OSCR

Electrophysiological Signatures of Sarcopenia: A Systematic Review of sEMG Features, Fatigue Indices and AI-Based Classifiers.

Code ↔ Paper

4 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 4 matches
  1. [1] § 2. Materials and Methods › 2.6. Clinical Reference Test Hand Grip Associated with Sensorimotor Response ↔ MetaEvaluation/MetaAnalysis_groups_final.m, lines 1–35 · score 0.74 · DerSimonian, Elderly Female, Elderly Male, Laird, subgroups, meta
  2. [2] § 3. Results › 3.3. Hand Grip-Based Clinical Reference for sEMG Assessment ↔ MetaEvaluation/validation_metafor.R, lines 194–255 · score 0.68 · prespecified independent subgroups, elderly females, elderly males, meta, REML
  3. [3] § 2. Materials and Methods › 2.6. Clinical Reference Test Hand Grip Associated with Sensorimotor Response ↔ MetaEvaluation/validation_metafor.R, lines 194–255 · score 0.62 · Elderly Female, Elderly Male, subgroups, meta, variance, Hu
  4. [4] § 2. Materials and Methods › 2.6. Clinical Reference Test Hand Grip Associated with Sensorimotor Response ↔ MetaEvaluation/MetaAnalysis_groups_final.m, lines 1–35 · score 0.58 · Elderly Female, Elderly Male, subgroup, interval, rows, DL

