Fig 1.
Simplified diagram of the thalamocortical loop considered in our previous FM model.
Blue lines with arrowhead: excitatory glutamatergic connections; red lines with hammer endings: inhibitory GABAergic connections.
Fig 2.
Influence on the thalamocortical system dynamics exerted by the coefficients of the differential equation variables.
The coefficient b shows a positive, non-linear correlation with , the bifurcation value of a. The coefficient θ influences the steepness of the correlation curve. The pink area highlights a range of b values within which the variation of θ has scarce influence on the corresponding values of
.
Fig 3.
Relationship between estimated allopregnanolone brain levels and the strength of GABAergic transmission, expressed by the coefficient a, as derived from Eq (4).
Top panel. The pink band indicates the transition zone separating two ranges of allopregnanolone where different effects on the GABAA receptor are prevalent: In the lower range the effect on GABAA α4 subunit expression, while in the higher range the positive allosteric modulation on GABAA activity. The points corresponding to allopregnanolone concentrations and a values at the follicular and luteal phases, and the value of the bifurcation point at the maximal glutamatergic strength (), are indicated. Bottom panel. Zoom-in view of the bottom left inset in the top graph. The point corresponding to allopregnanolone withdrawal and related a value is indicated. The horizontal red lines indicate the values taken by the bifurcation point at half-maximal glutamatergic strength (
), and for a 20% rise of b above this level (
). At allopregnanolone withdrawal, the thalamocortical loop system is still monostable for b = 0.5
, but it becomes bistable for b = 0.6
.
Table 1.
Representative steroid concentrations in the woman at different reproductive phases.
Table 2.
Hill function parameters derived from the curve fitting of allopregnanolone effects on GABAA receptors.
Table 3.
Table 4.
Hill function parameters determined by fitting to matched samples of gonadal hormone/corticosteroid plasma levels.
Fig 4.
Simplified diagram of the feedback loop system formed by the HPA and HPG axes.
Line ends as in Fig 1.
Table 5.
Values of the parameters in the differential equations describing the interactions among axes.
Fig 5.
Phase portrait of the dynamic system representing the HPG-HPA interaction according to the diagram of Fig 4.
The trajectories of the dynamic system have been computed with MATLAB by using Eqs (7) and (8) with the parameters reported in Table 5. Initial conditions have been randomly selected to be representative of different possible evolutions of the system. Each trajectory converges to one of the three stable equilibrium points (black dots). Black lines mark the boundaries between the basins of attraction of the three equilibria. The basin of attraction of the equilibrium point with high HPA and low HPG activity (which attracts the red trajectories) is assumed to represent the functional states leading to the onset of FM.
Fig 6.
Global representation of transitions leading to FM pathogenesis according to our neuroendocrine multistable model.
Top strip: Phase portrait of the HPA/HPG loop system, showing three stable equilibria (main graph). The lower-left (circadian) and lower-right (pathogenic) equilibria are connected with corresponding points on the graphs of the relationship between allopregnanolone brain concentration and GABAergic strength a (side graphs). The red lines in the side graphs indicate the bifurcation values , showing that the lower-right equilibrium point in the phase space leads to a value
. Bottom strip: The pain processing thalamocortical loop (left diagram), under the influence of the lower-right equilibrium point of the endocrine loop, crosses its bifurcation point, which leads to the appearance of two stable equilibria in its own phase space (right diagram). The high-firing-rate equilibrium represents the chronic pain condition and has a much wider basin of attraction. Therefore, once bistability has arisen, the thalamocortical system is prone to converging to the high-firing-rate equilibrium, thus causing the onset of FM symptoms. The variables considered in the endocrine phase space (top) represent the percent activities of the endocrine axes, e.g. estimated from the plasma levels of cortisol (HPA) and progesterone (HPG). The phase space shown in the bottom strip is a bidimensional projection on the VPL/SSC plane of the three-dimensional thalamocortical phase space, and the graph axes represent the percent firing rate above baseline of the thalamic ventroposterolateral nucleus (VPL) and the primary somatosensory cortex (SSC).