

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