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Dynamic image-informed selection of biomechanical tumor growth models.

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  1. [1] § Methods › Scalable Bayesian filtering and model plausibility ↔ BayesianInference/Rat-3_hyper.py, lines 178–205 · score 0.55 · Newton CG, globalized, gradient, misfit, MAP, Bayesian

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The authors' code

Python · 579 lines · 19 KB · no license · 1 match

  1. # ----------------------------------------------------------------------
  2. # Mech-RD Tumor Model___Inferring 3 Params (E, D, G)
  3. ########## Hyper-elasticity ###########
  4. ############## Rat-3 ###################
  5. # ----------------------------------------------------------------------
  7. import time
  8. import math
  9. import numpy as np
  10. import dolfin as dl
  11. from fenics import *
  12. import ufl
  13. import sys
  14. import os
  15. import argparse
  17. sep = "\n"+"#"*80+"\n"
  18. # hippylib setup
  19. sys.path.append('../hippylib/hippylib')
  20. from hippylib import BiLaplacianPrior
  21. from hippylib import *
  22. sys.path.append('..')
  23. from mech_hyper import MechCoupledTumorVarf
  24. from td_mechHyp import VectorTD, TimeDependentPDEVariationalProblem, MisfitTD
  25. from utils import interp, vector2Function
  27. # Start execution timer
  28. start_time = time.time()
  30. # Set log level
  31. dl.set_log_level(40)
  32. parameters["form_compiler"]["quadrature_degree"] = 4
  34. def computeGammaDelta(corr_len, std, alpha=2, ndim=2):
  35. nu = alpha - 0.5 * float(ndim)
  36. assert alpha > 0., "Alpha must be larger than ndim/2"
  37. kappa = math.sqrt(8. * nu) / corr_len
  38. gamma = math.sqrt(math.gamma(nu) / math.gamma(alpha)) / (math.pow(4.0 * math.pi, 0.25 * float(ndim)) * math.pow(kappa, nu) * std)
  39. delta = kappa * kappa * gamma
  40. return gamma, delta
  42. # ------------------------------
  43. # Problem Configuration Section
  44. # ------------------------------
  45. parser = argparse.ArgumentParser()
  46. parser.add_argument('--sigma', default=0.035, type=float)
  47. parser.add_argument('--rhoGM', default=800, type=float)
  48. parser.add_argument('--nsamples', default=500, type=int)
  49. args = parser.parse_args()
  51. # Load Mesh
  52. name = "W05_0"
  53. data_dir = "../mri_data/W05_data/2D/"
  54. mesh = dl.Mesh(data_dir + name + ".xml")
  55. dx = dl.Measure("dx", domain=mesh)
  57. # Function Space
  58. Vh2 = dl.FunctionSpace(mesh, 'Lagrange', 2)
  59. Vh1 = dl.FunctionSpace(mesh, 'Lagrange', 1)
  60. Vh_param = dl.FunctionSpace(mesh, dl.MixedElement([Vh1.ufl_element(), Vh1.ufl_element(), Vh1.ufl_element()]))
  61. Vh = [Vh2, Vh_param, Vh2]
  63. ndofs = [Vh[STATE].dim(), Vh[PARAMETER].dim(), Vh[ADJOINT].dim()]
  64. print(f"STATE={ndofs[0]}, PARAMETER={ndofs[1]}, ADJOINT={ndofs[2]}")
  66. # Load Data
  67. h5 = dl.HDF5File(mesh.mpi_comm(), data_dir + "W05.h5", "r")
  69. time_to_group = {
  70. 2: "/W05/W05_0",
  71. 4: "/W05/W05_1",
  72. 5: "/W05/W05_2",
  73. 6: "/W05/W05_3",
  74. 9: "/W05/W05_4",
  75. }
  77. data = {}
  78. tlist = [2,4,5,6,9]
  79. for t in tlist:
  80. u = dl.Function(Vh[STATE])
  81. h5.read(u, time_to_group[t])
  82. data[str(t)] = u
  84. h5.close()
  86. obs_out = dl.XDMFFile("TumorData.xdmf")
  87. obs_out.parameters["flush_output"] = True
  88. obs_out.parameters["functions_share_mesh"] = True
  90. for t in tlist:
  91. f = dl.Function(Vh[STATE])
  92. f.assign(data[str(t)])
