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Alterations in topological and dynamical parameters correlate with disease biomarkers and neuropsychological scores in prodromic stages of dementia.

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  1. [1] § Methods › Virtual brain modelling ↔ TVB_rww_notebook.ipynb, lines 147–175 · score 0.74 · Wong Wang, neural mass model, fMRI, BOLD signal, global coupling, denotes

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  1. # %% [markdown]
  2. # <h1 align="center"><font size="7" face="arial" color="#D9027D">Modelling Resting State with TVB</font></h1>
  4. # %% [markdown]
  5. # <h3 align="center"><span style="font-weight:normal"><font size="4.5" face="arial">
  6. # Anita Monteverdi, Fulvia Palesi, Marta Gaviraghi, and Roberta Maria Lorenzi </font></span></h3>
  8. # %% [markdown]
  9. # <h1><font size="6" face="arial" color="#BF026D">Context</font></h1>
  10. #
  11. # ***
  12. #
  13. # <p><div style="text-align: justify"><font size="4.5" face="time roman">A current topic in system neuroscience literature is the presence of brain activity in the absence of a task condition. These task-negative, spontaneous fluctuations occur in the so-called <b>rest state</b>, and a recurring theme of these fluctuations is that they have a network structure. Because TVB uses the structural connectivity of the brain as the backbone for simulating spontaneous activity, resting state activity and its network structure is a prime candidate for modeling in TVB.</font></div></p>
  15. # %% [markdown]
  16. # <h1><font size="6" face="arial" color="#BF026D">Objectives</font></h1>
  17. #
  18. # ***
  19. #
  20. # <p><div style="text-align: justify"><font size="4.5" face="time roman">In this notebook, we will start from <b>Zimmerman et al, 2018 </b> to:
  21. # <br>
  22. # <ul>
  23. # <li>Build a brain network model using subject-specific structural connectivity,</li>
  24. # <li>Globally optimize parameters of the models,</li>
  25. # <li>Define and simulate dynamics of the whole brain at rest,</li>
  26. # <li>Characterize the resting-state activity using the functional connectivity (FC).</li></ul></font></div></p>
  27. #
  28. # </br>
  29. # <br>
  30. # <p><div style="text-align: justify"><font size="4.5" face="time roman"><u>References:</u></font></div></p>
  31. # <p><div style="text-align: justify"><font size="4.5" face="time roman"><blockquote>
  32. # <li> Zimmermann, J., Perry, A., Breakspeare, M. et al. <b> Differentiation of Alzheimer's disease based on local and global parameters in personalized Virtual Brain models.</b> NeuroImage:Clinical, 2018, 19, 240-251.</li>
  34. # %% [markdown]
  35. # <h1><font size="6" face="arial" color="#BF026D">Exercise</font></h1>
  36. #
  37. # ***
  38. #
  39. # <p><div style="text-align: justify"><font size="4.5" face="time roman"></font></div></p>
  40. #
  41. # <h2><font size="5"face="arial" color="black">How to do it with TVB?</font></h2>
  42. #
  43. # <p><div style="text-align: justify"><font size="4.5" face="time roman">In the first part of this tutorial, we presents the basic anatomy of a region simulation using The Virtual Brain scripting interface.
  44. # The first thing we want to do is to import the modules we will need for a simulation.</font></div></p>
  46. # %%
  47. %pip install tvb
  49. # %%
  50. %matplotlib inline
  52. # %%
  53. %%capture
  54. # Import a bunch of stuff to ease command line usage
  55. import os
  56. import numpy as np
  57. import time as tm
  59. import matplotlib
  60. import matplotlib.pyplot as plt
  62. from tvb.simulator.lab import *
  63. from tvb.datatypes.time_series import TimeSeriesRegion
  64. from tvb.datatypes import graph
  66. # %% [markdown]
  67. # <h1><font size="5.5" face="arial" color="black">1. Load and prepare connectivity data</font></h1>
  68. #
  69. # <p><div style="text-align: justify"><font size="4.5" face="time roman">Load in and prepare the structural connectivity and functional connectivity from the source we are using.</font></div></p>
  70. #
  71. # <h2><font size="4.5"face="arial" color="black"> Subject-specific structural connectivity</font></h2>
  72. #
  73. # <p><div style="text-align: justify"><font size="4.5" face="time roman">Here, we use a <b>Structural Connectivity (SC) of 126 regions</b> derived from Diffusion Weighted Imaging (DWI) and Constrained Spherical Deconvolution tractography, as previously published in <b>Palesi et al. (2020)</b>. Connections in this SC matrix were defined with an ad-hoc parcellation scheme combining cerebral cortical and subcortical parcellations (<b>Tzourio-Mazoyer et al., 2002</b>) with cerebellar ones (SUIT, <b>Diedrichsen et al., 2009</b>).
