analysis_dynamic

Functional dynamic connectivity analysis

Table of Contents

1. Hidden Markov Model
2. Sliding Window

Hidden Markov Model

• Original paper:

  Vidaurre et al., "Brain network dynamics are hierarchically organized in time", PNAS, 2017. (https://www.pnas.org/content/114/48/12827)
  Full information at: https://github.com/OHBA-analysis/HMM-MAR/wiki

• Useful papers:

  (1) Vidaurre et al., "Discovering dynamic brain networks from big data in rest and task", NeuroImage, 2018. (https://www.sciencedirect.com/science/article/pii/S1053811917305487)

• Usage
  • Setup
    • Download HMM-MAR toolbox (https://github.com/OHBA-analysis/HMM-MAR)
    • Unzip the downloaded file and add the path to MATLAB: addpath(genpath('~/HMM-MAR'))
  • Train HMM
    • [hmm,Gamma,Xi,vpath,GammaInit,residuals,fehist] = hmmmar(data,T,options);
    • Inputs

      data: Time series in cell format (each cell contains: time point x ROIs)
      T: Length of each time point in cell format (each cell contains: # of time points)
      options: Hyperparameters for HMM
      --My options--
      options = struct();
      options.K = NumStates; % Maximum # of HMM states, which can be estimated via Elbow method or other approaches
      options.Fs = 1/TR; % Sampling frequency. Typically 1/repetion time
      options.order = 0; % Maximum order of the MAR model (0: HMM with Gaussian observation)
      options.covtype = 'full'; % Choice of the covariance matrix
      options.zeromean = 0; % if 1, the mean of the time series will not be used to drive the states
      options.standardise = 0; % Standardize with mean 0, SD 1 (0 if we already have standardized data, 1 if not)
      options.cyc = 500; % Maximum # of variational inference cycles
      options.tol = 1e-7; % Minimum relative decrement of free energy for the algorithm to stop
      options.inittype = 'HMM-MAR'; % 'hmmmar' for HMM-MAR initialization or 'random' for random initialization
      options.initrep = 3; % # of repetitions of the initialization algorithm
      options.initcyc = 10; % Maximum # of optimization cycles in the initialization algoritm, per repetition
      options.verbose = 1; % Whether to show algorithm progress
      if use_stochastic
      options.BIGNbatch = round(NumSubj/20); % the amount of subject in each batch (NumSubj: # of subjects)
      options.BIGcyc = 500; % Maximum # of variational inference cycles
      options.BIGtol = options.tol; % Minimum relative decrement of free energy for convergence to be considered
      options.BIGundertol_tostop = 5; % # of inference steps with free energy decrements for the algorithm to stop
      options.forgetrate = 0.7; % Learning rate function
      options.BIGdelay = 1.0; % Learning rate function
      options.BIGbase_weights = 0.9; % Promote a democratic sampling of the subjets
      options.BIGverbose = 1; % Whether to show progress in the stochastic inference
      end
      options.pca = 0.9; % if specified, the HMM will work on a reduced PCA space

    • Outputs

      hmm: A structure with the estimated HMM-MAR model
      Gamma: Matrix containing the state time courses (# of time points x # of states)
      Xi: Matrix joint probability of past and future states conditioned on data (# of time points x # of states x # of states)
      vpath: Vector with the Viterbi path (# of time points x 1)
      GammaInit: The state time courses used after initialization
      residuals: If the model is trained on the residuals, the value of such residuals
      fehist: Historial of the free energy, with one element per iteration of the variational inference

  • Decode HMM
    • [test_Gamma,test_Xi] = hmmdecode(data,T,hmm,0);
    • [test_vpath] = hmmdecode(data,T,hmm,1);
    • Inputs

      data: Time series for decoding (time point x ROIs)
      T: Length of the time point (# of time points)
      hmm: Trained hidden markov model

    • Outputs

      test_Gamma: Matrix containing the state time courses (# of time points x # of states)
      test_Xi: Matrix joint probability of past and future states conditioned on data (# of time points x # of states x # of states)
      test_vpath: Matrix joint probability of past and future states conditioned on data (# of time points x # of states x # of states)