  93. f.rename("tumor", "tumor") # IMPORTANT for consistent naming
  94. obs_out.write(f, float(t))
  96. obs_out.close()
  98. #correlation length and sigmas [E, D, G]
  99. lc1, sigma1 = 5.5, 0.1
  100. lc2, sigma2 = 6.5, 0.3
  101. lc3, sigma3 = 3.5, 0.08
  102. gamma1, delta1 = computeGammaDelta(lc1, sigma1)
  103. gamma2, delta2 = computeGammaDelta(lc2, sigma2)
  104. gamma3, delta3 = computeGammaDelta(lc3, sigma3)
  107. gamma = [gamma1, gamma2, gamma3]
  108. delta = [delta1, delta2, delta3]
  109. theta_x = 0.55
  110. theta_y = 0.55
  112. anis_diff = dl.Constant([[theta_x, 0.], [0., theta_y]])
  113. prior = VectorBiLaplacianPrior(Vh[PARAMETER], gamma, delta,Theta=anis_diff,robin_bc=True)
  115. mean = dl.Function(Vh[PARAMETER])
  117. # Create constant expressions for each field
  118. mean_val1 = dl.Constant(-0.1562)
  119. mean_val2 = dl.Constant(-0.3492)
  120. mean_val3 = dl.Constant(-1.8965)
  122. # Extract subspaces from the mixed space
  123. V0 = Vh[PARAMETER].sub(0).collapse()
  124. V1 = Vh[PARAMETER].sub(1).collapse()
  125. V2 = Vh[PARAMETER].sub(2).collapse()
  127. # Interpolate constants into the subspaces
  128. mean_0 = dl.interpolate(mean_val1, V0)
  129. mean_1 = dl.interpolate(mean_val2, V1)
  130. mean_2 = dl.interpolate(mean_val3, V2)
  132. # Assign the subfield values into the mixed function
  133. assigner = dl.FunctionAssigner(Vh[PARAMETER], [V0, V1,V2])
  134. assigner.assign(mean, [mean_0, mean_1, mean_2])
  136. # Set it as the prior mean
  137. prior.mean.axpy(1.0, mean.vector())
  139. #------------------------ Initial Condition -------------------------
  140. u0 = interp(data_dir + "tumor_t0.mat", "cells_t", Vh[STATE])
  142. #----------------------- PDE Model Setup ------------------------
  143. dt = 1.0
  144. obs_times = [2, 4, 5, 6]
  145. sim_times = [2, 4, 5, 6, 9]
  146. H_D_val = 1.5
  147. log_H_val = math.log(H_D_val)
  148. pde_varf = MechCoupledTumorVarf(Vh, dt, dx=dl.dx, log_H_fixed=dl.Constant(log_H_val))
  149. pde = TimeDependentPDEVariationalProblem(
  150. Vh,
  151. pde_varf,
  152. [],
  153. [],
  154. u0,
  155. t_init=sim_times[0],
  156. t_final=sim_times[-1],
  157. is_fwd_linear=False,
  158. times=sim_times
  159. )
  161. #--------------------- Misfit setup ------------------------
  163. misfits = []
  164. for t in obs_times:
  165. #t_val = float(t)
  166. misfit_t = ContinuousStateObservation(Vh[STATE], dl.dx, [])
  167. obs_vec = data.get(str(int(t)))
  168. if obs_vec is not None:
  169. misfit_t.d.axpy(1.0, obs_vec.vector())
  171. else:
  172. raise RuntimeError(f"Missing observation at time {t}")
  173. misfit_t.noise_variance = args.sigma**2
  174. misfits.append(misfit_t)
  176. misfit = MisfitTD(misfits, obs_times)
  178. #-------------------- Solve for the MAP estimate -------------------------
  179. print( sep, "Find the MAP point", sep)
  180. model = Model(pde, prior, misfit)
  181. m0 = prior.mean.copy()
  183. params = ReducedSpaceNewtonCG_ParameterList()
  185. params["rel_tolerance"] = 1e-6
  186. params["abs_tolerance"] = 1e-10
  187. params["max_iter"] = 200
  188. params["globalization"] = "LS"
  189. params["print_level"] = 0
  190. params["GN_iter"] = 10
  191. params["cg_coarse_tolerance"] = 1e-6
  192. params["cg_max_iter"] = 200
  193. params["gdm_tolerance"] = 1e-12
  195. solver = ReducedSpaceNewtonCG(model, params)
  196. x = solver.solve([None, m0, None])
  197. t_map = time.time() - start_time
  198. print("\n##################################################################")
  199. print ("Termination reason: ", solver.termination_reasons[solver.reason])
