Evolve Breathing Pattern Case Study
Intact core model of the pontine–medullary respiratory network
GENERATION OF THREE-PHASE RESPIRATORY OSCILLATIONS.
The intact (pontine–medullary) model shown in Fig. 1B with the basic set of parameters (see methods) generated stable oscillations with period T = 2.5 s, duration of inspiration TI = 0.9 s, and duration of expiration TE = 1.6 s (Fig. 2A). These values are within the physiological ranges of these characteristics observed in the arterially perfused preparations of the juvenile rat (Paton 1996; Paton et al. 2006; Smith et al. 2007).
Generation of the 3-phase respiratory pattern in the intact model. A: traces of model output activities for all 4 neurons. B: mathematical representation of the “bio” 3-phase pattern, projected to (V1, V2, V3). During the early-inspiratory...
During expiration, the post-I neuron demonstrates adapting (decrementing) activity (Fig. 2A) that is defined by the dynamic increase in its adaptation variable mAD3 (see Eqs. 2 and 5). The corresponding decline in inhibition from the post-I neuron shapes the augmenting profile of aug-E activity. This reduction in post-I inhibition also produces slow depolarization of pre-I and early-I neurons. In addition, the pre-I neuron is depolarizing because of the slow deinactivation of INaP (slow increase of hNaP; see Eq. 5). Finally, at some moment during expiration, the pre-I neuron rapidly activates, providing excitation of early-I. The latter inhibits both post-I and aug-E, completing the switch from expiration to inspiration (Fig. 2A). At a higher level of excitability (e.g., with a higher drive to this neuron), early-I can release from inhibition first and initiate the transition to inspiration itself.
The abruptness of the switch to inspiration arises naturally from the dynamics of the model. To understand this, we define a fast subsystem of our model, consisting of the four voltage variables. Numerically, we can track the fast subsystem equilibrium surfaces along which these variables are relatively constant and we can also detect bifurcation curves, where solutions will jump away from each surface (see methods). During expiration, the system drifts along near an equilibrium surface (Fig. 2B). It is important to note that, although the expiratory period can be conditionally subdivided into postinspiration (with a dominant post-I activity) and late expiration (with reduced post-I and expressed aug-E activity), there is no clear switching between post-I and aug-E phases in the three-phase rhythm. In contrast, the moment of pre-I activation occurs when the system reaches a bifurcation curve along the post-I/aug-E equilibrium surface (Fig. 2B). This event allows the fast voltage variables to evolve quickly until they again reach an equilibrium surface, yielding a fast jump to the inspiratory phase (early-I in Fig. 2B).
During inspiration, the system drifts near this new equilibrium surface, with its dynamics governed by Eq. 5. Specifically, the early-I neuron demonstrates adapting (decrementing) activity (Fig. 2A), defined by the dynamic increase in its adaptation variable mAD2 (see Eqs. 2 and 5). The decline in inhibition from this neuron produces a slow depolarization of the post-I and aug-E neurons. Eventually, the system reaches another bifurcation curve and a second fast jump occurs (Fig. 2B). Within this fast jump, the post-I neuron rapidly activates and inhibits both inspiratory neurons (pre-I and early-I) and the aug-E neuron (initially), producing the switch from inspiration to expiration (Figs. 1B and 2A).
Since the post-I and aug-E regimes represent a continuous curve along the same equilibrium surface, without a fast jump between them, the three-phase respiratory rhythm remains two-phase in a mathematical sense. We call this regime a “biological” (or “bio”) three-phase pattern, in contrast to another regime, described later, representing a “mathematical” (or “math”) three-phase pattern, complete with three fast jumps. Since the bio three-phase pattern includes only two fast jumps, it is informative to consider projections of the corresponding trajectories and transition curves to two-dimensional phase planes. An example of such a projection is shown in Fig. 2C. Two distinct transition curves, for the inspiration-to-expiration and expiration-to-inspiration fast jumps, are evident and the oscillatory trajectory becomes a loop between these curves, with one part of the loop corresponding to the inspiratory (early-I active) phase and a second corresponding to both expiratory (post-I and aug-E) phases.