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The authors' code

MATLAB · 1,383 lines · 32 KB · no license · 2 matches

  1. %% MetaAnalysis_groups_final.m
  2. % MATLAB R2024b compatible
  3. %
  4. % Meta-analysis of Mean Differences (MD)
  5. % Random-effects models:
  6. % 1) DerSimonian-Laird (DL)
  7. % 2) REML
  8. %
  9. % Three prespecified subgroup-specific meta-analyses:
  10. % - Elderly_Female: k = 2
  11. % - Elderly_Male: k = 2
  12. % - Elderly: k = 4
  13. %
  14. % IMPORTANT:
  15. % No overall pooled estimate is calculated across the 8 rows because
  16. % some studies contribute to more than one subgroup analysis.
  17. %
  18. % Prediction intervals:
  19. % - Calculated only when k >= 3
  20. % - Not calculated for k < 3
  21. % - Results with k < 5 should be interpreted cautiously.
  22. %
  23. % Sensitivity analysis:
  24. % - Exclude Hu(2021) from Elderly group.
  25. %
  26. % Effect direction:
  27. % MD = Mean_Control - Mean_Sarcopenia
  28. % Positive MD = higher value in controls than in sarcopenia.
  29. %
  30. % MATLAB R2024b
  31. % -------------------------------------------------------------------------
  33. clear;
  34. close all;
  35. clc;
  37. %% ========================================================================
  38. % DATA
  39. % Each row:
  40. % {StudyName, GroupLabel, nControl, meanControl, sdControl,
  41. % nCase, meanCase, sdCase}
  42. % ========================================================================
  44. T = {
  45. 'He(2024)_F', 'Elderly_Female', 68, 20.4, 3.6, 36, 14.8, 2.6;
  46. 'Li(2024)_F', 'Elderly_Female', 29, 22.4, 3.0, 31, 14.4, 2.8;
  48. 'He(2024)_M', 'Elderly_Male', 30, 32.1, 5.3, 19, 24.1, 2.9;
  49. 'Li(2024)_M', 'Elderly_Male', 16, 34.1, 5.4, 17, 23.8, 2.2;
  51. 'Sepulveda(2025)','Elderly', 22, 24.5, 7.4, 13, 19.8, 5.9;
  52. 'He(2024)', 'Elderly', 98, 23.9, 7.0, 55, 18.0, 5.2;
  53. 'Li(2024)', 'Elderly', 45, 26.6, 6.9, 48, 17.7, 5.2;
  54. 'Hu(2021)', 'Elderly', 5, 29.6, 8.88, 5, 20.0, 3.74;
  55. };
  57. %% ========================================================================
  58. % CONVERT DATA
  59. % ========================================================================
  61. studies = T(:,1);
  62. groups = T(:,2);
  64. nC = cell2mat(T(:,3));
  65. mC = cell2mat(T(:,4));
  66. sdC = cell2mat(T(:,5));
  68. nT = cell2mat(T(:,6));
  69. mT = cell2mat(T(:,7));
  70. sdT = cell2mat(T(:,8));
  72. %% ========================================================================
  73. % STUDY-LEVEL EFFECT SIZES
  74. % ========================================================================
  76. % Mean Difference:
  77. % Control - Sarcopenia
  78. MD = mC - mT;
  80. % Within-study variance of the MD
  81. var_within = (sdC.^2)./nC + (sdT.^2)./nT;
  83. % Standard error
  84. se_within = sqrt(var_within);
  86. %% ========================================================================
  87. % OUTPUT DIRECTORY
  88. % ========================================================================
  90. outdir = fullfile(pwd,'outputs');
  92. if ~exist(outdir,'dir')
  93. mkdir(outdir);
  94. end
  96. %% ========================================================================
  97. % STUDY-LEVEL TABLE
  98. % ========================================================================
  100. T_out = table( ...
  101. studies(:), ...
  102. groups(:), ...
  103. nC(:), ...
  104. nT(:), ...
  105. MD(:), ...
  106. se_within(:), ...
  107. var_within(:), ...
  108. 'VariableNames', ...
  109. {'Study','Subgroup','nControl','nCase','MD','SE','Var'});
  111. writetable( ...
  112. T_out, ...
  113. fullfile(outdir,'per_study_table_allrows.xlsx'));
  115. %% ========================================================================
  116. % PROCESS EACH PREDEFINED GROUP
  117. % ========================================================================
  119. uniqueGroups = unique(groups,'stable');
  121. OutGroups = struct();
  123. summary_rows = {};
  125. for ig = 1:numel(uniqueGroups)
  127. grp = uniqueGroups{ig};
  129. fprintf('\n============================================================\n');
  130. fprintf('Processing group: %s\n',grp);
  131. fprintf('============================================================\n');
  133. %% ---------------------------------------------------------------
  134. % Select studies belonging to this subgroup
  135. % ---------------------------------------------------------------
  137. idx = find(strcmp(groups,grp));
  139. y = MD(idx)';
  140. v = var_within(idx)';
  142. k = numel(y);
  144. fprintf('Number of studies: k = %d\n',k);
  146. if k == 0
  147. warning('No studies found for group %s. Skipping.',grp);
  148. continue;
  149. end
  151. %% ---------------------------------------------------------------
  152. % FIXED-EFFECT WEIGHTS
  153. % ---------------------------------------------------------------
  155. w_fixed = 1 ./ v;
  157. theta_fixed = ...
  158. sum(w_fixed .* y) / sum(w_fixed);
  160. %% ---------------------------------------------------------------
  161. % COCHRAN Q
  162. % ---------------------------------------------------------------
  164. Q = sum( ...
  165. w_fixed .* ...
  166. (y - theta_fixed).^2);
  168. df_Q = k - 1;
  170. %% ---------------------------------------------------------------
  171. % DL CONSTANT C
  172. % ---------------------------------------------------------------
  174. C = ...
  175. sum(w_fixed) - ...
  176. (sum(w_fixed.^2) / sum(w_fixed));
  178. %% ---------------------------------------------------------------
  179. % DER SIMONIAN-LAIRD TAU^2
  180. % ---------------------------------------------------------------
  182. if k > 1 && C > 0
  184. tau2_DL = max( ...
  185. 0, ...
  186. (Q - df_Q) / C);
  188. else
  190. tau2_DL = 0;
  192. end
  194. %% ---------------------------------------------------------------
  195. % DL POOLED EFFECT
  196. % ---------------------------------------------------------------
  198. [theta_DL,var_theta_DL] = ...
  199. pooled_given_tau(y,v,tau2_DL);
  201. se_theta_DL = sqrt(var_theta_DL);
  203. ci_DL = ...
  204. theta_DL + ...
  205. norminv([0.025 0.975]) .* se_theta_DL;
  207. %% ---------------------------------------------------------------
  208. % DL WEIGHTS
  209. % ---------------------------------------------------------------
  211. wi_DL = 1 ./ (v + tau2_DL);
  213. weights_pct_DL = ...
  214. 100 .* wi_DL ./ sum(wi_DL);
  216. %% ---------------------------------------------------------------
  217. % I2
  218. % ---------------------------------------------------------------
  220. if Q > 0 && k > 1