  200. print ("Final gradient norm: ", solver.final_grad_norm)
  201. print ("Final cost: ", solver.final_cost)
  202. print ("Final simulation time (min): ", t_map/60)
  203. convergence = solver.converged
  204. print( "\nConverged in ", solver.it, " iterations.")
  205. print("##################################################################")
  207. # Save MAP
  208. map_func = vector2Function(x[PARAMETER], Vh[PARAMETER], name="MAP")
  209. dlx = dl.XDMFFile("MAP.xdmf")
  210. dlx.parameters["flush_output"] = True
  211. dlx.parameters["functions_share_mesh"] = True
  212. dlx.write(map_func, 0.0)
  213. dlx.close()
  215. # Save Prediction
  216. pde.solveFwd(x[STATE], x)
  217. pde.exportState(x[STATE], "state_trajectory.xdmf")
  219. print(sep, "Compute low-rank Gaussian Approximation of the posterior", sep)
  221. model.setPointForHessianEvaluations(x, gauss_newton_approx=True)
  222. Hmisfit = ReducedHessian(model, misfit_only=True)
  224. k = 50 # number of dominant modes
  225. p = 20 # oversampling
  226. print(f"Double Pass Algorithm: computing {k} modes with oversampling {p}")
  228. Omega = MultiVector(x[PARAMETER], k + p)
  229. parRandom.normal(1.0, Omega)
  231. d, eU = doublePassG(Hmisfit, prior.R, prior.Rsolver, Omega, k, s=1, check=False)
  232. posterior = GaussianLRPosterior(prior, d, eU)
  233. posterior.mean = x[PARAMETER]
  235. # ----------------------------------------------------------------------
  236. # Compute Model Evidence (Laplace Approximation)
  237. # ----------------------------------------------------------------------
  238. print(sep, "Computing model evidence (Laplace Approximation)", sep)
  239. print("\nRunning detailed evidence diagnostics...")
  241. Nd_check = 0
  242. for t in obs_times:
  243. v = data[str(t)].vector().get_local()
  244. Nd_check += v.size
  245. print("Total Nd from data =", Nd_check)
  247. residuals = []
  248. for t in obs_times:
  249. xi_t = pde.generate_static_state()
  250. x[STATE].retrieve(xi_t, float(t))
  251. pred = vector2Function(xi_t, Vh[STATE])
  252. obs_vec = data[str(t)]
  253. r = pred.vector().get_local() - obs_vec.vector().get_local()
  254. residuals.append(r)
  255. res_all = np.hstack(residuals)
  256. Phi_direct = 0.5 * np.dot(res_all, res_all) / (args.sigma**2)
  257. print(f"Phi_direct (manual residual) = {Phi_direct:.4e}")
  259. # --- Misfit term Φ(m_MAP) ---
  260. Phi_MAP = model.misfit.cost(x)
  261. print("Φ(m_MAP) =", Phi_MAP)
  263. # --- Prior norm term: (m_MAP - m_pr)^T Γ_pr^{-1} (m_MAP - m_pr) ---
  264. m_diff = x[PARAMETER].copy()
  265. m_diff.axpy(-1.0, prior.mean) # m_MAP - m_pr
  267. # Solve R * y = m_diff for y, then prior_norm_sq = m_diff^T y
  268. y_temp = dl.Vector(m_diff) # allocate solution vector
  269. prior.Rsolver.solve(y_temp, m_diff) # solves R y_temp = m_diff
  270. prior_norm_sq = m_diff.inner(y_temp)
  271. print("Prior norm squared =", prior_norm_sq)
  273. # --- Noise variance / normalization term ---
  274. sigma_noise = args.sigma
  275. try:
  276. Nd = sum([m.d.size() for m in misfits]) # if misfit stores .d vector with .size()
  277. except Exception:
  278. Nd = 0
  279. for m in misfits:
  280. try:
  281. Nd += m.d.size()
  282. except Exception:
  283. try:
  284. Nd += len(m.d)
  285. except Exception:
  286. pass
  288. term_noise = -0.5 * Nd * math.log(2.0 * math.pi * sigma_noise**2)
  289. print("Noise term =", term_noise, " (Nd =", Nd, ", sigma_noise =", sigma_noise, ")")
  291. lambda_vals = np.asarray(d).ravel() # shape (k,)