  74. # <br>We start by loading and visualizing the SC matrix that represents the set of all existing connections between brain areas.</font></div></p>
  75. #
  76. # <h2><font size="4.5"face="arial" color="black"> Subject-specific functional connectivity</font></h2>
  77. #
  78. # <p><div style="text-align: justify"><font size="4.5" face="time roman">For the same subject, we use a static <b>Functional Connectivity (FC) </b> whose edges were defined as the correlation between the time-courses of pairs of the 126 regions.
  79. # <br>We start by loading and visualizing the SC matrix that represents the set of all existing connections between brain areas.</font></div></p>
  80. #
  81. # <p><div style="text-align: justify"><font size="4.5" face="time roman"><u>References:</u></font></div></p>
  82. # <p><div style="text-align: justify"><font size="4.5" face="time roman"><blockquote>(Palesi et al., 2020): Palesi, F., Lorenzi, R. M., Casellato, C., Ritter, P., Jirsa, V., Wheeler- kingshott, C. A. M. G., and Angelo, E. D. (2020). <b>The importance of cerebellar connectivity on simulated brain dynamics. </b>Frontiers in Cellular Neuroscience, 14,1–11. <br />
  83. # <br>(Monteverdi et al., 2022): Monteverdi A, Palesi F, Costa A, Vitali P, Pichiecchio A, Cotta Ramusino M, Bernini S, Jirsa V,
  84. # Gandini Wheeler-Kingshott CAM and D’Angelo E (2022) <b>Subject-specific features of excitation/inhibition profiles in neurodegenerative diseases.</b>
  85. # Front. Aging Neurosci. 14:868342. doi: 10.3389/fnagi.2022.868342<br />
  86. # <br>(Tzourio-Mazoyer et al., 2002): Tzourio-Mazoyer, N., Landeau, B., Papathanassiou, D., Crivello, F., Etard, O., Delcroix, N., et al. (2002). <b>Automated anatomical labeling ofactivations in SPM using a macroscopic anatomical parcellation of the MNI MRI single-subject brain. </b>Neuroimage 15, 273–289. doi: 10.1006/nimg.2001.0978.<br />
  87. # <br>(Diedrichsen et al., 2009): Diedrichsen, J., Balsters, J. H., Flavell, J., Cussans, E., and Ramnani, N. (2009). <b>A probabilistic MR atlas of the human cerebellum.</b> Neuroimage 46, 39–46. doi: 10.1016/j.neuroimage.2009.01.045.<br /></blockquote></font></div></p>
  89. # %%
  90. from google.colab import drive
  91. drive.mount('/content/gdrive')
  93. # %%
  94. # Change the path of your Google Drive with the Tutorial folder
  95. root_path = '/content/gdrive/MyDrive/04_TVB/'
  97. # %%
  98. # Define paths for importing empirical structural (SC) and functional connectivity (FC)
  99. pathSC = root_path + 'TVB_data/Conn_plusCRBL.zip'
  100. pathFC = root_path + 'TVB_data/functZ_sparse.txt'
  102. # %%
  103. # Import empirical connectivities
  105. #STRUCTURAL
  106. con = connectivity.Connectivity.from_file(pathSC)
  107. #Define the average axonal speed
  108. con.speed = np.array(10)
  109. print ('')
  110. print ('Maximum SC value = %10.4f' % np.max(con.weights))
  112. #FUNCTIONAL
  113. con_FC = np.genfromtxt(pathFC)
  115. # %%
  116. # Visualize the empirical SC, time delays along SC edges, and FC matrices
  117. fig=plt.figure(figsize=(12,5))
  118. #labels=con.region_labels[0:126:5]
  119. labels=con.region_labels[0:-1:5]
  121. # SC
  122. plt.subplot(131)
  123. #cs=imshow(np.log10(con.weights), cmap='jet', aspect='equal', interpolation='none')
  124. cs=plt.imshow(con.weights, interpolation='none', aspect='equal', cmap='jet', vmax=0.005)
  125. plt.title('Empirical SC', fontsize=14)
  126. plt.xticks(np.arange(0, len(con.region_labels)-1, step=5), labels, fontsize=7, rotation=90)
  127. plt.yticks(np.arange(0, len(con.region_labels)-1, step=5), labels, fontsize=7)
  128. axcb=plt.colorbar(cs, shrink=0.4)
  129. axcb.set_label('weights', fontsize=11)
  131. #delays
  132. plt.subplot(132)
  133. plt.imshow(con.tract_lengths/con.speed, interpolation='none', aspect='equal', cmap='jet')
  134. plt.title('Conduction delays', fontsize=14)
  135. axcb=plt.colorbar(shrink=0.4)
  136. axcb.set_label('delays [ms]', fontsize=11)
  138. # empirical FC
  139. plt.subplot(133)
  140. plt.imshow(con_FC, interpolation='nearest', aspect='equal', cmap='jet')
  141. plt.title('Empirical FC', fontsize=14)
  142. cb=plt.colorbar(shrink=0.4, ticks=[-0.2, 0.0, 0.2, 0.4, 0.6, 0.8, 1.0])
  143. cb.set_label('PPC', fontsize=11)
  145. plt.show
  147. # %% [markdown]
  148. # <h3><font size="5" face="arial" color="black"> 2 Model</font></h3>
  149. #
  150. #
  151. # <p><div style="text-align: justify"><font size="4.5" face="time roman">In this tutorial, we will use a computational model of resting-state network dynamics: the <b>Reduced Wong-Wang</b>, previously introduced in <b>(Hansen et al., 2015)</b>. This model is a reduction of the model presented in <b>(Wong &#38; Wang, 2006)</b> to a single population model and used in a modeling study of resting-state <b>(Deco et al., 2013; Hansen et al., 2015)</b>. The neural activity of each node is given by the following equations:</font></div></p>