  222. I2 = max( ...
  223. 0, ...
  224. ((Q - df_Q) / Q) * 100);
  226. else
  228. I2 = 0;
  230. end
  232. %% =================================================================
  233. % REML ESTIMATION
  234. % =================================================================
  235. % ============================================================
  236. % REML estimation of tau^2
  237. % ============================================================
  239. opt = optimset( ...
  240. 'TolX', 1e-10, ...
  241. 'MaxIter', 1000, ...
  242. 'Display', 'off');
  244. % Conservative upper bound for tau^2
  245. upper = max([ ...
  246. 100 * max(v), ...
  247. 100 * var(y), ...
  248. 1]);
  250. fun = @(t) restrictedLogLik(t, y, v);
  252. try
  254. tau2_REML = fminbnd(fun, 0, upper, opt);
  256. % Numerical protection
  257. tau2_REML = max(0, tau2_REML);
  259. catch ME
  261. warning( ...
  262. 'REML optimization failed for group %s: %s. tau2_REML set to 0.', ...
  263. grp, ME.message);
  265. tau2_REML = 0;
  267. end
  269. %% ---------------------------------------------------------------
  270. % REML POOLED EFFECT
  271. % ---------------------------------------------------------------
  273. [theta_REML,var_theta_REML] = ...
  274. pooled_given_tau( ...
  275. y,v,tau2_REML);
  277. se_theta_REML = sqrt(var_theta_REML);
  279. ci_REML = ...
  280. theta_REML + ...
  281. norminv([0.025 0.975]) .* se_theta_REML;
  283. %% ---------------------------------------------------------------
  284. % REML WEIGHTS
  285. % ---------------------------------------------------------------
  287. wi_REML = ...
  288. 1 ./ (v + tau2_REML);
  290. weights_pct_REML = ...
  291. 100 .* wi_REML ./ sum(wi_REML);
  293. %% =================================================================
  294. % PREDICTION INTERVALS
  295. % =================================================================
  296. %
  297. % PI is NOT calculated for k < 3.
  298. %
  299. % For k >= 3:
  300. %
  301. % PI = theta +/- t_(k-2,0.975)
  302. % * sqrt(SE_theta^2 + tau^2)
  303. %
  304. % NOTE:
  305. % Prediction intervals with very small k remain highly uncertain.
  306. % A warning is generated when k < 5.
  307. % =================================================================
  309. PI_DL = [NaN NaN];
  310. PI_REML = [NaN NaN];
  312. PI_status = "Not calculated";
  314. if k >= 3
  316. if k < 5
  318. warning( ...
  319. ['Prediction interval for group %s is based on only ' ...
  320. 'k=%d studies and should be interpreted cautiously.'], ...
  321. grp,k);
  323. PI_status = "Calculated with k<5; interpret cautiously";
  325. else
  327. PI_status = "Calculated";
  329. end
  331. df_PI = k - 2;
  333. tcrit = tinv(0.975,df_PI);
  335. %% DL PI
  337. PI_se_DL = ...
  338. sqrt(var_theta_DL + tau2_DL);
  340. PI_DL = ...
  341. theta_DL + ...
  342. [-1 1] .* tcrit .* PI_se_DL;
  344. %% REML PI
  346. PI_se_REML = ...
  347. sqrt(var_theta_REML + tau2_REML);
  349. PI_REML = ...
  350. theta_REML + ...
  351. [-1 1] .* tcrit .* PI_se_REML;
  353. end
  355. %% =================================================================
  356. % STORE GROUP RESULTS
  357. % =================================================================
  359. G = struct();
  361. G.group = grp;
  362. G.k = k;
  363. G.idx = idx;
  365. G.studies = studies(idx);
  367. G.y = y;
  368. G.v = v;
  370. G.Q = Q;
  371. G.df_Q = df_Q;
  372. G.I2 = I2;
  374. % DL
  375. G.tau2_DL = tau2_DL;
  376. G.theta_DL = theta_DL;
  377. G.se_theta_DL = se_theta_DL;
  378. G.ci_DL = ci_DL;
  379. G.weights_pct_DL = weights_pct_DL;
  381. % REML
  382. G.tau2_REML = tau2_REML;
  383. G.theta_REML = theta_REML;
  384. G.se_theta_REML = se_theta_REML;
  385. G.ci_REML = ci_REML;
  386. G.weights_pct_REML = weights_pct_REML;
  388. % Prediction intervals
  389. G.PI_DL = PI_DL;
  390. G.PI_REML = PI_REML;
  391. G.PI_status = PI_status;
  393. %% Store structure
  395. fieldName = ...
  396. matlab.lang.makeValidName(grp);
  398. OutGroups.(fieldName) = G;
  400. %% =================================================================
  401. % SUMMARY TABLE
  402. % =================================================================
  404. summary_rows(end+1,:) = { ...
  405. grp, ...
  406. k, ...
  407. theta_DL, ...
  408. ci_DL(1), ...
  409. ci_DL(2), ...
  410. PI_DL(1), ...
  411. PI_DL(2), ...
  412. tau2_DL, ...
  413. theta_REML, ...
  414. ci_REML(1), ...
  415. ci_REML(2), ...
  416. PI_REML(1), ...
  417. PI_REML(2), ...
  418. tau2_REML, ...
  419. Q, ...
  420. df_Q, ...
  421. I2, ...
  422. PI_status};
  424. %% =================================================================
  425. % FOREST PLOTS
  426. % =================================================================
  428. makeForestGroup( ...
  429. 'DL', ...
  430. G, ...
  431. outdir);
  433. makeForestGroup( ...
  434. 'REML', ...
  435. G, ...
  436. outdir);
  438. %% =================================================================
  439. % CONSOLE OUTPUT
  440. % =================================================================
  442. fprintf('\nGroup: %s\n',grp);
  443. fprintf('k = %d\n',k);
  445. fprintf( ...
  446. 'DL : theta = %.3f [%.3f, %.3f], tau2 = %.4f\n', ...
  447. theta_DL, ...
  448. ci_DL(1), ...
  449. ci_DL(2), ...
  450. tau2_DL);
  452. fprintf( ...
  453. 'REML : theta = %.3f [%.3f, %.3f], tau2 = %.4f\n', ...
  454. theta_REML, ...
  455. ci_REML(1), ...
  456. ci_REML(2), ...
  457. tau2_REML);
  459. fprintf( ...
  460. 'Q = %.3f, df = %d, I2 = %.2f%%\n', ...
  461. Q,df_Q,I2);
  463. if k >= 3
  465. fprintf( ...
  466. 'DL PI = [%.3f, %.3f]\n', ...
  467. PI_DL(1),PI_DL(2));
  469. fprintf( ...
  470. 'REML PI = [%.3f, %.3f]\n', ...
  471. PI_REML(1),PI_REML(2));
  473. else
  475. fprintf( ...
  476. 'Prediction intervals: NOT calculated (k < 3)\n');
  478. end
  480. end
  482. %% ========================================================================
  483. % SUMMARY TABLE
  484. % ========================================================================
  486. Tsum = cell2table( ...
  487. summary_rows, ...
  488. 'VariableNames',{ ...
  489. 'Group', ...
  490. 'k', ...
  491. 'Theta_DL', ...
  492. 'CIlo_DL', ...
  493. 'CIhi_DL', ...
  494. 'PIlo_DL', ...
  495. 'PIhi_DL', ...
  496. 'tau2_DL', ...
  497. 'Theta_REML', ...
  498. 'CIlo_REML', ...
  499. 'CIhi_REML', ...
  500. 'PIlo_REML', ...
  501. 'PIhi_REML', ...
  502. 'tau2_REML', ...
  503. 'Q', ...
  504. 'df', ...
  505. 'I2', ...
  506. 'PI_status'});
  508. writetable( ...
  509. Tsum, ...
  510. fullfile(outdir,'summary_by_group.xlsx'));