Interestingly, when projected to the (mAD2, mAD3) plane, the transition curve from expiration to inspiration is composed of two branches (Fig. 2C), corresponding to release (upper branch) and escape (lower branch) components of transition, respectively (e.g., Skinner et al. 1994). Note that the fast jumps themselves are not visible in this projection, since the changes in mAD2, mAD3 across these jumps are negligible. The difference between release and escape may be explained as follows. From a starting condition in the expiratory regime, a trajectory would require an increase in mAD3 to reach the uppermost of these two branches. An increase in mAD3 would yield a drop in V3 and thus a decrease in inhibition from post-I to pre-I/early-I. We can think of this as a transition facilitated by release of the pre-I and early-I cells from inhibition, although technically the inhibition from aug-E to pre-I/early-I would still be increasing during this period. In fact, however, we find that trajectories always reach the other, lower branch of the transition curve, rather than the release branch (Fig. 2C). This other branch is reached via a decrease in mAD3, such that the inhibition from post-I to pre-I/early-I is increasing again (along with the inhibition from aug-E) when the transition occurs, but V1, V2 are nonetheless able to escape from this inhibition and jump up, due to the rise in hNaP and the decay in mAD2. The transition from inspiration to expiration, in contrast, is always facilitated by release, with mAD2 growing throughout inspiration. These transition mechanisms have implications for the control of oscillation frequencies and phase durations (see also Curtu et al. 2008). Which mechanism governs a particular transition cannot be predicted from knowledge of the relevant connection strengths (say bij and bji) alone and an advantage of the reduced model formulation is that it allows us to identify these mechanisms.
CONTROL OF OSCILLATION PERIOD AND PHASE DURATIONS IN THE THREE-PHASE RHYTHM-GENERATING STATE.
To study the possible control of period and phase durations in the intact respiratory network state we investigated the effects of variations in the total excitatory drive to each neuron on the oscillation period (T) and on the durations of inspiration (TI) and expiration (TE). The results are summarized in Fig. 3, whereas Fig. 4 shows projections to the (mAD2, mAD3) plane that are useful in understanding why the observed changes occur.
Control of oscillation period and phase durations in the 3-phase rhythm-generating state. Changes of the oscillation period (T) and durations of inspiration (TI) and expiration (TE) were produced by the changes in total (dimensionless) drives to the preinspiratory...
Effects of changes in drives Di to each neuron in the 3-phase rhythm-generating state, in (mAD2, mAD3) space. As in Fig. 2C, solid curves are trajectories, dashed curves denote I-to-E transitions, and dash-dotted curves denote E-to-I transitions. As in...
An increase in total drive to the pre-I neuron (D1) from 0 to 0.6 produced monotonic shortening in the durations of both expiration and, to a lesser degree, inspiration, with the maximal value of T equal to 4.4-fold its minimal value (Fig. 3A). The reduction of TE occurs because an increase in drive to the pre-I neuron allows this neuron to escape from inhibition earlier, inducing an earlier switch to inspiration. Indeed, although the increased drive would slow deinactivation of INaP (see Eq. 5), its dominant effect is lowering the threshold for the pre-I cell (see Daun et al. 2009). Note that because this transition occurs earlier, the early-I neuron jumps up with a larger value of mAD2 (Fig. 4A). The reduction of TI occurs because, given the larger value of mAD2 at the start of inspiration, less time is needed for early-I to adapt sufficiently to terminate inspiration (i.e., to reach the inspiration-to-expiration transition curve; see Fig. 4A).
An increase in total drive to the early-I neuron (D2) from 0.5 to 0.85 reduces T approximately by half (Fig. 3B). This reduction results from a strong shortening of TE that overcomes a slight increase in TI, seen here but not when the drive to the pre-I neuron was increased. The shortening of TE results from an earlier escape of pre-I/early-I from inhibition and a corresponding earlier switch to inspiration (Fig. 4B). Indeed, as is subsequently discussed further in the following text, with a sufficient increase in D2 the early-I cell replaces the pre-I cell as the initiator of the transition to inspiration. The slight prolongation of TI occurs because inspiration cannot be terminated until there is an additional increase in mAD2, corresponding to further adaptation of the early-I cell, to compensate for the enhanced drive to early-I (Fig. 4B).