  152. #
  153. # \begin{eqnarray}
  154. # \dfrac{\text{d}S_{i}}{\text{d}t} &=& \dfrac{-S_{i}}{\tau_{s}} + \gamma \ (1 - S_{i})\ H(x_{i}) + \sigma\eta_{i}(t)\\
  155. # &\\
  156. # H(x_{i}) &=& \dfrac{ax_{i} - b}{1 - \exp(-d \ (ax_{i} - b))}\\
  157. # &\\
  158. # x_{i} &=& wJ_{N}S_{i} + J_{N}G\sum_{j}C_{ij}S_{j} + I_{0}
  159. # \end{eqnarray}
  160. #
  161. # <p><div style="text-align: justify"><font size="4.5" face="time roman">where $S_{i}$ denotes the average synaptic gating variable at the local area $i$, $H(x_{i})$ is a sigmoid function that converts the input synaptic activity $x_{i}$ into an output population firing rate.</font></div></p>
  162. # <p><div style="text-align: justify"><font size="4.5" face="time roman">$C_{ij}$ are the entries of the anatomical structural connectivity matrix reweigthed by the global coupling parameter $G$, with which we will study the optimal dynamical working region where the simulations maximally fit the empirical FC. $\eta_{i}(t)$ is a Gaussian white noise with a noise amplitude $\sigma = 0.001.$</font></div></p>
  163. #
  164. #
  165. # <p><div style="text-align: justify"><font size="4.5" face="time roman">This <b>biologically realistic</b> neural mass model is able to reproduce <b>time-averaged resting state FC</b> as well as the recently introduced <b>FC dynamics</b> with fMRI BOLD signals.</font></div></p>
  166. #
  167. # <p><div style="text-align: justify"><font size="4.5" face="time roman"><u>References:</u></font></div></p>
  168. # <p><div style="text-align: justify"><font size="4.5" face="time roman"><blockquote>(Wong &#38; Wang, 2006): Wong, K.-F. &#38; Wang, X.-J. <b>A recurrent network mechanism of time integration in perceptual decision.</b> J. Neurosci., 2006, 26, 1314-1328. <br />
  169. # <br>(Deco et al., 2013): Deco, G., Ponce-Alvarez, A., Mantini, D., Romani, G.L., Hagmann, P. &#38; Corbetta, M. <b>Resting-state functional connectivity emerges from structurally and dynamically shaped slow linear fluctuations.</b> J. Neurosci., 32(27), 11239-11252, 2013.<br />
  170. # <br>(Hansen et al., 2015): Hansen, E.C., Battaglia, D., Spiegler, A., Deco, G. &#38; Jirsa V.K. <b>Functional connectivity dynamics: modeling the switching behavior of the resting-state.</b> NeuroImage, 105(2015), 525-535.<br />
  172. # %%
  173. # Initialise a Model.
  174. g2d = models.ReducedWongWang()
  175. g2d
  177. # %% [markdown]
  178. # <h3><font size="5"face="arial" color="black"> 3 Coupling function</font></h3>
  179. # <p><div style="text-align: justify"><font size="4.5" face="time roman">The coupling function is used to join the local model dynamics at distinct spatial locations.</font></div></p>
  181. # %%
  182. # Initialise a Coupling function.
  183. G = np.array(7.5)
  184. con_coupling = coupling.Scaling(a=G)
  186. # %% [markdown]
  187. # <h3><font size="5"face="arial" color="black"> 4 Integrator</font></h3>
  188. # <p><div style="text-align: justify"><font size="4.5" face="time roman">Now that we have defined our structure and dynamics, we need to select an integration scheme.
  189. #
  190. # <br>We use a stochastic integration scheme where the noise is added. The shape of the noise must correspond to the number of state variables in neural mass models, here equal to 1.
  191. # We integrate the coupling and the stochastic terms using a <b>HeunStochastic</b> method, otherwise you can use the detrministic version <b>HeunDeterministic</b>. The step size for the simulation is 0.5.
  192. # <br>By default in TVB, the stochastic method assumes that the standard deviation of the noise is a constant equal to: $\sqrt{(2\sigma)}$.
  193. #
  194. # <br>
  195. #
  196. # <b>NOTE</b> that the most important thing here is to use a step size that is small enough for the integration to be numerically stable.</font></div></p>
  198. # %%
  199. # Initialise an Integrator scheme.
  200. dt = 0.5 #integration steps [ms]
  202. #Change dt to assess how much it impact on the final results
  204. # We can use the deteministic integrator:
  205. # heunint = integrators.HeunDeterministic(dt=dt)
  207. D = 0.001 #standard deviation of the noise
  208. heunstoc=integrators.HeunStochastic(dt=dt, noise=noise.Additive(nsig=np.array([(D**2)/2])))
  210. # %% [markdown]
  211. # <h3><font size="5"face="arial" color="black"> 5 Monitors</font></h3>
  212. # <p><div style="text-align: justify"><font size="4.5" face="time roman">The last component is Monitor: observer models.
  213. #
  214. # <br>Here we select two monitors to get the time series of the model state variables. First, one of the simplest:
  215. #
  216. # * the <b>TemporalAverage</b> monitor averages over a time window of length period returning one time point every period (given in ms).
  217. #
  218. # Then, among other Monitors which apply a biophysical measurement process to the simulated neural activity, such as EEG, MEG, etc, we would like to relate the simulated neural activity to recent fMRI studies, thus we chose:
  219. #
  220. # * the <b>BOLD</b> monitor to generate BOLD signal for each regions by using a hemodynamic model.</font></div></p>
  222. # %%
  223. # Initialise some Monitors with period in physical time.
  224. mon_tavg = monitors.TemporalAverage(period=1.) #1000 Hz
  225. TR = 720
  226. mon_bold = monitors.Bold(period=TR)
  228. #Bundle them
  229. what_to_watch = (mon_tavg,mon_bold)
  231. # %% [markdown]
  232. # <h1 align="center"><font size="6"face="arial" color="black">Go! Simulate</font></h1>
  233. #
  234. # <p><div style="text-align: justify"><font size="4.5" face="time roman">The last step is to bring all these components together into a <b>Simulator</b> object. We then need to run the configure method, which basically just acts to calculate information necessary for the simulation that draws on specific combinations of the components.</font></div></p>
  236. # %%
  237. # Initialise the Simulator.
  238. regime={'w':np.array(1.), 'I_o':np.array(0.3)}
  239. sim = simulator.Simulator(
  240. model=models.ReducedWongWang(**regime),
  241. connectivity=con,
  242. coupling=con_coupling,
  243. conduction_speed=float(con.speed),
  244. integrator=heunstoc,
  245. monitors=what_to_watch)
  246. sim.initial_conditions = 0.001*np.ones((1, 1, con.weights.shape[0], 1))
  247. sim.configure()
  249. # %% [markdown]
  250. # <p><div style="text-align: justify"><font size="4.5" face="time roman">Now, we can run the simulation. All we need to do is iterate for some length, which we provide in *ms*, and collect the output.
  251. #
  252. # The data returned by the simulator is in the form of a list of arrays.</font></div></p>
  254. # %%
  255. # Perform the simulation.
  256. tic = tm.time()
  258. tavg_data, tavg_time = [], []
  259. bold_data, bold_time = [], []
  261. for tavg, bold in sim(simulation_length=360000.):
  263. if not tavg is None:
  264. tavg_time.append(tavg[0])
  265. tavg_data.append(tavg[1])
  267. if not bold is None:
  268. bold_time.append(bold[0])
  269. bold_data.append(bold[1])
  272. 'simulation required %0.3f seconds.' % (tm.time()-tic)
  274. # %% [markdown]
  275. # <h1 align="center"><font size="6"face="arial" color="black">Visualize our simulation</font></h1>
  276. #
  277. # <p><div style="text-align: justify"><font size="4.5" face="time roman">And finally, we can look at the results of our simulation, first in terms of time series...</font></div></p>
  279. # %%
  280. # Normalize the time series
  281. tavg_data /= (np.max(tavg_data, 0) - np.min(tavg_data, 0))
  283. # Make the lists numpy.arrays for easier use.
  284. TAVG = np.squeeze(np.array(tavg_data))
  286. # Plot the temporally averaged time series
  287. fig2 = plt.figure(figsize=(12,8))
  288. plt.subplot(3,1,1)
  289. plt.plot(tavg_time[:], TAVG[:, 0], 'r')
  290. plt.ylabel(con.region_labels[0],fontsize=13)
  291. plt.subplot(3,1,2)
  292. plt.plot(tavg_time[:], TAVG[:, 1], 'c')
  293. plt.ylabel(con.region_labels[1],fontsize=13)
  294. plt.subplot(3,1,3)
  295. plt.plot(tavg_time[:], TAVG[:, 2], 'g')
  296. plt.xlabel('Time [ms]', fontsize=13)
  297. plt.ylabel(con.region_labels[2],fontsize=13)
  299. plt.show()
  301. # %% [markdown]
  302. # <p><div style="text-align: justify"><font size="4.5" face="time roman">...And then reconstructing the simulated FC</font></div></p>
  304. # %%
  305. def eval_fc(tsr):
  306. input_shape = tsr.data.shape
  307. result_shape = (input_shape[2], input_shape[2], input_shape[1], input_shape[3])
  308. result = np.zeros(result_shape)
  310. for mode in range(result_shape[3]):
  311. for var in range(result_shape[2]):
  312. data = tsr.data[:,var,:, mode].squeeze()
  313. result[:, :, var, mode] = np.corrcoef(data.T)
  315. corr_coeff = graph.CorrelationCoefficients(source=tsr, array_data=result)
  316. return corr_coeff
  318. # %%
  319. # Discarded first 10 volumes
  320. data = np.array(bold_data[10:int(360000/720)])
  321. # Build a TimeSeries Dataype
  322. tsr = TimeSeriesRegion(connectivity=con,
  323. data=data,
  324. sample_period=sim.monitors[1].period)
  325. tsr.configure()
  326. # Compute FC
  327. corrcoeff_data = eval_fc(tsr)
  328. FC = corrcoeff_data.array_data[..., 0, 0]
  330. empFC_wb = np.triu(con_FC, 1) #triangle matrix
  331. simFC_wb = np.triu(FC, 1)
  332. pcc_wb = np.corrcoef(empFC_wb.ravel(), simFC_wb.ravel())[0, 1]