  512. %% ========================================================================
  513. % SAVE MATLAB RESULTS
  514. % ========================================================================
  516. save( ...
  517. fullfile(outdir, ...
  518. 'MetaAnalysis_groups_results.mat'), ...
  519. 'OutGroups', ...
  520. 'T_out', ...
  521. 'Tsum');
  523. %% ========================================================================
  524. % SENSITIVITY ANALYSIS
  525. % EXCLUDE HU(2021) FROM ELDERLY GROUP
  526. % ========================================================================
  528. groupName = 'Elderly';
  530. fieldName = ...
  531. matlab.lang.makeValidName(groupName);
  533. if ~isfield(OutGroups,fieldName)
  535. warning( ...
  536. 'Group %s not found. Sensitivity analysis skipped.', ...
  537. groupName);
  539. else
  541. S = OutGroups.(fieldName);
  543. idx = S.idx;
  545. %% ---------------------------------------------------------------
  546. % Locate Hu(2021)
  547. % ---------------------------------------------------------------
  549. hu_label = 'Hu(2021)';
  551. hu_global_idx = ...
  552. find(strcmp(studies,hu_label),1);
  554. if isempty(hu_global_idx)
  556. warning( ...
  557. 'Hu(2021) was not found.');
  559. elseif ~ismember(hu_global_idx,idx)
  561. warning( ...
  562. 'Hu(2021) is not part of the Elderly group.');
  564. else
  566. %% -----------------------------------------------------------
  567. % Dataset without Hu
  568. % -----------------------------------------------------------
  570. idx_no_hu = ...
  571. idx(idx ~= hu_global_idx);
  573. y_s = MD(idx_no_hu)';
  574. v_s = var_within(idx_no_hu)';
  576. k_s = numel(y_s);
  578. fprintf('\n============================================================\n');
  579. fprintf('Sensitivity analysis: Excluding Hu(2021)\n');
  580. fprintf('Original k = %d\n',numel(idx));
  581. fprintf('Without Hu k = %d\n',k_s);
  582. fprintf('============================================================\n');
  584. %% -----------------------------------------------------------
  585. % DL
  586. % -----------------------------------------------------------
  588. w_fixed_s = 1 ./ v_s;
  590. theta_fixed_s = ...
  591. sum(w_fixed_s .* y_s) / ...
  592. sum(w_fixed_s);
  594. Q_s = ...
  595. sum(w_fixed_s .* ...
  596. (y_s - theta_fixed_s).^2);
  598. df_s = k_s - 1;
  600. C_s = ...
  601. sum(w_fixed_s) - ...
  602. sum(w_fixed_s.^2) / ...
  603. sum(w_fixed_s);
  605. if k_s > 1 && C_s > 0
  607. tau2_DL_s = max( ...
  608. 0, ...
  609. (Q_s - df_s) / C_s);
  611. else
  613. tau2_DL_s = 0;
  615. end
  617. [theta_DL_s,var_theta_DL_s] = ...
  618. pooled_given_tau( ...
  619. y_s,v_s,tau2_DL_s);
  621. se_DL_s = sqrt(var_theta_DL_s);
  623. ci_DL_s = ...
  624. theta_DL_s + ...
  625. norminv([0.025 0.975]) .* se_DL_s;
  627. if Q_s > 0 && k_s > 1
  629. I2_s = max( ...
  630. 0, ...
  631. ((Q_s-df_s)/Q_s)*100);
  633. else
  635. I2_s = 0;
  637. end
  638. % ============================================================
  639. % REML for sensitivity analysis
  640. % ============================================================
  642. if k_s >= 1
  644. opt = optimset( ...
  645. 'TolX', 1e-10, ...
  646. 'MaxIter', 1000, ...
  647. 'Display', 'off');
  649. upper_bound_s = max([ ...
  650. 100 * max(v_s), ...
  651. 100 * var(y_s), ...
  652. 1]);
  654. fun_s = @(t) restrictedLogLik(t, y_s, v_s);
  656. try
  658. tau2_REML_s = fminbnd( ...
  659. fun_s, ...
  660. 0, ...
  661. upper_bound_s, ...
  662. opt);
  664. tau2_REML_s = max(0, tau2_REML_s);
  666. catch ME
  668. warning( ...
  669. 'REML sensitivity optimization failed: %s. tau2_REML_s set to 0.', ...
  670. E.message);
  672. tau2_REML_s = 0;
  674. end
  676. [theta_REML_s, var_theta_REML_s] = ...
  677. pooled_given_tau(y_s, v_s, tau2_REML_s);
  679. se_theta_REML_s = sqrt(var_theta_REML_s);
  681. ci_REML_s = theta_REML_s + ...
  682. norminv([0.025 0.975]) * se_theta_REML_s;
  684. else
  686. tau2_REML_s = NaN;
  687. theta_REML_s = NaN;
  688. ci_REML_s = [NaN NaN];
  690. end
  692. [theta_REML_s,var_theta_REML_s] = ...
  693. pooled_given_tau( ...
  694. y_s,v_s,tau2_REML_s);
  696. se_REML_s = ...
  697. sqrt(var_theta_REML_s);
  699. ci_REML_s = ...
  700. theta_REML_s + ...
  701. norminv([0.025 0.975]) .* se_REML_s;
  703. %% -----------------------------------------------------------
  704. % Prediction intervals after excluding Hu
  705. % -----------------------------------------------------------
  707. PI_DL_s = [NaN NaN];
  708. PI_REML_s = [NaN NaN];
  710. if k_s >= 3
  712. if k_s < 5
  714. warning( ...
  715. ['Sensitivity PI uses only k=%d studies. ' ...
  716. 'Interpret cautiously.'],k_s);
  718. end
  720. df_PI_s = k_s - 2;
  722. tcrit_s = ...
  723. tinv(0.975,df_PI_s);
  725. PI_DL_s = ...
  726. theta_DL_s + ...
  727. [-1 1] .* ...
  728. tcrit_s .* ...
  729. sqrt(var_theta_DL_s + tau2_DL_s);
  731. PI_REML_s = ...
  732. theta_REML_s + ...
  733. [-1 1] .* ...
  734. tcrit_s .* ...
  735. sqrt(var_theta_REML_s + tau2_REML_s);
  737. end
  739. %% -----------------------------------------------------------
  740. % Sensitivity table
  741. % -----------------------------------------------------------
  743. sens_rows = { ...
  744. 'Original_with_Hu_DL', ...
  745. theta_DL, ...
  746. S.ci_DL(1), ...
  747. S.ci_DL(2), ...
  748. S.PI_DL(1), ...
  749. S.PI_DL(2), ...
  750. S.tau2_DL, ...
  751. S.Q, ...
  752. S.I2;
  754. 'Original_with_Hu_REML', ...
  755. theta_REML, ...
  756. S.ci_REML(1), ...
  757. S.ci_REML(2), ...
  758. S.PI_REML(1), ...
  759. S.PI_REML(2), ...
  760. S.tau2_REML, ...
  761. NaN, ...
  762. NaN;
  764. 'Exclude_Hu_DL', ...
  765. theta_DL_s, ...
  766. ci_DL_s(1), ...
  767. ci_DL_s(2), ...
  768. PI_DL_s(1), ...
  769. PI_DL_s(2), ...
  770. tau2_DL_s, ...
  771. Q_s, ...
  772. I2_s;
  774. 'Exclude_Hu_REML', ...
  775. theta_REML_s, ...
  776. ci_REML_s(1), ...
  777. ci_REML_s(2), ...
  778. PI_REML_s(1), ...
  779. PI_REML_s(2), ...
  780. tau2_REML_s, ...
  781. NaN, ...
  782. NaN};
  784. T_sens = cell2table( ...
  785. sens_rows, ...
  786. 'VariableNames',{ ...
  787. 'Scenario', ...
  788. 'Theta', ...
  789. 'CI_lo', ...
  790. 'CI_hi', ...
  791. 'PI_lo', ...
  792. 'PI_hi', ...
  793. 'tau2', ...
  794. 'Q', ...
  795. 'I2'});
  797. writetable( ...
  798. T_sens, ...
  799. fullfile( ...
  800. outdir, ...
  801. 'sensitivity_exclude_Hu2021.xlsx'));
  803. %% -----------------------------------------------------------
  804. % Percentage change
  805. % -----------------------------------------------------------