  292. r = lambda_vals.size
  293. if r == 0:
  294. term_eig = 0.0
  295. else:
  296. # numerically stable log(1+lambda) via log1p
  297. term_eig = -0.5 * np.sum(np.log1p(lambda_vals))
  298. print(f"Using r = {r} eigenvalues; Eigenvalue correction = {term_eig:.6f}")
  299. # --- Effective dimension (diagnostic) ---
  300. eff_dim = np.sum(lambda_vals / (1.0 + lambda_vals))
  301. print(f"Effective dimension = {eff_dim:.3f}")
  303. # Detailed evidence breakdown
  304. log_evidence = -Phi_MAP - 0.5 * prior_norm_sq + term_noise + term_eig
  305. print("\nEVIDENCE COMPONENTS:")
  306. print(f" -Phi_MAP = {-Phi_MAP:.4e}")
  307. print(f" -0.5*prior_norm_sq = {-0.5*prior_norm_sq:.4e}")
  308. print(f" term_noise = {term_noise:.4e}")
  309. print(f" term_eig (correction) = {term_eig:.4e}")
  311. print("\n######################## Model Evidence ########################")
  312. print(f"log_evidence = {log_evidence:.12e}")
  313. try:
  314. evidence_val = math.exp(log_evidence)
  315. print(f"Evidence = {evidence_val:.6e}")
  316. except OverflowError:
  317. print("Evidence too small to exponentiate safely (underflow). Keep log_evidence instead.")
  318. print("################################################################")
  320. # ------------------------
  321. # ------------------------
  322. def compute_dice_score(f1, f2, threshold=0.25):
  323. """
  324. Computes DICE between two FEniCS Functions by DOF thresholding.
  325. """
  326. f1_vals = f1.vector().get_local()
  327. f2_vals = f2.vector().get_local()
  329. f1_mask = (f1_vals > threshold).astype(np.int8)
  330. f2_mask = (f2_vals > threshold).astype(np.int8)
  332. intersection = np.sum(f1_mask * f2_mask)
  333. total = np.sum(f1_mask) + np.sum(f2_mask)
  335. return (2.0 * intersection) / (total + 1e-12)
  337. # ----------------------------------------------------------------------
  338. # Posterior NTA Evaluation: 50 samples per time point
  339. # ----------------------------------------------------------------------
  340. print(sep, "Evaluating NTA across posterior samples", sep)
  342. num_nta_samples = 50
  344. # Evaluate NTA at ALL internal solver times
  345. eval_times = list(pde.times)
  347. brain_area = dl.assemble(dl.Constant(1.0) * dx)
  349. # Storage
  350. nta_results = {t: [] for t in eval_times}
  351. nta_mri_dict = {}
  353. # Compute MRI NTA only where MRI exists
  354. for t in eval_times:
  355. key = str(int(t))
  356. if key in data:
  357. true = data[key]
  358. true_indicator = dl.Function(Vh[STATE])
  359. true_indicator.vector().set_local(
  360. np.where(true.vector().get_local() > 0.25, 1.0, 0.0)
  361. )
  362. nta_mri_dict[t] = dl.assemble(true_indicator * dx) / brain_area
  363. else:
  364. nta_mri_dict[t] = np.nan
  366. # Initialize noise vector
  367. noise = dl.Vector()
  368. posterior.init_vector(noise, "noise")
  370. # File for all NTA samples
  371. with open("NTA_posterior_samples.txt", "w") as f:
  372. f.write("Time,SampleID,NTA_model,NTA_mri\n")
  374. for i in range(num_nta_samples):
  375. print(f"NTA posterior sample {i+1}/{num_nta_samples}")
  376. parRandom.normal(1.0, noise)
  378. # Draw posterior sample
  379. pr_s = model.generate_vector(PARAMETER)
  380. post_s = model.generate_vector(PARAMETER)
  381. posterior.sample(noise, pr_s, post_s, add_mean=True)
  383. # Solve PDE forward for this sample
  384. u = pde.generate_state()
  385. x_sample = [u, post_s, None]
  386. pde.solveFwd(x_sample[STATE], x_sample)
  388. for t in eval_times:
  389. xi_t = pde.generate_static_state()
