.. DO NOT EDIT. .. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY. .. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE: .. "auto_tutorials/tutorial_02_model_comparison_free_energy.py" .. LINE NUMBERS ARE GIVEN BELOW. .. only:: html .. note:: :class: sphx-glr-download-link-note :ref:`Go to the end ` to download the full example code .. rst-class:: sphx-glr-example-title .. _sphx_glr_auto_tutorials_tutorial_02_model_comparison_free_energy.py: Laminar model comparison using free energy ========================================== This tutorial demonstrates how to perform laminar inference using model comparison based on free energy as a metric of model fit, described in [Bonaiuto et al., 2018, Non-invasive laminar inference with MEG: Comparison of methods and source inversion algorithms](https://doi.org/10.1016/j.neuroimage.2017.11.068). A 20Hz oscillation is simulated at a particular cortical location in various layers. Source reconstruction is performed using the Empirical Bayesian Beamformer on the simulated sensor data using forward models based on different layer meshes. These models are then compared using free energy. .. GENERATED FROM PYTHON SOURCE LINES 17-21 Setting up the simulations -------------------------- Simulations are based on an existing dataset, which is used to define the sampling rate, number of trials, duration of each trial, and the channel layout. .. GENERATED FROM PYTHON SOURCE LINES 21-55 .. code-block:: default import os import shutil import numpy as np import nibabel as nib import matplotlib.pyplot as plt import tempfile from lameg.invert import coregister, invert_ebb from lameg.simulate import run_current_density_simulation from lameg.laminar import model_comparison from lameg.util import get_surface_names, load_meg_sensor_data, get_fiducial_coords from lameg.viz import show_surface import spm_standalone # Subject information for data to base the simulations on subj_id = 'sub-104' ses_id = 'ses-01' # Fiducial coil coordinates nas, lpa, rpa = get_fiducial_coords(subj_id, '../test_data/participants.tsv') # Data file to base simulations on data_file = os.path.join( '../test_data', subj_id, 'meg', ses_id, 'spm/spm-converted_autoreject-sub-104-ses-01-001-btn_trial-epo.mat' ) spm = spm_standalone.initialize() .. GENERATED FROM PYTHON SOURCE LINES 56-57 For source reconstructions, we need an MRI and a surface mesh. The simulations will be based on a forward model using the multilayer mesh, and the model comparison will use each layer mesh .. GENERATED FROM PYTHON SOURCE LINES 57-77 .. code-block:: default # Native space MRI to use for coregistration mri_fname = os.path.join('../test_data', subj_id, 'mri', 's2023-02-28_13-33-133958-00001-00224-1.nii' ) # Mesh to use for forward model in the simulations multilayer_mesh_fname = os.path.join('../test_data', subj_id, 'surf', 'multilayer.11.ds.link_vector.fixed.gii') # Load multilayer mesh and compute the number of vertices per layer mesh = nib.load(multilayer_mesh_fname) n_layers = 11 verts_per_surf = int(mesh.darrays[0].data.shape[0]/n_layers) # Get name of each mesh that makes up the layers of the multilayer mesh - these will be used for the source # reconstruction layer_fnames = get_surface_names( n_layers, os.path.join('../test_data', subj_id, 'surf'), 'link_vector.fixed' ) .. GENERATED FROM PYTHON SOURCE LINES 78-79 We're going to copy the data file to a temporary directory and direct all output there. .. GENERATED FROM PYTHON SOURCE LINES 79-100 .. code-block:: default # Extract base name and path of data file data_path, data_file_name = os.path.split(data_file) data_base = os.path.splitext(data_file_name)[0] # Where to put simulated data tmp_dir = tempfile.mkdtemp() # Copy data