  807. PercentChange = table( ...
  808. {'Theta_DL'; ...
  809. 'tau2_DL'; ...
  810. 'I2_DL'; ...
  811. 'Theta_REML'; ...
  812. 'tau2_REML'}, ...
  813. [ ...
  814. 100*(theta_DL_s-S.theta_DL)/S.theta_DL; ...
  815. 100*(tau2_DL_s-S.tau2_DL)/S.tau2_DL; ...
  816. 100*(I2_s-S.I2)/S.I2; ...
  817. 100*(theta_REML_s-S.theta_REML)/S.theta_REML; ...
  818. 100*(tau2_REML_s-S.tau2_REML)/S.tau2_REML], ...
  819. 'VariableNames', ...
  820. {'Metric','PercentChange'});
  822. writetable( ...
  823. PercentChange, ...
  824. fullfile( ...
  825. outdir, ...
  826. 'sensitivity_percent_change_Hu2021.xlsx'));
  828. %% -----------------------------------------------------------
  829. % Console
  830. % -----------------------------------------------------------
  832. fprintf('\nSensitivity results:\n');
  834. fprintf( ...
  835. 'DL original : %.3f [%.3f, %.3f]\n', ...
  836. S.theta_DL,S.ci_DL(1),S.ci_DL(2));
  838. fprintf( ...
  839. 'DL no Hu : %.3f [%.3f, %.3f]\n', ...
  840. theta_DL_s,ci_DL_s(1),ci_DL_s(2));
  842. fprintf( ...
  843. 'REML original : %.3f [%.3f, %.3f]\n', ...
  844. S.theta_REML,S.ci_REML(1),S.ci_REML(2));
  846. fprintf( ...
  847. 'REML no Hu : %.3f [%.3f, %.3f]\n', ...
  848. theta_REML_s,ci_REML_s(1),ci_REML_s(2));
  850. fprintf('\n');
  852. fprintf( ...
  853. 'DL tau2: %.6f -> %.6f\n', ...
  854. S.tau2_DL,tau2_DL_s);
  856. fprintf( ...
  857. 'REML tau2: %.6f -> %.6f\n', ...
  858. S.tau2_REML,tau2_REML_s);
  860. %% -----------------------------------------------------------
  861. % Forest plots without Hu
  862. % -----------------------------------------------------------
  864. S_s = struct();
  866. S_s.group = 'Elderly_noHu';
  867. S_s.k = k_s;
  869. S_s.studies = studies(idx_no_hu);
  871. S_s.y = y_s(:);
  872. S_s.v = v_s(:);
  874. S_s.theta_DL = theta_DL_s;
  875. S_s.ci_DL = ci_DL_s;
  876. S_s.tau2_DL = tau2_DL_s;
  878. S_s.theta_REML = theta_REML_s;
  879. S_s.ci_REML = ci_REML_s;
  880. S_s.tau2_REML = tau2_REML_s;
  882. S_s.PI_DL = PI_DL_s;
  883. S_s.PI_REML = PI_REML_s;
  885. S_s.weights_pct_DL = ...
  886. 100*(1./(v_s+tau2_DL_s)) ./ ...
  887. sum(1./(v_s+tau2_DL_s));
  889. S_s.weights_pct_REML = ...
  890. 100*(1./(v_s+tau2_REML_s)) ./ ...
  891. sum(1./(v_s+tau2_REML_s));
  893. makeForestGroup( ...
  894. 'DL', ...
  895. S_s, ...
  896. outdir);
  898. makeForestGroup( ...
  899. 'REML', ...
  900. S_s, ...
  901. outdir);
  903. end
  904. end
  906. %% ========================================================================
  907. % FINISH
  908. % ========================================================================
  910. fprintf('\n============================================================\n');
  911. fprintf('META-ANALYSIS COMPLETED\n');
  912. fprintf('Results saved in:\n%s\n',outdir);
  913. fprintf('============================================================\n');
  916. %% ========================================================================
  917. % LOCAL FUNCTION 1. ajustada por el tipo de analisis
  918. % REML RESTRICTED LOG-LIKELIHOOD
  919. % ========================================================================
  921. function nll = restrictedLogLik(tau2, y, v)
  922. % ============================================================
  923. % Restricted log-likelihood for REML estimation of tau^2
  924. % Random-effects meta-analysis with a single pooled intercept
  925. %
  926. % y = study-level effect estimates
  927. % v = within-study sampling variances
  928. % tau2 = between-study variance
  929. %
  930. % The function returns the NEGATIVE restricted log-likelihood,
  931. % because fminbnd performs minimization.
  932. % ============================================================
  934. % Ensure column vectors
  935. y = y(:);
  936. v = v(:);
  938. % Invalid values
  939. if tau2 < 0 || any(v <= 0) || any(~isfinite(v)) || any(~isfinite(y))
  940. nll = Inf;
  941. return;
  942. end
  944. % Total variance for each study
  945. sigma2 = v + tau2;
  947. % Random-effects weights
  948. w = 1 ./ sigma2;
  950. % Sum of weights
  951. W = sum(w);
  953. % Estimated pooled effect for this value of tau2
  954. mu_hat = sum(w .* y) / W;
  956. % Weighted residual sum of squares
  957. residuals = y - mu_hat;
  958. Q_tau = sum(w .* residuals.^2);
  960. % Restricted negative log-likelihood
  961. %
  962. % REML for a model with one fixed effect (the pooled mean):
  963. %
  964. % -2 log L_REML =
  965. % sum(log(sigma2))
  966. % + log(W)
  967. % + Q_tau
  968. %
  969. % Constants independent of tau2 are omitted.
  971. nll = 0.5 * ( ...
  972. sum(log(sigma2)) + ...
  973. log(W) + ...
  974. Q_tau );
  976. % Numerical protection
  977. if ~isfinite(nll)
  978. nll = Inf;
  979. end
  980. end
  981. % function out = restrictedLogLik_REML(tau2,y,v)
  982. %
  983. % % Ensure non-negative tau2
  984. % tau2 = max(tau2,0);
  985. %
  986. % % Total variance
  987. % vi = v + tau2;
  988. %
  989. % if any(~isfinite(vi)) || any(vi <= 0)
  990. %
  991. % out = Inf;
  992. % return;
  993. %
  994. % end
  995. %
  996. % % Random-effects weights
  997. % w = 1 ./ vi;
  998. %
  999. % % Sum of weights
  1000. % W = sum(w);
  1001. %
  1002. % if ~isfinite(W) || W <= 0
  1003. %
  1004. % out = Inf;
  1005. % return;
  1006. %
  1007. % end
  1008. %
  1009. % % Weighted pooled estimate
  1010. % theta = ...
  1011. % sum(w .* y) / W;
  1012. %
  1013. % % Weighted residual heterogeneity
  1014. % Q_tau = ...
  1015. % sum(w .* (y-theta).^2);
  1016. %
  1017. % k = numel(y);
  1018. %
  1019. % % Need at least 2 studies
  1020. % if k < 2 || Q_tau <= 0
  1021. %
  1022. % out = Inf;
  1023. % return;
  1024. %
  1025. % end
  1026. %
  1027. % % REML objective function
  1028. % %
  1029. % % Constants independent of tau2 are omitted.
  1030. % %
  1031. % % -2 log L_REML =
  1032. % % sum(log(vi))
  1033. % % + log(sum(w))
  1034. % % + (k-1)*log(Q_tau)
  1035. %
  1036. % out = 0.5 * ( ...
  1037. % sum(log(vi)) + ...
  1038. % log(W) + ...
  1039. % (k-1)*log(Q_tau) );
  1040. %
  1041. % if ~isfinite(out)
  1042. %
  1043. % out = Inf;
  1044. %
  1045. % end
  1046. %
  1047. % end
  1048. %
  1049. %
  1050. %% ========================================================================
  1051. % LOCAL FUNCTION 2
  1052. % POOLED EFFECT GIVEN TAU2
  1053. % ========================================================================
  1055. function [theta,var_theta] = ...
  1056. pooled_given_tau(y,v,tau2)
  1058. w = 1 ./ (v + tau2);
  1060. theta = ...
  1061. sum(w .* y) / sum(w);
  1063. var_theta = ...
  1064. 1 / sum(w);
  1066. end