  333. print ('Similarity between empFC and simFC in the whole-brain network: %10.4f' % pcc_wb)
  335. # Visualize and compare the simulated FC and the empirical FC
  336. fig=plt.figure(figsize=(17,7))
  337. # whole-brain network: FC_wb
  338. plt.subplot(131)
  339. p1=plt.imshow(FC, interpolation='nearest', aspect='equal', cmap='jet')
  340. plt.title('Whole-brain simFC', fontsize=14)
  341. cb1=plt.colorbar(p1, shrink=0.325, ticks=[-0.2, 0.0, 0.2, 0.4, 0.6, 0.8, 1.0])
  343. plt.subplot(132)
  344. p1=plt.imshow(con_FC, interpolation='nearest', aspect='equal', cmap='jet')
  345. plt.title('Whole-brain empFC', fontsize=14)
  346. cb1=plt.colorbar(p1, shrink=0.325, ticks=[-0.2, 0.0, 0.2, 0.4, 0.6, 0.8, 1.0])
  348. # %% [markdown]
  349. # <h1 align="center"><font size="6"face="arial" color="#BF026D">Optimize the model!</font></h1>
  350. #
  351. # <p><div style="text-align: justify"><font size="4.5" face="time roman">The simulation is ended but the model wasn't tune and optimize. Here we add a function for the optimization steps. </font></div></p>
  353. # %%
  354. def run_rww_sim_pcc(con, G, regime, D, dt, TR, simlen):
  355. # Initialise Simulator.
  356. sim = simulator.Simulator(
  357. model=models.ReducedWongWang(**regime),
  358. connectivity=con,
  359. coupling=coupling.Scaling(a=np.array(G)),
  360. conduction_speed=float(con.speed),
  361. integrator=integrators.HeunStochastic(dt=dt, noise=noise.Additive(nsig=np.array([(D**2)/2]))),
  362. monitors=(monitors.Bold(period=TR),)
  363. )
  364. sim.initial_conditions = (0.001)*np.ones((1, 1, con.weights.shape[0], 1))
  365. sim.configure()
  366. # Lunch simulation
  367. (t, B), = sim.run(simulation_length=simlen)
  369. # Remove transcient time
  370. B = B[10:int(simlen/TR), :, :, :]
  372. # Built a TiemSeries Datatype
  373. tsr = TimeSeriesRegion(connectivity=con,
  374. data=B,
  375. sample_period=sim.monitors[0].period)
  376. tsr.configure()
  378. # Compute FC
  379. corrcoeff_data = eval_fc(tsr)
  380. FC = corrcoeff_data.array_data[..., 0, 0]
  382. # Take triangular upper part of FC
  383. FC_triu = np.triu(FC, 1)
  385. # Compute Pearson correlation
  386. pcc_FC = np.corrcoef(np.triu(con_FC, 1).ravel(), FC_triu.ravel())[0, 1]
  387. pcc_SC = np.corrcoef(np.triu(con.weights, 1).ravel(), FC_triu.ravel())[0, 1]
  389. return pcc_FC, pcc_SC
  391. # %%
  392. #IT TAKES ABOUT 15-20 MINUTES
  394. tic = tm.time()
  396. # Run G sweep
  397. Gs = np.arange(5, 30, 0.5)
  398. regime = {'a': np.array(270.), 'b':np.array(108.), 'd':np.array(0.154),
  399. 'gamma':np.array(0.641/1000), 'w':np.array(1.), 'I_o':np.array(0.3)}
  401. pcc_FC = np.zeros((len(Gs)))
  402. pcc_SC = np.zeros((len(Gs)))
  403. print('simulation start.')
  404. for iG, G in enumerate(Gs):
  405. print("simulation : G %1.1f" % G)
  406. pcc_FC[iG], pcc_SC[iG] = run_rww_sim_pcc(con, Gs[iG], regime, 0.001, 1, 720, 60000)
  409. 'simulation required %0.3f seconds.' % (tm.time()-tic)
  411. # %%
  412. #DON'T RUN THIS CELL IF YOU DIDN'T RUN THE CELL ABOVE
  413. # Visualize
  414. plt.figure(figsize=(10,8))
  416. # FC and SC
  417. plt.plot(Gs, pcc_FC, '-*', label='FC - FC')
  418. plt.plot(Gs, pcc_SC, '-*g', label='SC - FC')
  420. plt.xlabel('$G_{coupl}$', fontsize=20);
  421. plt.title('Correlation Diagram', fontsize=20)
  423. plt.legend(bbox_to_anchor=(1.05, 1), loc=2, borderaxespad=0.)
  425. plt.show()
  426. Gopt = Gs[np.argmax(pcc_FC)]
  427. print ('The optimal value for the global coupling is: %5.1f' % Gopt)
  429. # %%
  430. # Initialise a Coupling function at the optimal value of G
  431. G = np.array(26)
  432. con_coupling = coupling.Scaling(a=G)
  434. # %%
  435. #IT IS NOT NEEDED SINCE WE HAVE ALREADY INITIALISED IT
  436. # Initialise an Integrator scheme.
  437. dt = 0.5 #integration steps [ms]
  439. D = 0.001 #standard deviation of the noise
  440. heunstoc=integrators.HeunStochastic(dt=dt, noise=noise.Additive(nsig=np.array([(D**2)/2])))
  442. # %%
  443. #IT IS NOT NEEDED SINCE WE HAVE ALREADY INITIALISED IT
  444. # Initialise some Monitors with period in physical time.
  445. mon_tavg = monitors.TemporalAverage(period=1.) #1000 Hz
  446. TR = 720
  447. mon_bold = monitors.Bold(period=TR)
  449. #Bundle them
  450. what_to_watch = (mon_tavg,mon_bold)
  452. # %%
  453. # Initialise the Simulator.
  454. regime={'w':np.array(1.), 'I_o':np.array(0.3)}
  455. sim = simulator.Simulator(
  456. model=models.ReducedWongWang(**regime),
  457. connectivity=con,
  458. coupling=con_coupling,
  459. conduction_speed=float(con.speed),
  460. integrator=heunstoc,
  461. monitors=what_to_watch)
  462. sim.initial_conditions = 0.001*np.ones((1, 1, con.weights.shape[0], 1))
  463. sim.configure()
  465. # %%