    • test_hmm = subject_hmm(data,T,hmm,test_Gamma,test_Xi);
    • Inputs

      Same as above

    • Outputs

      test_hmm: A structure with the estimated HMM-MAR model

  • Useful tools
    • TP = getTransProbs(test_hmm);
    • Inputs

      test_hmm: A structure with the estimated HMM-MAR model

    • Outputs

      TP: Transition probability

    • FO = getFractionalOccupancy(test_hmm,T,options);
    • Inputs

      test_hmm: A structure with the estimated HMM-MAR model
      test_T: Length of the time point (# of time points)
      options: The options defined above

    • Outputs

      FO: Fractional occupancy (how much time the HMM spends on each state)

• You can find details at: https://github.com/OHBA-analysis/HMM-MAR/wiki
  If have difficulty: Say "HELLO! GIVE ME YOUR CODE!" to Bo-yong!

Sliding Window

• Original paper:

  Allen et al., "Tracking whole-brain connectivity dynamics in the resting state", Cerebral Cortex, 2012. (https://academic.oup.com/cercor/article/24/3/663/394348)

• Useful papers:

  (1) Damaraju et al., "Dynamic functional connectivity analysis reveals transient states of dysconnectivity in schizophrenia", NeuroImage: Clinical, 2014. (https://www.sciencedirect.com/science/article/pii/S2213158214000953)
  (2) Rashid et al., "Dynamic connectivity states estimated from resting fMRI Identify differences among Schizophrenia, bipolar disorder, and healthy control subjects", Frontier in Human Neuroscience, 2014. (https://www.frontiersin.org/articles/10.3389/fnhum.2014.00897/full)
  (3) Park et al., "Dynamic functional connectivity analysis reveals improved association between brain networks and eating behaviors compared to static analysis", Behavioural Brain Research, 2018. (https://www.sciencedirect.com/science/article/pii/S0166432817314249?via%3Dihub)
  (4) Park et al., "Structural and Functional Brain Connectivity Changes Between People With Abdominal and Non-abdominal Obesity and Their Association With Behaviors of Eating Disorders", Frontiers in Neuroscience, 2018. (https://www.frontiersin.org/articles/10.3389/fnins.2018.00741/full)
  (5) Lee et al., "Dynamic functional connectivity of migraine brain: a resting-state functional magnetic resonance imaging study", PAIN, 2019. (https://journals.lww.com/pain/fulltext/2019/12000/Dynamic_functional_connectivity_of_the_migraine.11.aspx)

• Usage

  • Setup
    • Download FuNP toolbox (https://gitlab.com/by9433/funp)
    • Unzip the SurfaceAtlas and FuNP
    • Add the downloaded folder (SurfaceAtlas & FuNP) in MATLAB: addpath(genpath('~/FuNP'))
  • Run in MATLAB: Construct dynamic connectivity matrices
    • [OrigMat, RegMat, best_lambda] = MyDynConn(ts, Nroi, wsize, sigma, num_repetitions);
    • Inputs

      ts: Time series (time point x ROIs)
      Nroi: Number of ROI
      wsize: Size of the sliding window (unit of TRs)
      (theoretically: 1/Slowest frequency [e.g., HPF cutoff = 0.01Hz -> 100s -> if TR = 2s, then wsize = 50])
      (practically: wsize = 44~66s)
      sigma: Gaussian kernel (usually set to 3)
      num_repetitions: Number of repetitions for L1 regularization (usually set to 10)

    • Outputs

      OrigMat: Un-regularized dynamic connectivity matrix
      RegMat: Regularized dynamic connectivity matrix (USE THIS!!)
      best_lambda: Regularization factor for L1 regularization

• Steps of group analysis

  (1) Construct functional dynamic connectivity matrices for all subjects
  (2) Perform subject-wise clustering to find the optimal number of clusters
  (3) Perform group-wise clustering with the optimal number of clusters -> We can obtain group-wise brain state matrices
  (4) Match the subject- and group-wise brain state matrices \

  [Code request]
  Visit: https://gitlab.com/by9433/dynamicconnectivity
  If have difficulty: Say "HELLO! GIVE ME YOUR CODE!" to Bo-yong!