  1069. %% ========================================================================
  1070. % LOCAL FUNCTION 3
  1071. % FOREST PLOT
  1072. % ========================================================================
  1074. function makeForestGroup(method,G,outdir)
  1076. studies = G.studies;
  1077. y = G.y(:);
  1078. v = G.v(:);
  1080. k = G.k;
  1082. %% ---------------------------------------------------------------
  1083. % Select estimator
  1084. % ---------------------------------------------------------------
  1086. if strcmpi(method,'DL')
  1088. theta = G.theta_DL;
  1089. ci = G.ci_DL;
  1090. tau2 = G.tau2_DL;
  1092. if isfield(G,'weights_pct_DL')
  1094. weights_pct = ...
  1095. G.weights_pct_DL;
  1097. else
  1099. weights_pct = ...
  1100. 100*(1./(v+tau2)) ./ ...
  1101. sum(1./(v+tau2));
  1103. end
  1105. else
  1107. theta = G.theta_REML;
  1108. ci = G.ci_REML;
  1109. tau2 = G.tau2_REML;
  1111. if isfield(G,'weights_pct_REML')
  1113. weights_pct = ...
  1114. G.weights_pct_REML;
  1116. else
  1118. weights_pct = ...
  1119. 100*(1./(v+tau2)) ./ ...
  1120. sum(1./(v+tau2));
  1122. end
  1124. end
  1126. %% ---------------------------------------------------------------
  1127. % Figure
  1128. % ---------------------------------------------------------------
  1130. fig = figure( ...
  1131. 'Visible','off', ...
  1132. 'Units','pixels', ...
  1133. 'Position',[100 100 1100 650]);
  1135. ax = axes('Parent',fig);
  1137. hold(ax,'on');
  1139. %% ---------------------------------------------------------------
  1140. % Plot study effects
  1141. % ---------------------------------------------------------------
  1143. ypos = (1:k)';
  1145. max_w = max(weights_pct);
  1147. if max_w <= 0
  1148. max_w = 1;
  1149. end
  1151. for i = 1:k
  1153. xi = y(i);
  1155. sei = sqrt(v(i));
  1157. ci_low = ...
  1158. xi - 1.96*sei;
  1160. ci_high = ...
  1161. xi + 1.96*sei;
  1163. % Confidence interval
  1164. plot( ...
  1165. ax, ...
  1166. [ci_low ci_high], ...
  1167. [ypos(i) ypos(i)], ...
  1168. 'k-', ...
  1169. 'LineWidth',1.4);
  1171. % Study marker
  1172. sz = ...
  1173. max(25, ...
  1174. 150*weights_pct(i)/max_w);
  1176. scatter( ...
  1177. ax, ...
  1178. xi, ...
  1179. ypos(i), ...
  1180. sz, ...
  1181. 'k', ...
  1182. 'filled');
  1184. end
  1186. %% ---------------------------------------------------------------
  1187. % X limits
  1188. % ---------------------------------------------------------------
  1190. xleft = ...
  1191. min([y - 3*sqrt(v); ci(1)]);
  1193. xright = ...
  1194. max([y + 3*sqrt(v); ci(2)]);
  1196. if ~isfinite(xleft) || ...
  1197. ~isfinite(xright) || ...
  1198. xleft == xright
  1200. xleft = min(y)-1;
  1201. xright = max(y)+1;
  1203. end
  1205. xmargin = ...
  1206. 0.12*(xright-xleft);
  1208. if xmargin == 0
  1210. xmargin = ...
  1211. max(1,0.1*abs(xright));
  1213. end
  1215. xlim(ax, ...
  1216. [xleft-xmargin xright+xmargin]);
  1218. %% ---------------------------------------------------------------
  1219. % Null line
  1220. % ---------------------------------------------------------------
  1222. yl = [0 k+1];
  1224. plot( ...
  1225. ax, ...
  1226. [0 0], ...
  1227. yl, ...
  1228. '--', ...
  1229. 'Color',[0.5 0.5 0.5], ...
  1230. 'LineWidth',1);
  1232. %% ---------------------------------------------------------------
  1233. % Pooled diamond
  1234. % ---------------------------------------------------------------
  1236. diamond_y = 0.35;
  1238. diamond_h = 0.45;
  1240. patch_x = [ ...
  1241. ci(1), ...
  1242. theta, ...
  1243. ci(2), ...
  1244. theta];
  1246. patch_y = ...
  1247. diamond_y + ...
  1248. [-diamond_h/2, ...
  1249. 0, ...
  1250. diamond_h/2, ...
  1251. 0];
  1253. patch( ...
  1254. ax, ...
  1255. patch_x, ...
  1256. patch_y, ...
  1257. 'k', ...
  1258. 'FaceAlpha',0.4, ...
  1259. 'EdgeColor','k');
  1261. %% ---------------------------------------------------------------
  1262. % Y-axis
  1263. % ---------------------------------------------------------------
  1265. set( ...
  1266. ax, ...
  1267. 'YTick',ypos, ...
  1268. 'YTickLabel',studies, ...
  1269. 'YDir','reverse');
  1271. %% ---------------------------------------------------------------
  1272. % Pooled annotation
  1273. % ---------------------------------------------------------------
  1275. txtPooled = sprintf( ...
  1276. 'Pooled = %.2f [%.2f, %.2f]', ...
  1277. theta,ci(1),ci(2));
  1279. text( ...
  1280. ax, ...
  1281. mean(ci), ...
  1282. diamond_y+0.55, ...
  1283. txtPooled, ...
  1284. 'HorizontalAlignment','center', ...
  1285. 'FontWeight','bold');
  1287. %% ---------------------------------------------------------------
  1288. % Study estimates and weights
  1289. % ---------------------------------------------------------------
  1291. xlims = xlim(ax);
  1293. xtext = ...
  1294. xlims(2) - ...
  1295. 0.015*range(xlims);
  1297. for i = 1:k
  1299. txt = sprintf( ...
  1300. '%.2f [%.2f, %.2f] (%.1f%%)', ...
  1301. y(i), ...
  1302. y(i)-1.96*sqrt(v(i)), ...
  1303. y(i)+1.96*sqrt(v(i)), ...
  1304. weights_pct(i));
  1306. text( ...
  1307. ax, ...
  1308. xtext, ...
  1309. ypos(i), ...
  1310. txt, ...
  1311. 'HorizontalAlignment','right', ...
  1312. 'FontSize',9);
  1314. end
  1316. %% ---------------------------------------------------------------
  1317. % Labels
  1318. % ---------------------------------------------------------------
  1320. xlabel( ...
  1321. ax, ...
  1322. 'Mean Difference (Control - Sarcopenia)');
  1324. if isfield(G,'group')
  1326. groupTitle = G.group;
  1328. else
  1330. groupTitle = 'Meta-analysis';
  1332. end
  1334. title( ...
  1335. ax, ...
  1336. sprintf('%s - %s', ...
  1337. groupTitle,upper(method)), ...
  1338. 'Interpreter','none');
  1340. grid(ax,'on');
  1342. %% ---------------------------------------------------------------
  1343. % Save
  1344. % ---------------------------------------------------------------
  1346. safeGroup = ...
  1347. matlab.lang.makeValidName(groupTitle);
  1349. fname = fullfile( ...
  1350. outdir, ...
  1351. sprintf( ...
  1352. 'Forest_%s_%s', ...
  1353. safeGroup, ...
  1354. upper(method)));
  1356. try
  1358. exportgraphics( ...
  1359. fig, ...
  1360. [fname '.png'], ...
  1361. 'Resolution',300, ...
  1362. 'ContentType','image');
  1364. exportgraphics( ...
  1365. fig, ...
  1366. [fname '.pdf'], ...
  1367. 'ContentType','vector');
  1369. catch
  1371. saveas( ...
  1372. fig, ...
  1373. [fname '.png']);
  1375. saveas( ...
  1376. fig, ...
  1377. [fname '.pdf']);
  1379. end
  1381. close(fig);
  1383. end