  390. x_sample[STATE].retrieve(xi_t, float(t))
  391. pred = vector2Function(xi_t, Vh[STATE])
  393. # Compute NTA_model
  394. nta_indicator = dl.Function(Vh[STATE])
  395. nta_indicator.vector().set_local(np.where(pred.vector().get_local() > 0.25, 1.0, 0.0))
  396. nta_model = dl.assemble(nta_indicator * dx) / brain_area
  398. nta_results[t].append(nta_model)
  399. f.write(f"{t},{i},{nta_model:.6f},{nta_mri_dict[t]:.6f}\n")
  401. # --- Compute summary statistics ---
  402. mean_nta = [np.mean(nta_results[t]) for t in eval_times]
  403. std_nta = [np.std(nta_results[t]) for t in eval_times]
  404. nta_mri_values = [nta_mri_dict[t] for t in eval_times]
  406. # Save summary results
  407. with open("NTA_summary.txt", "w") as f:
  408. f.write("Time,NTA_model,NTA_mri\n")
  409. for t, mean_val, nta_mri_val in zip(eval_times, mean_nta, nta_mri_values):
  410. f.write(f"{t},{mean_val:.6f},{nta_mri_val:.6f}\n")
  412. # ----------------------------------------------------------------------
  413. # Posterior DICE Evaluation: Mean ± Std across posterior samples
  414. # ----------------------------------------------------------------------
  415. print(sep, "Evaluating posterior DICE", sep)
  417. num_dice_samples = 50
  418. eval_times = [t for t in sim_times if str(t) in data]
  420. dice_results = {t: [] for t in eval_times}
  422. noise = dl.Vector()
  423. posterior.init_vector(noise, "noise")
  425. for i in range(num_dice_samples):
  426. print(f"DICE posterior sample {i+1}/{num_dice_samples}")
  427. parRandom.normal(1.0, noise)
  429. pr_s = model.generate_vector(PARAMETER)
  430. post_s = model.generate_vector(PARAMETER)
  431. posterior.sample(noise, pr_s, post_s, add_mean=True)
  433. u = pde.generate_state()
  434. x_sample = [u, post_s, None]
  435. pde.solveFwd(x_sample[STATE], x_sample)
  437. for t in eval_times:
  438. xi_t = pde.generate_static_state()
  439. x_sample[STATE].retrieve(xi_t, float(t))
  440. pred = vector2Function(xi_t, Vh[STATE])
  441. true = data[str(t)]
  443. score = compute_dice_score(pred, true, threshold=0.25)
  444. dice_results[t].append(score)
  446. # Save raw samples
  447. with open("DICE_posterior_samples.txt","w") as f:
  448. f.write("Time,SampleID,DICE\n")
  449. for t in eval_times:
  450. for i,val in enumerate(dice_results[t]):
  451. f.write(f"{t},{i},{val:.6f}\n")
  453. mean_dice = [np.mean(dice_results[t]) for t in eval_times]
  454. std_dice = [np.std(dice_results[t]) for t in eval_times]
  456. # ----------------------------------------------------------------------
  457. # FINAL MAP MECHANICS EXPORT: Displacement and Hyper-elastic Stress
  458. # ----------------------------------------------------------------------
  459. print(sep, "Computing MAP Mechanics (Stress/Displacement) for Trajectory", sep)
  461. # File Setup
  462. mech_xdmf = dl.XDMFFile("MAP_mechanics_results.xdmf")
  463. mech_xdmf.parameters["flush_output"] = True
  464. mech_xdmf.parameters["functions_share_mesh"] = True
  466. # Function Space for Magnitudes and visualization
  467. V_mag = Vh1
  469. # Extract the MAP parameter for Stiffness (log_E)
  470. # map_func is already created from x[PARAMETER] earlier in the script
  471. log_E_map, _, _ = map_func.split(deepcopy=True)
  473. # Iterate through all simulation times (start from t=2)
  474. for t in sim_times:
  475. xi_t = pde.generate_static_state()
  476. x[STATE].retrieve(xi_t, float(t))
  477. pred_tumor = vector2Function(xi_t, Vh[STATE])
  479. if float(t) == float(sim_times[0]):
