Table 1

Pseudo-code for nonlinear SC-to-FC completion (FC virtual duals to SC)

Algorithm non-linear SC-to-FC completion is
External input: empirical SC (SCemp)
Output: non-linear virtual FC (FCMFM)
Fixed parameters: noise level ( σ), simulation time (T), range to scan Gstart ≤ G ≤ Gstop, range to scan τstart ≤ τ  ≤  τstop, other frozen Wong-Wang neural mass parameters
Begin
 1. Construct a MFM embedding SCemp and the default frozen Wong-Wang neural mass parameters
 For Gstart ≤ G ≤ Gstop
  For τstart ≤ τ  ≤  τstop
   2.1 Simulate the MFM with current parameter values for a short time 0.2*T (discarding an initial transient)
   2.2 Compute surrogate BOLD from MFM time series via Balloon–Windkessel model
   2.3 Compute Corr(BOLD), i.e. the time-averaged FC matrix
   2.4 Compute stream of time-resolved FC(t) and the associated dFC matrix
   2.5 Compute and store Crit1[G, τ] (Spatial heterogeneity of activations)
   2.6 Compute and store Crit2[G, τ] (Clustering coefficient of time-averaged FC matrix)
   2.7 Compute and store Crit3[G, τ] (Clustering coefficient of dFC matrix)
  End
 End
 3. Identify G* and τ* for which Crit1[G, τ], Crit2[G, τ] and Crit3[G, τ] are jointly optimum
 4. Simulate the MFM with parameter values G* and τ* for a time T (discarding an initial transient)
 5. Compute surrogate BOLD from MFM time series via Balloon–Windkessel model
 6. Compute C = Corr(BOLD), i.e. the time-averaged FC matrix at G* and τ*
 Return FCMFM = C
End