MetaAnalysis_groups_final.m at commit 4825af5, no license · at the source

Overview

Authors: Karen-Victoria Villanueva-De-Luna1, Laura-Ivoone Garay-Jimenez1, Joel Lomelí-González2, Javier M Antelis3, Omar Mendoza-Montoya3, Blanca-Alicia Rico-Jiménez1, Blanca Tovar-Corona1
ORCID iDs: Laura-Ivoone Garay-Jimenez, Joel Lomelí-González, Javier M Antelis, Omar Mendoza-Montoya, Blanca-Alicia Rico-Jiménez, Blanca Tovar-Corona
  1. Instituto Politécnico Nacional, Unidad Profesional Interdisciplinaria en Ingeniería y Tecnologías Avanzadas (UPIITA), Mexico City 07340, Mexico; (K.-V.V.-D.-L.); (L.-I.G.-J.); (B.-A.R.-J.)
  2. Instituto Politécnico Nacional, Escuela Superior de Medicina (ESM), Mexico City 07738, Mexico
  3. Tecnologico de Monterrey, Escuela de Ingeniería y Ciencias, Monterrey 64849, Mexico; (J.M.A.); (O.M.-M.)
Institutions: Instituto Politécnico Nacional (Mexico); Tecnológico de Monterrey (Mexico)
Journal: Sensors (Basel, Switzerland), volume 26, issue 16, article 5121
Dates: received 11 June 2026; accepted 6 August 2026; published online 13 August 2026
Type: Review · Language: English
License: CC BY
Identifiers: DOI 10.3390/s26165121 · PMID 42655431 · PMCID PMC13517259 · OpenAlex W7202383377
Open access: gold, a free copy (OpenAlex)
Status: code verified
Categories: other (modality), human (organism)
Methods: Physiology & signal measures
Keywords: surface electromyography, sarcopenia, machine learning, neuromuscular function, aged, muscle strength, hand grip, meta-analysis
MeSH: Electromyography*, Sarcopenia*, Humans, Machine Learning, Muscle, Skeletal (* major topic)
Topic: Nutrition and Health in Aging (Physiology, Medicine), according to OpenAlex
Funding: Instituto Politécnico Nacional and Tecnológico de Monterrey (SIP20253731, SIP20250622, and SECTEI/082/2024)
Citations: not cited yet (Europe PMC); 46 references in the paper

Abstract

Age-related sarcopenia involves structural and functional neuromuscular changes. Electrophysiological measures from surface electromyography (sEMG) capture activation dynamics, spectral fatigue indices and motor unit properties that may constitute objective signatures of sarcopenia. The objective of this work is to systematically review sEMG features, fatigability metrics and AI-based classification/regression approaches reported for sarcopenia assessment between 2019 and 2026. PRISMA guidelines were followed, and IEEE Xplore, PubMed and Scopus were searched for open access human studies. Extracted information comprised sample characteristics, muscles and tasks, signal acquisition and preprocessing, extracted time/frequency/time–frequency and motor unit features, fatigue metrics, machine learning pipelines, validation schemes and dataset accessibility. Studies were classified into activation, fatigue, ML, and neural control groups; risk of bias was assessed. A total of 12 studies fulfilled the inclusion criteria. Recurrent electrophysiological signatures included reduced distal activation with compensatory proximal recruitment and higher antagonist co-activation; diminished MF/IMDF fatigue slopes indicative of Type II fiber loss and altered motor unit recruitment; motor unit analyses revealed decreased discharge rates and larger MUAP amplitudes. AI-based models combining multidomain features (time, spectral, CWT/EMD, and motor unit metrics) yielded reasonable screening performance (AUC/accuracy 0.73–0.89) when using robust feature selection and explainability tools. Heterogeneity in acquisition, normalization, small cohorts and sparse data sharing limited comparability and external validity. The findings indicate that sEMG-derived electrophysiological signatures are promising for sarcopenia detection and monitoring. To translate signatures into reliable clinical tools, standardized protocols, larger shared datasets, multimodal features, including motor unit metrics, and rigorous external validation of AI models are required.