  480. # Force EVERYTHING to be absolute zero at the start
  481. disp_mag = dl.interpolate(dl.Constant(0.0), V_mag)
  482. piola_mag = dl.interpolate(dl.Constant(0.0), V_mag)
  484. print(f"Time t = {t:.2f}: Using forced absolute zeros.")
  485. else:
  486. # solve mechanics for all time after the initial MRI time point
  487. u_mech = pde_varf.solve_mechanics(pred_tumor, log_E_map, pde_varf.log_H_fixed)
  489. # Calculate magnitudes
  490. disp_mag = project(sqrt(dot(u_mech, u_mech)), V_mag)
  492. P2_tensor = pde_varf.first_piola_from_energy(u_mech, log_E_map)
  493. piola_mag = project(sqrt(inner(P2_tensor, P2_tensor)), V_mag)
  495. # Rename for Paraview consistency (Important!)
  496. disp_mag.rename("Displacement_Magnitude", "disp_mag")
  497. piola_mag.rename("First_Piola_Kirchhoff_Magnitude", "piola_mag")
  499. # Export
  500. mech_xdmf.write(disp_mag, float(t))
  501. mech_xdmf.write(piola_mag, float(t))
  503. mech_xdmf.close()
  504. print("MAP Mechanics saved to 'MAP_mechanics_results.xdmf'")
  507. # --------------------------------------------------------
  508. # MAP DICE + NTA + Volume block
  509. # --------------------------------------------------------
  510. print(sep, "Computing MAP DICE / NTA / Volume", sep)
  512. eval_times = [t for t in sim_times if str(t) in data]
  514. dice_file = open("DICE_scores.txt", "w")
  515. dice_file.write("Time,DICE\n")
  517. nta_file = open("nta.txt", "w")
  518. nta_file.write("Time,NTA_model,NTA_mri\n")
  520. vol_file = open("TumorVolumes.txt", "w")
  521. vol_file.write("Time,Volume\n")
  523. brain_area = dl.assemble(dl.Constant(1.0) * dx)
  525. # --- Paraview writers ---
  526. map_pred_xdmf = dl.XDMFFile("MAP_predictions.xdmf")
  527. map_pred_xdmf.parameters["flush_output"] = True
  528. map_pred_xdmf.parameters["functions_share_mesh"] = True
  530. map_mask_xdmf = dl.XDMFFile("MAP_indicator_masks.xdmf")
  531. map_mask_xdmf.parameters["flush_output"] = True
  532. map_mask_xdmf.parameters["functions_share_mesh"] = True
  534. for t in eval_times:
  535. # retrieve state at time t
  536. xi_t = pde.generate_static_state()
  537. x[STATE].retrieve(xi_t, float(t))
  538. pred = vector2Function(xi_t, Vh[STATE], name=f"MAP_pred_t{t}")
  539. true = data[str(t)]
  541. # --- Save tumor field for paraview ---
  542. map_pred_xdmf.write(pred, float(t))
  544. # --- New DICE ---
  545. dice_score = compute_dice_score(pred, true, threshold=0.25)
  547. # --- New NTA / Volume ---
  548. pred_indicator = dl.Function(Vh[STATE], name=f"MAP_indicator_t{t}")
  549. pred_indicator.vector().set_local(
  550. np.where(pred.vector().get_local() > 0.25, 1.0, 0.0)
  551. )
  553. # save mask for paraview
  554. map_mask_xdmf.write(pred_indicator, float(t))
  556. nta_model = dl.assemble(pred_indicator * dx) / brain_area
  558. true_indicator = dl.Function(Vh[STATE])
  559. true_indicator.vector().set_local(
  560. np.where(true.vector().get_local() > 0.25, 1.0, 0.0)
  561. )
  562. nta_mri = dl.assemble(true_indicator * dx) / brain_area
  564. # volume (non-normalized)
  565. vol = dl.assemble(pred_indicator * dx)
  567. # --- Save text values ---
  568. dice_file.write(f"{t},{dice_score:.6f}\n")
  569. nta_file.write(f"{t},{nta_model:.6f},{nta_mri:.6f}\n")
  570. vol_file.write(f"{t},{vol:.6f}\n")
  572. dice_file.close()
  573. nta_file.close()
  574. vol_file.close()
  575. map_pred_xdmf.close()
  576. map_mask_xdmf.close()
  578. print("MAP DICE / NTA / Volume stored in TXT + XDMF files.")
  579. print("Inference complete. Results stored as XDMF and PVD files.")