  466. # Perform the simulation.
  467. tic = tm.time()
  469. tavg_data, tavg_time = [], []
  470. bold_data, bold_time = [], []
  472. for tavg, bold in sim(simulation_length=360000.):
  474. if not tavg is None:
  475. tavg_time.append(tavg[0])
  476. tavg_data.append(tavg[1])
  478. if not bold is None:
  479. bold_time.append(bold[0])
  480. bold_data.append(bold[1])
  483. 'simulation required %0.3f seconds.' % (tm.time()-tic)
  485. # %% [markdown]
  486. # <p><div style="text-align: justify"><font size="4.5" face="time roman">Visualize the simulation</font></div></p>
  488. # %%
  489. # Normalize the time series
  490. tavg_data /= (np.max(tavg_data, 0) - np.min(tavg_data, 0))
  492. # Make the lists numpy.arrays for easier use.
  493. TAVG = np.squeeze(np.array(tavg_data))
  495. # Plot the temporally averaged time series
  496. fig2 = plt.figure(figsize=(12,8))
  497. plt.subplot(3,1,1)
  498. plt.plot(tavg_time[:], TAVG[:, 0], 'r')
  499. plt.ylabel(con.region_labels[0],fontsize=13)
  500. plt.subplot(3,1,2)
  501. plt.plot(tavg_time[:], TAVG[:, 1], 'c')
  502. plt.ylabel(con.region_labels[1],fontsize=13)
  503. plt.subplot(3,1,3)
  504. plt.plot(tavg_time[:], TAVG[:, 2], 'g')
  505. plt.xlabel('Time [ms]', fontsize=13)
  506. plt.ylabel(con.region_labels[2],fontsize=13)
  508. plt.show()
  510. # %%
  511. # Normalize the time series
  512. tavg_data /= (np.max(tavg_data, 0) - np.min(tavg_data, 0))
  514. # Make the lists numpy.arrays for easier use.
  515. TAVG = np.squeeze(np.array(tavg_data))
  517. # Plot the temporally averaged time series
  518. fig2 = plt.figure(figsize=(12,8))
  519. plt.subplot(3,1,1)
  520. plt.plot(tavg_time[10:int(360000/720)], TAVG[10:int(360000/720), 0], 'r')
  521. plt.ylabel(con.region_labels[0],fontsize=13)
  522. plt.subplot(3,1,2)
  523. plt.plot(tavg_time[10:int(360000/720)], TAVG[10:int(360000/720), 1], 'c')
  524. plt.ylabel(con.region_labels[1],fontsize=13)
  525. plt.subplot(3,1,3)
  526. plt.plot(tavg_time[10:int(360000/720)], TAVG[10:int(360000/720), 2], 'g')
  527. plt.xlabel('Time [ms]', fontsize=13)
  528. plt.ylabel(con.region_labels[2],fontsize=13)
  530. plt.show()
  532. # %% [markdown]
  533. # <p><div style="text-align: justify"><font size="4.5" face="time roman">...And then reconstructing the simulated FC</font></div></p>
  535. # %%
  536. # Discarded first 10 volumes
  537. data = np.array(bold_data[10:int(360000/720)])
  538. # Build a TimeSeries Dataype
  539. tsr = TimeSeriesRegion(connectivity=con,
  540. data=data,
  541. sample_period=sim.monitors[1].period)
  542. tsr.configure()
  543. # Compute FC
  544. corrcoeff_data = eval_fc(tsr)
  545. FC = corrcoeff_data.array_data[..., 0, 0]
  547. empFC_wb = np.triu(con_FC, 1) #triangle matrix
  548. simFC_wb = np.triu(FC, 1)
  549. pcc_wb = np.corrcoef(empFC_wb.ravel(), simFC_wb.ravel())[0, 1]
  550. print ('Similarity between empFC and simFC in the whole-brain network: %10.4f' % pcc_wb)
  552. # Visualize and compare the simulated FC and the empirical FC
  553. fig=plt.figure(figsize=(17,7))
  554. # whole-brain network: FC_wb
  555. plt.subplot(131)
  556. p1=plt.imshow(FC, interpolation='nearest', aspect='equal', cmap='jet')
  557. plt.title('Whole-brain simFC', fontsize=14)
  558. cb1=plt.colorbar(p1, shrink=0.325, ticks=[-0.2, 0.0, 0.2, 0.4, 0.6, 0.8, 1.0])
  560. plt.subplot(132)
  561. p1=plt.imshow(con_FC, interpolation='nearest', aspect='equal', cmap='jet')
  562. plt.title('Whole-brain empFC', fontsize=14)
  563. cb1=plt.colorbar(p1, shrink=0.325, ticks=[-0.2, 0.0, 0.2, 0.4, 0.6, 0.8, 1.0])
  565. # %% [markdown]
  566. # <h1><font size="6" face="arial" color="#BF026D">Now, it's up to you!!</font></h1>
  567. #
  568. # ***
  569. #
  570. # <p><div style="text-align: justify"><font size="4.5" face="time roman">These results are starting point for modelling resting state, from which we can base our next simulations.
  571. #
  572. # You can choose one of the following further analyses:
  573. # <br>
  574. #
  575. # * Change the integration step of the Heun Stocastic integrator. Try with 1. What does it change?
  576. # * <b>Generate optimal whole-brain dynamics in a pathological subject</b>, like an Alzheimer's disease patient. To do this you can use data from files ending with _AD. **(TR = 3010 ms, simlen = 360000 ms)**
  577. # * <b>Simulate optimal brain dynamics in a local circuit </b> instead of whole-brain network. To do this you have to define a network that contains only few specific regions that are known to be functinally related one another. For example, the first 93 nodes are belonging to the cerebral connectivity. <i>Tip: for SC you have to set con.weights con.tract_lengths con.centres con.region_labels </i>
  578. #
  579. # </font></div></p>