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

Repository

Its files are read in the Code ↔ Paper reader above, with 4 matches between paragraphs and lines of code.

c4macho/LIPS_ARTICULOS

License: none: the authors keep all their rights
State: the link answers, verified on 27 September 2026
Evidence: files inventoried
Commit: 4825af5b7c14c232dbfb4e9eaead3cbfaa7d3cc8, 30 July 2026
Languages: MATLAB (2), R (1)
Size: 159 files, 3 scripts
Software Heritage: not archived
Found in: “Data Availability Statement”
Not found: README, license file, CITATION.cff, environment file, tests, continuous integration, documentation
Tools: Statistics and Machine Learning Toolbox (2 files), metafor (1 file)
Availability: 1 check, the latest on 27 September 2026: the link answers
  • 27 September 2026: the link answers
3 files
At the source: github.com/c4macho/LIPS_ARTICULOS

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

Tracing map

Proposed by the machine: these links were found in the paper and verified at the source, without human review. The map will receive a Zenodo DOI once one of the paper's authors has validated it with their ORCID.

What the map holds:

  • 1 repository of the authors' code, each at its verified commit, with its license and how the link was found in the paper;
  • 3 scripts, each with its path and the digest of its content;
  • 4 matches between paragraphs of the paper and lines of the code (method lexical-v1);
  • neither the text of the paper nor the code itself.

Its JSON (tracing-map.json) is deposited on Zenodo with its DOI once the map is validated.

Data

No dataset and no data link were found in the paper.

Data Availability Statement

The source code and Supplementary Material are available in the GitHub repository: https://github.com/c4macho/LIPS_ARTICULOS (accessed on 5 August 2026).

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

Versions

The history of this record: each version stored by the harvester or made by a correction of its authors or of the maintainers of its code, and what changed in its facts. The texts of the paper (its abstract, its availability statements) are not part of it; versions that changed only those are not listed.

Version 1, 27 September 2026: the first record

Recorded: type, language, journal, volume, issue, pages, dates, 7 authors, 8 keywords, 5 MeSH terms, 1 funder, 39 references.

Cite

This paper

Villanueva-De-Luna, K.-V., Garay-Jimenez, L.-I., Lomelí-González, J., Antelis, J. M., Mendoza-Montoya, O., Rico-Jiménez, B.-A., & Tovar-Corona, B. (2026). Electrophysiological Signatures of Sarcopenia: A Systematic Review of sEMG Features, Fatigue Indices and AI-Based Classifiers. Sensors (Basel, Switzerland), 26(16), 5121. https://doi.org/10.3390/s26165121

BibTeX

@article{villanuevadeluna2026electrophysiological,
author = {Villanueva-De-Luna, Karen-Victoria and Garay-Jimenez, Laura-Ivoone and Lomelí-González, Joel and Antelis, Javier M and Mendoza-Montoya, Omar and Rico-Jiménez, Blanca-Alicia and Tovar-Corona, Blanca},
title = {{Electrophysiological Signatures of Sarcopenia: A Systematic Review of sEMG Features, Fatigue Indices and AI-Based Classifiers}},
journal = {Sensors (Basel, Switzerland)},
year = {2026},
month = aug,
volume = {26},
number = {16},
pages = {5121},
publisher = {Multidisciplinary Digital Publishing Institute (MDPI)},
issn = {1424-8220},
doi = {10.3390/s26165121},
url = {https://doi.org/10.3390/s26165121},
pmid = {42655431},
pmcid = {PMC13517259}
}

RIS

TY - JOUR
AU - Villanueva-De-Luna, Karen-Victoria
AU - Garay-Jimenez, Laura-Ivoone
AU - Lomelí-González, Joel
AU - Antelis, Javier M
AU - Mendoza-Montoya, Omar
AU - Rico-Jiménez, Blanca-Alicia
AU - Tovar-Corona, Blanca
TI - Electrophysiological Signatures of Sarcopenia: A Systematic Review of sEMG Features, Fatigue Indices and AI-Based Classifiers
T2 - Sensors (Basel, Switzerland)
J2 - Sensors (Basel)
PY - 2026
DA - 2026/08/13
VL - 26
IS - 16
SP - 5121
SN - 1424-8220
PB - Multidisciplinary Digital Publishing Institute (MDPI)
DO - 10.3390/s26165121
UR - https://doi.org/10.3390/s26165121
LA - en
ER -

CSL-JSON

{
"id": "10.3390/s26165121",
"type": "article-journal",
"title": "Electrophysiological Signatures of Sarcopenia: A Systematic Review of sEMG Features, Fatigue Indices and AI-Based Classifiers",
"container-title": "Sensors (Basel, Switzerland)",
"author": [
{
"family": "Villanueva-De-Luna",
"given": "Karen-Victoria"
},
{
"family": "Garay-Jimenez",
"given": "Laura-Ivoone"
},
{
"family": "Lomelí-González",
"given": "Joel"
},
{
"family": "Antelis",
"given": "Javier M"
},
{
"family": "Mendoza-Montoya",
"given": "Omar"
},
{
"family": "Rico-Jiménez",
"given": "Blanca-Alicia"
},
{
"family": "Tovar-Corona",
"given": "Blanca"
}
],
"container-title-short": "Sensors (Basel)",
"volume": "26",
"issue": "16",
"page": "5121",
"DOI": "10.3390/s26165121",
"PMID": "42655431",
"PMCID": "PMC13517259",
"ISSN": "1424-8220",
"publisher": "Multidisciplinary Digital Publishing Institute (MDPI)",
"URL": "https://doi.org/10.3390/s26165121",
"language": "en",
"issued": {
"date-parts": [
[
2026,
8,
13
]
]
}
}

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