An increase in total drive to the post-I neuron (D3) causes a relatively small reduction of both TI and TE (and T) (Fig. 3C). TE becomes shorter because the additional drive to post-I leads to stronger inhibition on aug-E. The resulting weaker activation of aug-E leads to a net weaker inhibition of pre-I and early-I, allowing a slightly earlier escape to inspiration. The reduction in TI results from two main effects. First, a shorter expiration yields a slightly larger mAD2 at the start of inspiration (Fig. 4C), which promotes a shorter inspiration. Second, the stronger drive to post-I allows it to initiate the switch to expiration with slightly less reduction in inhibition from early-I to post-I (Fig. 4C).
An increase in total drive to the aug-E neuron (D4) produces a strong increase in TE and a small increase in TI, leading to an overall large increase in T (Fig. 3D). The prolongation of TE results from a stronger aug-E inhibition of inspiratory neurons that decreases V1 and V2 and necessitates a greater recovery from adaptation and inactivation before inspiration can begin, yielding a delay in the onset of inspiration (Fig. 4D). A small increase in TI follows the TE prolongation because the greater early-I recovery from adaptation during the prolonged expiratory period implies that mAD2 is smaller at the start of inspiration (Fig. 4D). Since aug-E has little effect on the end of inspiration, this change means that more time is needed for the early-I neuron to adapt sufficiently such that the transition to the next expiratory phase can occur.
In summary, variations in drive to different cells in the network influence the durations of inspiration and expiration, and the overall oscillatory period, differently (Fig. 3). These effects are determined by the particular features of the cells’ activity patterns, which translate into the forms of the transition curves between phases, and the distinctive role each cell plays in the transitions between phases, seen in the effects that changes in drive have on the transition curves (Fig. 4).
ROLE OF THE INTRINSIC INAP-DEPENDENT MECHANISMS.
In experimental studies, the role of intrinsic INaP-dependent mechanisms in rhythmogenesis is usually studied by administration of specific blockers of this current (e.g., riluzole) and investigation of the effects of these blockers on rhythm generation and characteristics of oscillations. In our model, only the pre-I cell has INaP. To investigate the role of this current in the intact pontine–medullary model and predict possible effects of such blockers, we investigated how period and amplitude of the pre-I output change with the reduction of maximal conductance of the persistent sodium channels (g¯NaP) from the basic value (5 nS) to zero (Fig. 5, A–D). Even a complete suppression of INaP in the pre-I neuron (g¯NaP = 0) does not stop oscillations in the network (Fig. 5B). Both the amplitude and the duration of inspiratory (pre-I) bursts decline with a decrease in g¯NaP, reaching about 50% of their original levels at g¯NaP = 0 (Fig. 5, B and C). The reduction in inspiratory phase duration arises because the pre-I neuron excites the early-I neuron more weakly and is itself less capable of maintaining a high activity state, such that less adaptation of early-I is needed for inspiration to end (Fig. 5D).
Role of INaP in generation of 3-phase oscillations. A: output activity of all neurons at the basic value of g¯NaP = 5.0 nS. B: output activity of all neurons with fully suppressed INaP, i.e., g¯NaP = 0. C: relative changes...
The oscillation period also changes with a reduction of g¯NaP, in a way that depends on the relative excitability of the pre-I and early-I neurons. If the excitability of the pre-I neuron is higher than the excitability of the early-I neuron, so that the pre-I neuron escapes from inhibition first and initiates the transition to inspiration, then the reduction of pre-I excitability with lowering of g¯NaP delays the transition to inspiration. This effect increases the duration of expiration and the overall burst period (Fig. 5, C and D). Indeed, the difficulty in initiating inspiration in this regime is apparent in Fig. 5D, where the curve in the (mAD2, mAD3) plane corresponding to g¯NaP = 0 nS shows an additional inflection, and mAD2 begins to grow, before the expiration-to-inspiration transition curve (Fig. 5D, dash-dotted) is reached. Alternatively, if the escape of the early-I neuron defines the transition from expiration to inspiration, then the shortened inspiratory phase is the dominant effect and the burst period decreases as g¯NaP is reduced (data not shown).