files to tmp directory shutil.copy( os.path.join(data_path, f'{data_base}.mat'), os.path.join(tmp_dir, f'{data_base}.mat') ) shutil.copy( os.path.join(data_path, f'{data_base}.dat'), os.path.join(tmp_dir, f'{data_base}.dat') ) # Construct base file name for simulations base_fname = os.path.join(tmp_dir, f'{data_base}.mat') .. GENERATED FROM PYTHON SOURCE LINES 101-102 Invert the subject's data using the multilayer mesh. This step only has to be done once - this is just to compute the forward model that will be used in the simulations .. GENERATED FROM PYTHON SOURCE LINES 102-129 .. code-block:: default # Patch size to use for inversion (in this case it matches the simulated patch size) patch_size = 5 # Number of temporal modes to use for EBB inversion n_temp_modes = 4 # Coregister data to multilayer mesh coregister( nas, lpa, rpa, mri_fname, multilayer_mesh_fname, base_fname, spm_instance=spm ) # Run inversion [_,_] = invert_ebb( multilayer_mesh_fname, base_fname, n_layers, patch_size=patch_size, n_temp_modes=n_temp_modes, spm_instance=spm ) .. GENERATED FROM PYTHON SOURCE LINES 130-133 Simulating a signal on the pial surface --------------------------------------- We're going to simulate 1s of a 20Hz sine wave with a dipole moment of 10nAm .. GENERATED FROM PYTHON SOURCE LINES 133-149 .. code-block:: default # Frequency of simulated sinusoid (Hz) freq = 20 # Strength of simulated activity (nAm) dipole_moment = 10 # Sampling rate (must match the data file) s_rate = 600 # Generate 1s of a sine wave at a sampling rate of 600Hz (to match the data file) time = np.linspace(0,1,s_rate+1) sim_signal = np.sin(time*freq*2*np.pi).reshape(1,-1) plt.plot(time,dipole_moment*sim_signal[0,:]) plt.xlabel('Time (s)') plt.ylabel('Amplitude (nAm)') .. GENERATED FROM PYTHON SOURCE LINES 150-153 .. image:: ../_static/tutorial_02_sim_signal.png :width: 800 :alt: .. GENERATED FROM PYTHON SOURCE LINES 155-156 We need to pick a location (mesh vertex) to simulate at .. GENERATED FROM PYTHON SOURCE LINES 156-176 .. code-block:: default # Vertex to simulate activity at sim_vertex=24585 pial_ds_mesh_fname = os.path.join('../test_data', subj_id, 'surf', 'pial.ds.link_vector.fixed.gii') pial_ds_mesh = nib.load(pial_ds_mesh_fname) pial_coord = pial_ds_mesh.darrays[0].data[sim_vertex,:] pial_mesh_fname = os.path.join('../test_data', subj_id, 'surf', 'pial.gii') pial_mesh = nib.load(pial_mesh_fname) cam_view = [152, 28, 15, 3.5, 26, 38.5, 0, 0, 1] plot = show_surface( pial_mesh, opacity=1, coords=pial_coord, coord_size=2, camera_view=cam_view ) .. GENERATED FROM PYTHON SOURCE LINES 177-180 .. image:: ../_static/tutorial_02_sim_location.png :width: 800 :alt: .. GENERATED FROM PYTHON SOURCE LINES 182-183 We'll simulate a 5mm patch of activity with -5 dB SNR at the sensor level. The desired level of SNR is achieved by adding white noise to the projected sensor signals .. GENERATED FROM PYTHON SOURCE LINES 183-212 .. code-block:: default # Simulate at a vertex on the pial surface pial_vertex = sim_vertex prefix = f'sim_{sim_vertex}_pial_' # Size of simulated patch of activity (mm) sim_patch_size = 5 # SNR of simulated data (dB) SNR = -5 # Generate simulated data pial_sim_fname = run_current_density_simulation( base_fname, prefix, pial_vertex, sim_signal, dipole_moment, sim_patch_size, SNR, spm_instance=spm ) # Load simulated sensor data and plot pial_sim_sensor_data, time, ch_names = load_meg_sensor_data(pial_sim_fname) _ = plt.plot(time, np.mean(pial_sim_sensor_data,axis=-1).T) plt.xlabel('Time (s)') plt.ylabel('Amplitude (fT)') plt.ylim([-225, 225]) .. GENERATED FROM PYTHON SOURCE LINES 213-216 .. image:: ../_static/tutorial_02_pial_sim_sensor_signal.png :width: 800 :alt: .. GENERATED FROM PYTHON