Rat-3_hyper.py at commit 7e048e0, no license · at the source

Overview

Authors: Abdullah Al Noman1, Pratyush Kumar Singh1, David A Hormuth II2, Danial Faghihi1
  1. Department of Mechanical and Aerospace Engineering, University at Buffalo, Buffalo, NY USA
  2. Oden Institute for Computational Engineering and Sciences, Livestrong Cancer Institutes, University of Texas at Austin, Austin, TX USA
Institutions: University at Buffalo, State University of New York (United States); The University of Texas at Austin (United States)
Journal: Biomechanics and modeling in mechanobiology, volume 25, issue 5, article 97
Dates: received 6 April 2026; accepted 12 August 2026; published online 31 August 2026; in print 2026
Type: Research article · Language: English
License: CC BY
Identifiers: DOI 10.1007/s10237-026-02121-2 · PMID 42675182 · PMCID PMC13529865 · OpenAlex W7204846453
Open access: hybrid, a free copy (OpenAlex)
Status: code verified
Categories: structural MRI / diffusion (modality), mouse (organism), other condition (population)
Methods: Spectral & time-frequency, Connectivity, fMRI & imaging
Keywords: Biomechanical tumor growth, Finite deformation elasticity, Dynamic model selection, Image-informed modeling
MeSH: Brain Neoplasms*, Magnetic Resonance Imaging*, Models, Biological*, Animals, Bayes Theorem, Biomechanical Phenomena, Cell Proliferation, Elasticity, Mice, Stress, Mechanical (* major topic)
Topic: Mathematical Biology Tumor Growth (Modeling and Simulation, Mathematics), according to OpenAlex
Funding: State University of New York (SUNY) Research Seed Grant (1191358); U.S. National Science Foundation (NSF) through CAREER Award (CMMI-2143662); U.S. National Science Foundation (NSF) (DMS-2436499)
Citations: not cited yet (Europe PMC); 45 references in the paper