TVB_rww_notebook.ipynb at commit 0aa8af8, no license · at the source

Overview

Authors: Anita Monteverdi1, Matteo Cotta Ramusino2, Francesca Conca3, Sofia Manzon4, Alberto Redolfi5, Eleonora Lupi4, Marialaura De Grazia4, Roberta Maria Lorenzi4, Marta Gaviraghi4, Laura Mazzocchi6, Lisa M. Farina6, Alfredo Costa2,4, Anna Pichiecchio4,6, Stefano F. Cappa3,7, Claudia A. M. Gandini Wheeler-Kingshott1,4,8, Fulvia Palesi1,4, Egidio D’Angelo1,4
ORCID iDs: Anita Monteverdi, Eleonora Lupi, Alfredo Costa, Claudia A. M. Gandini Wheeler-Kingshott
  1. Digital Neuroscience Centre, IRCCS Mondino Foundation,Pavia, Italy
  2. Unit of Behavioral Neurology, IRCCS Mondino Foundation,Pavia, Italy
  3. Institute for Advanced Studies (IUSS),Pavia, Italy
  4. Department of Brain and Behavioral Sciences, University of Pavia,Pavia, Italy
  5. Laboratory of Neuroinformatics, IRCCS Istituto Centro San Giovanni di Dio Fatebenefratelli,Brescia, Italy
  6. Advanced Imaging and Artificial Intelligence Center, IRCCS Mondino Foundation,Pavia, Italy
  7. IRCCS Istituto Auxologico Italiano,Milan, Italy
  8. Department of Neuroinflammation, Queen Square Multiple Sclerosis Centre, NMR Research Unit, UCL Queen Square Institute of Neurology,London, UK
Institutions: Fondazione Istituto Neurologico Nazionale Casimiro Mondino (Italy); Istituto Universitario di Studi Superiori di Pavia (Italy); University of Pavia (Italy); Centro San Giovanni di Dio Fatebenefratelli (Italy); IRCCS Istituto Auxologico Italiano (Italy); UCL Queen Square Institute of Neurology (United Kingdom)
Journal: Scientific reports, volume 16, issue 1, article 28541
Dates: received 20 June 2025; accepted 31 May 2026; published online 8 June 2026
Type: Research article · Language: English
License: CC BY-NC-ND
Identifiers: DOI 10.1038/s41598-026-56387-8 · PMID 42260290 · PMCID PMC13572441 · OpenAlex W4409722271
Open access: gold, a free copy (OpenAlex)
Preprint: doi:10.2139/ssrn.5227250
Status: code verified
Categories: structural MRI / diffusion (modality), human (organism), Alzheimer's / dementia (population), clinical / translational (subfield)
Methods: Spectral & time-frequency, Statistics, Smoothing, state filtering, decompositions, Machine learning, Preprocessing, Connectivity, Graphs, fMRI & imaging
Keywords: Excitatory/inhibitory balance, Mild cognitive impairment, Alzheimer’s disease, Resting-state networks, Virtual brain modelling, Graph theory, Computational models, Neurological disorders
MeSH: Alzheimer Disease*, Biomarkers*, Brain*, Cognitive Dysfunction*, Dementia*, Aged, Amyloid beta-Peptides, Female, Humans, Magnetic Resonance Imaging, Male, Neuropsychological Tests (* major topic)
Topic: Functional Brain Connectivity Studies (Cognitive Neuroscience, Neuroscience), according to OpenAlex
Funding: Ministero della Salute (Ministry of Health, Italy)
Citations: not cited yet (Europe PMC); 85 references in the paper

Abstract

The abstract is not reproduced here: the paper's license (CC BY-NC-ND) does not allow it. Read it in the paper, at the publisher or on Europe PMC.