SOURCE LINES 218-221 Model comparison (pial - white matter) -------------------------------------- Now we can run model comparison between source models based on the pial and white matter surfaces using free energy. Specifically, we'll look at the difference in free energy between the two models (pial - white matter). This should be positive (more model evidence for the pial surface model) because we simulated activity on the pial surface .. GENERATED FROM PYTHON SOURCE LINES 221-241 .. code-block:: default # Run model comparison between the first layer (pial) and the last layer (white matter) [F,_] = model_comparison( nas, lpa, rpa, mri_fname, [layer_fnames[0], layer_fnames[-1]], pial_sim_fname, spm_instance=spm, invert_kwargs={ 'patch_size': patch_size, 'n_temp_modes': n_temp_modes } ) # The difference in free energy is an approximation of the Bayes factor between the two models # This value should be positive (more model evidence for the pial layer model) F[0]-F[1] .. GENERATED FROM PYTHON SOURCE LINES 242-245 White matter surface simulation with pial - white matter model comparison ------------------------------------------------------------------------- Let's simulate the same pattern of activity, in the same location, but on the white matter surface. This time, model comparison should yield greater model evidence for the white matter surface, and therefore the difference in free energy (pial - white matter) should be negative. .. GENERATED FROM PYTHON SOURCE LINES 245-280 .. code-block:: default # Simulate at the corresponding vertex on the white matter surface white_vertex = (n_layers-1)*verts_per_surf+sim_vertex prefix = f'sim_{sim_vertex}_white_' # Generate simulated data white_sim_fname = run_current_density_simulation( base_fname, prefix, white_vertex, sim_signal, dipole_moment, sim_patch_size, SNR, spm_instance=spm ) # Run model comparison between the first layer (pial) and the last layer (white matter) [F,_] = model_comparison( nas, lpa, rpa, mri_fname, [layer_fnames[0], layer_fnames[-1]], white_sim_fname, spm_instance=spm, invert_kwargs={ 'patch_size': patch_size, 'n_temp_modes': n_temp_modes, } ) # The difference in free energy is an approximation of the Bayes factor between the two models # This value should be negative (more model evidence for the white matter layer model) F[0]-F[1] .. GENERATED FROM PYTHON SOURCE LINES 281-282 Here's the sensor signals from the simulation of activity on the white matter surface. It's very similar to the sensor signals from the pial surface simulation .. GENERATED FROM PYTHON SOURCE LINES 282-290 .. code-block:: default # Load simulated sensor data and plot white_sim_sensor_data, time, ch_names = load_meg_sensor_data(white_sim_fname) _ = plt.plot(time, np.mean(white_sim_sensor_data,axis=-1).T) plt.xlabel('Time (s)') plt.ylabel('Amplitude (fT)') plt.ylim([-225, 225]) .. GENERATED FROM PYTHON SOURCE LINES 291-294 .. image:: ../_static/tutorial_02_white_sim_sensor_signal.png :width: 800 :alt: .. GENERATED FROM PYTHON SOURCE LINES 296-297 The difference between the two simulated sensor signals is quite small .. GENERATED FROM PYTHON SOURCE LINES 297-304 .. code-block:: default sensor_diff = pial_sim_sensor_data - white_sim_sensor_data _ = plt.plot(time, np.mean(sensor_diff,axis=-1).T) plt.xlabel('Time (s)') plt.ylabel('Amplitude (fT)') plt.ylim([-225, 225]) .. GENERATED FROM PYTHON SOURCE LINES 305-308 .. image:: ../_static/tutorial_02_pial_white_sim_sensor_difference.png :width: 800 :alt: .. GENERATED FROM PYTHON SOURCE LINES 310-313 Simulation in each layer with model comparison across layers ------------------------------------------------------------ That was model comparison with two candidate models: one based on