Fig 1.
Fig 2.
Basic response of an isolated area to inputs.
The fraction of open channels sn and the corresponding BOLD signal are reported in reaction to successive stimulations. Time course of stimulations are made typical of a TNT task with stimulation steps during 3 s, separated by random intervals between 2.4 and 3.6 s (as in [32]). The BOLD signal is driven by sn as modelled in [33].
Fig 3.
(A) One excitatory pool, either excitatory or inhibitory. (B) One area with two coupled pools. (C) Two coupled areas.
Fig 4.
Response of excitatory pool to inputs, feedback gain and sensitivities.
(A) Fixed point values of are numerically extracted by root-finding of Eq 5, for values of
and
. Vertical dashed line correspond to
nA. (B) Corresponding firing rates, following Eq 2. (C) Corresponding feedback gain values, following Eq 13. (D) Corresponding close loop sensitivities, following Eq 15. See comments in Sec 3.1.
Fig 5.
Response of inhibitory pool to inputs, feedback gain and sensitivities.
(A) Fixed point values of are numerically extracted by root-finding, for values of
and
. Vertical dashed line correspond to
nA. (B) Corresponding firing rates, following Eq 2. (C) Corresponding feedback gain values. (D) Corresponding (close loop) sensitivities, following 15. See comments in Sec 3.1.
Fig 6.
Connectivity that are considered.
(A) Mutual excitation (E-E), (B) Target-to-Control inhibition (I-E), (C) Mutual inhibition (I-I), (D) Control-to-Target inhibition (E-I). We denote the connectivity by where first □ denotes the reception pools (E or I) for the Control (in blue) and second one for the Target (in orange) areas respectively.
Table 1.
Sensitivities for in Control and Target area to perturbation upon
, the input current into Control Area.
Fig 7.
Sensitivities and responses of excitatory pool in an isolated area.
(A—C) Response to external input upon the excitatory pool, (D—F) Response to external input upon the inhibitory pool. (A, D) Sensitivities, (B, E) , (C, F)
. See comments in Sec 3.2.
Fig 8.
Responses and sensitivities of excitatory pools in two-area system with connectivity E-E.
(A) Illustration of the connectivity. (B) Feedback gain (Eq 22). (C, D) Sensitivities of sn to perturbations upon excitatory pool of Control Area, in Control and Target areas respectively. (E,F) Corresponding firing rates. See comments in Sec 3.3.
Fig 9.
Responses and sensitivities of excitatory pools in two-area system with connectivity I-E.
Same legend as in Fig 8. See comments in Sec 3.3.
Fig 10.
Responses and sensitivities of excitatory pools in two-area system with connectivity I-I.
Same legend as in Fig 8. See comments in Sec 3.3.
Fig 11.
Responses and sensitivities of excitatory pools in two-area system with connectivity E-I.
Same legend as in Fig 8. See comments in Sec 3.3.
Fig 12.
Response as BOLD signals in E-E and E-I connectivities.
Left: E-E connectivity, right E-I connectivity. (A, B) A stimulation of 0.1 nA is applied upon the excitatory pool of the Control area during 20 s. (C, D) Time course of stimulations are made typical of a TNT task with stimulation steps during 3 s, separated by random intervals between 2.4 and 3.6 s. See comments in Sec 3.4.1.
Fig 13.
Effect of varying , the self-inhibitory strength within Target area, upon response to step activation of Control area.
In order by lines: EE, IE, II, EI. Left: Control area, Right: Target area. Dotted lines correspond to the value of yielding firing rates at 3 Hz in both areas when the system is at rest (
). See comments in Sec 3.4.2.