Repositories

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Anita-93/TVB_rww_tutorial

License: none: the authors keep all their rights
State: the link answers, verified on 27 September 2026
Evidence: files inventoried
Commit: 0aa8af8fa4f1685327f27e97f081a9e3b11e3088, 23 April 2026
Languages: Jupyter (1)
Size: 2 files, 1 script
Software Heritage: not archived
Found in: “Data availability”
Holds: README, 1 notebook
Not found: license file, CITATION.cff, environment file, tests, continuous integration, documentation
Tools: Matplotlib (1 file), NumPy (1 file), The Virtual Brain (1 file)
Availability: 1 check, the latest on 27 September 2026: the link answers
  • 27 September 2026: the link answers
2 files
At the source: github.com/Anita-93/TVB_rww_tutorial

wiki.ebrains.eu/bin/view

License: none: the authors keep all their rights
State: the link answers, verified on 27 September 2026
Evidence: the link answers
Software Heritage: not checked
Found in: “Data availability”
Not found: README, license file, CITATION.cff, environment file, tests, continuous integration, documentation
Availability: 1 check, the latest on 27 September 2026: the link answers (HTTP 200)
  • 27 September 2026: the link answers (HTTP 200)
At the source: wiki.ebrains.eu/bin/view/Collabs/tvb-ww-tutorial/

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

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Read it in the paper: doi.org/10.1038/s41598-026-56387-8.

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Version 1, 27 September 2026: the first record

Recorded: type, language, journal, volume, issue, pages, dates, 17 authors, 8 keywords, 12 MeSH terms, 1 funder, 81 references.

Cite

This paper

Monteverdi, A., Cotta Ramusino, M., Conca, F., Manzon, S., Redolfi, A., Lupi, E., De Grazia, M., Lorenzi, R. M., Gaviraghi, M., Mazzocchi, L., Farina, L. M., Costa, A., Pichiecchio, A., Cappa, S. F., Gandini Wheeler-Kingshott, C. A. M., Palesi, F., & D’Angelo, E. (2026). Alterations in topological and dynamical parameters correlate with disease biomarkers and neuropsychological scores in prodromic stages of dementia. Scientific reports, 16(1), 28541. https://doi.org/10.1038/s41598-026-56387-8

BibTeX

@article{monteverdi2026alterations,
author = {Monteverdi, Anita and Cotta Ramusino, Matteo and Conca, Francesca and Manzon, Sofia and Redolfi, Alberto and Lupi, Eleonora and De Grazia, Marialaura and Lorenzi, Roberta Maria and Gaviraghi, Marta and Mazzocchi, Laura and Farina, Lisa M. and Costa, Alfredo and Pichiecchio, Anna and Cappa, Stefano F. and Gandini Wheeler-Kingshott, Claudia A. M. and Palesi, Fulvia and D’Angelo, Egidio},
title = {{Alterations in topological and dynamical parameters correlate with disease biomarkers and neuropsychological scores in prodromic stages of dementia}},
journal = {Scientific reports},
year = {2026},
month = jun,
volume = {16},
number = {1},
pages = {28541},
publisher = {Nature Publishing Group},
issn = {2045-2322},
doi = {10.1038/s41598-026-56387-8},
url = {https://doi.org/10.1038/s41598-026-56387-8},
pmid = {42260290},
pmcid = {PMC13572441}
}

RIS

TY - JOUR
AU - Monteverdi, Anita
AU - Cotta Ramusino, Matteo
AU - Conca, Francesca
AU - Manzon, Sofia
AU - Redolfi, Alberto
AU - Lupi, Eleonora
AU - De Grazia, Marialaura
AU - Lorenzi, Roberta Maria
AU - Gaviraghi, Marta
AU - Mazzocchi, Laura
AU - Farina, Lisa M.
AU - Costa, Alfredo
AU - Pichiecchio, Anna
AU - Cappa, Stefano F.
AU - Gandini Wheeler-Kingshott, Claudia A. M.
AU - Palesi, Fulvia
AU - D’Angelo, Egidio
TI - Alterations in topological and dynamical parameters correlate with disease biomarkers and neuropsychological scores in prodromic stages of dementia
T2 - Scientific reports
J2 - Sci Rep
PY - 2026
DA - 2026/06/08
VL - 16
IS - 1
SP - 28541
SN - 2045-2322
PB - Nature Publishing Group
DO - 10.1038/s41598-026-56387-8
UR - https://doi.org/10.1038/s41598-026-56387-8
LA - en
ER -

CSL-JSON

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"id": "10.1038/s41598-026-56387-8",
"type": "article-journal",
"title": "Alterations in topological and dynamical parameters correlate with disease biomarkers and neuropsychological scores in prodromic stages of dementia",
"container-title": "Scientific reports",
"author": [
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"family": "Monteverdi",
"given": "Anita"
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"given": "Matteo"
},
{
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"given": "Francesca"
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{
"family": "Manzon",
"given": "Sofia"
},
{
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{
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{
"family": "De Grazia",
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{
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{
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"family": "Farina",
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"given": "Fulvia"
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{
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"given": "Egidio"
}
],
"container-title-short": "Sci Rep",
"volume": "16",
"issue": "1",
"page": "28541",
"DOI": "10.1038/s41598-026-56387-8",
"PMID": "42260290",
"PMCID": "PMC13572441",
"ISSN": "2045-2322",
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