Abstract

Glioblastoma progression is strongly influenced by evolving mechanical interactions between the tumor and surrounding brain tissue. However, the extent to which finite-deformation mechanics and constitutive assumptions improve subject-specific prediction as tumor burden evolves remains unclear. We introduce a sequential Bayesian inference and dynamic model selection framework that assimilates longitudinal murine magnetic resonance imaging (MRI) data to calibrate spatially varying tumor diffusivity, proliferation rate, and tissue stiffness in biomechanical tumor growth models. Competing formulations were compared at each imaging time, including reaction–diffusion without mechanics and reaction–diffusion coupled to linear elasticity or hyperelastic mechanics, using posterior model plausibility to adapt model choice for individualized one-scan-ahead prediction as new MRI scans are acquired. Across the studied animals, mechanically coupled models were consistently more plausible than the uncoupled reaction–diffusion model, and the evolution of model plausibility indicated an increasing role of mass effect and stress-mediated feedback of tumor growth during progression. While linear and hyperelastic coupled tumor growth models often produced similar tumor morphology, they yield distinct stress, deformation, and inferred stiffness fields, with the hyperelastic formulation often receiving higher posterior plausibility at later imaging times. These results indicate that, within the present longitudinal murine dataset, mechanical coupling is favored for image-informed glioma growth prediction and that constitutive assumptions should be evaluated sequentially for each subject rather than fixed a priori.

Supplementary Information: The online version contains supplementary material available at https://doi.org/10.1007/s10237-026-02121-2.

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

Repository

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PCELab/RecursiveGliomaInference

License: none: the authors keep all their rights
State: the link answers, verified on 27 September 2026
Evidence: files inventoried
Commit: 7e048e0eab5133a9686a1445ac3fc677d2424a78, 5 July 2026
Languages: Python (4)
Size: 10 files, 4 scripts
Software Heritage: not archived
Found in: “Data availability”
Holds: README
Not found: license file, CITATION.cff, environment file, tests, continuous integration, documentation
Tools: NumPy (3 files), SciPy (1 file)
Availability: 1 check, the latest on 27 September 2026: the link answers
  • 27 September 2026: the link answers
5 files
At the source: github.com/PCELab/RecursiveGliomaInference

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

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Data availability

The data supporting the findings of this study are available from the corresponding author upon reasonable request. The computational code used in this study is available at https://github.com/PCELab/RecursiveGliomaInference.

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

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Version 2, 28 September 2026

  • Publisher: n/a → Springer Science+Business Media

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Recorded: type, language, journal, volume, issue, pages, dates, 4 authors, 4 keywords, 10 MeSH terms, 3 funders, 29 references.

Cite

This paper

Noman, A. A., Singh, P. K., Hormuth, D. A., & Faghihi, D. (2026). Dynamic image-informed selection of biomechanical tumor growth models. Biomechanics and modeling in mechanobiology, 25(5), 97. https://doi.org/10.1007/s10237-026-02121-2

BibTeX

@article{noman2026dynamic,
author = {Noman, Abdullah Al and Singh, Pratyush Kumar and Hormuth, David A and Faghihi, Danial},
title = {{Dynamic image-informed selection of biomechanical tumor growth models}},
journal = {Biomechanics and modeling in mechanobiology},
year = {2026},
month = aug,
volume = {25},
number = {5},
pages = {97},
publisher = {Springer Science+Business Media},
issn = {1617-7959},
doi = {10.1007/s10237-026-02121-2},
url = {https://doi.org/10.1007/s10237-026-02121-2},
pmid = {42675182},
pmcid = {PMC13529865}
}

RIS

TY - JOUR
AU - Noman, Abdullah Al
AU - Singh, Pratyush Kumar
AU - Hormuth, David A
AU - Faghihi, Danial
TI - Dynamic image-informed selection of biomechanical tumor growth models
T2 - Biomechanics and modeling in mechanobiology
J2 - Biomech Model Mechanobiol
PY - 2026
DA - 2026/08/31
VL - 25
IS - 5
SP - 97
SN - 1617-7959
PB - Springer Science+Business Media
DO - 10.1007/s10237-026-02121-2
UR - https://doi.org/10.1007/s10237-026-02121-2
LA - en
ER -

CSL-JSON

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