the white matter surface, and one on the pial. Let's now simulate on each layer, and for each simulation, run model comparison across all layers. We'll turn off SPM visualization here. .. GENERATED FROM PYTHON SOURCE LINES 313-351 .. code-block:: default # Now simulate at the corresponding vertex on each layer, and for each simulation, run model comparison across # all layers all_layerF = [] for l in range(n_layers): print(f'Simulating in layer {l}') l_vertex = l*verts_per_surf+sim_vertex prefix = f'sim_{sim_vertex}_{l}_' l_sim_fname = run_current_density_simulation( base_fname, prefix, l_vertex, sim_signal, dipole_moment, sim_patch_size, SNR, spm_instance=spm ) [layerF,_] = model_comparison( nas, lpa, rpa, mri_fname, layer_fnames, l_sim_fname, viz=False, spm_instance=spm, invert_kwargs={ 'patch_size': patch_size, 'n_temp_modes': n_temp_modes } ) all_layerF.append(layerF) all_layerF = np.array(all_layerF) .. GENERATED FROM PYTHON SOURCE LINES 352-353 For each simulation, we can plot the free energy for all models relative to the worst model. The layer model with the highest free energy should correspond to the layer that the activity was simulated in. .. GENERATED FROM PYTHON SOURCE LINES 353-382 .. code-block:: default col_r = plt.cm.cool(np.linspace(0,1, num=n_layers)) plt.figure(figsize=(10,4)) # For each simulation, plot the free energy of each layer model relative to that of the worst # model for that simulation plt.subplot(1,2,1) for l in range(n_layers): layerF = all_layerF[l,:] plt.plot(layerF-np.min(layerF), label=f'{l}', color=col_r[l,:]) plt.legend() plt.xlabel('Eval layer') plt.ylabel(r'$\Delta$F') # For each simulation, find which layer model had the greatest free energy plt.subplot(1,2,2) peaks = [] for l in range(n_layers): layerF = all_layerF[l,:] pk = np.argmax(layerF) peaks.append(pk) plt.plot(peaks) plt.xlim([-0.5,10.5]) plt.ylim([-0.5,10.5]) plt.plot([0,10],[0,10],'k--') plt.xlabel('Sim layer') plt.ylabel(r'Peak $\Delta$F') plt.tight_layout() .. GENERATED FROM PYTHON SOURCE LINES 383-386 .. image:: ../_static/tutorial_02_results.png :width: 800 :alt: .. GENERATED FROM PYTHON SOURCE LINES 386-407 .. code-block:: default # Normalization step norm_layerF = np.zeros(all_layerF.shape) for l in range(n_layers): norm_layerF[l,:] = all_layerF[l,:] - np.min(all_layerF[l,:]) # Transpose for visualization im=plt.imshow(norm_layerF.T,cmap='Spectral_r') # Find the indices of the max value in each column max_indices = np.argmax(norm_layerF, axis=1) # Plot an 'X' at the center of the square for each column's maximum for idx, max_idx in enumerate(max_indices): plt.text(idx, max_idx, 'X', fontsize=12, ha='center', va='center', color='black', weight='bold') plt.xlabel('Simulated layer', fontsize=14) plt.ylabel('Evaluated layer', fontsize=14) cb=plt.colorbar(im) cb.set_label(r'$\Delta F$', fontsize=14) .. GENERATED FROM PYTHON SOURCE LINES 408-411 .. image:: ../_static/tutorial_02_results_matrix.png :width: 800 :alt: .. GENERATED FROM PYTHON SOURCE LINES 413-420 .. code-block:: default spm.terminate() # Delete simulation files shutil.rmtree(tmp_dir) .. rst-class:: sphx-glr-timing **Total running time of the script:** (0 minutes 0.000 seconds) .. _sphx_glr_download_auto_tutorials_tutorial_02_model_comparison_free_energy.py: .. only:: html .. container:: sphx-glr-footer sphx-glr-footer-example .. container:: sphx-glr-download sphx-glr-download-python :download:`Download Python source code: tutorial_02_model_comparison_free_energy.py ` .. container:: sphx-glr-download sphx-glr-download-jupyter :download:`Download Jupyter notebook: tutorial_02_model_comparison_free_energy.ipynb ` .. only:: html .. rst-class:: sphx-glr-signature `Gallery generated by Sphinx-Gallery `_