Medullary model and generation of two-phase oscillations
Experimental studies in an in situ perfused rat brain stem–spinal cord preparation have demonstrated that brain stem transections at the pontine–medullary junction (see Fig. 1A) (or more caudal transections through the RTN) convert the normal three-phase respiratory pattern to a two-phase pattern lacking the postinspiratory phase (Rybak et al. 2007; Smith et al. 2007). Modeling described in these studies has also suggested that this transformation results from the elimination of pontine drive to VRC, and especially the drive to post-I neurons whose activity is most dependent on this drive. The term “medullary model” is applied here to a reduced basic model lacking tonic drive from the pons (Fig. 1B, under conditions when d1 = 0). Switching to d1 = 0 in the model reduces the excitatory drive to all neurons, but this reduction most strongly affects the post-I neuron, which becomes completely inhibited by the aug-E neuron during inspiration and by the early-I neuron during inspiration. Therefore in the medullary model, the post-I neuron is always inhibited and does not contribute to rhythm generation or the resultant two-phase inspiratory–expiratory oscillations (Fig. 6). With the basic set of parameters (see methods), these oscillations exhibit a period T = 3.23 s, an inspiratory duration TI = 1.38 s, and an expiratory duration TE = 1.85 s (Fig. 6A). These values are within the physiological ranges of these characteristics observed in the arterially perfused preparations of the mature rat (Smith et al. 2007).
Generation of the 2-phase respiratory pattern in the medullary model. A: traces of output activities of all 4 neurons. B: projections of a trajectory and corresponding transition curves to (mAD2, mAD4) space. Arrows indicate the direction of evolution...
It is important to note that the lack of post-I activity in the two-phase oscillations dramatically changes the shape of the aug-E activity pattern in comparison with the intact state. In the intact model, because of the slow disinhibition from the adapting post-I neuron, the aug-E neuron showed a classical augmenting burst shape (see Fig. 2A). In the medullary model with the lack of post-I inhibition, this neuron is active throughout expiration and exhibits an adapting pattern (Fig. 6A) defined by the dynamic increase in its adaptation variable mAD4 (see Eq. 5 and Fig. 6B). This change in the aug-E firing pattern with the switch to two-phase oscillations has not been considered experimentally and represents a prediction from our model for further experimental studies.
The decline in inhibition from the decrementing activity of the aug-E neuron allows a slow depolarization of the pre-I and early-I neurons (Fig. 6A). In addition, the slow deinactivation of INaP (slow increase of hNaP; see Eq. 5) promotes the depolarization of the pre-I neuron. After some time during which these effects accumulate, the system reaches a transition curve, at which the pre-I neuron activates and thus excites the early-I cell. The latter inhibits aug-E, completing the switch from expiration to inspiration (Fig. 6A). Note that the aug-E neuron plays the same role in the generation of two-phase oscillations as the post-I played in the three-phase oscillations in the intact model. Unlike the transition from expiration to inspiration in the three-phase oscillation, however, the gradual release of the inspiratory cells from inhibition now continues right up to the fast jump, together with an escape component provided by these cells’ recovery from adaptation and inactivation, respectively (Fig. 6B). At a higher level of excitability (e.g., with a higher drive to this neuron), early-I can release from inhibition first and initiate the transition to inspiration itself.
During inspiration, the early-I neuron demonstrates adapting (decrementing) activity (Fig. 6A) defined by the dynamic increase in its adaptation variable mAD2 (see Eq. 5 and Fig. 6B). The decay in inhibition from this neuron allows a slow depolarization of aug-E. Eventually, the system reaches a transition curve, at which the aug-E neuron activates and inhibits both inspiratory neurons (pre-I and early-I), producing a switch from inspiration to expiration (Fig. 6, A and B).
Both the bio three-phase oscillations discussed earlier and the biological two-phase oscillations feature two fast jumps, qualifying as two-phase oscillations mathematically (see Figs. 2, B and C and 6B). It is important to note, however, that the expiratory phase is spent on different equilibrium surfaces or, possibly, distinct branches of a single equilibrium surface, in the bio three-phase and two-phase oscillations. Clearly, the values and dynamics of V3, V4 are very different on these different expiratory equilibrium surfaces. We will explore their distinctiveness more fully later in the text, when we specifically discuss transitions between oscillatory states.
Figure 7, A–C shows how the period of oscillation (T) and phase durations (TI and TE) change with variation in the drive to each neuron in the medullary model. An increase in total drive to the pre-I neuron (D1) from 0.025 to about 0.1 causes a steep drop in the duration of expiration (TE) and, correspondingly, the oscillation period T (Fig. 7A). This occurs because at a relatively low drive to the pre-I neuron, its escape from inhibition is mostly defined by the dynamics of persistent sodium inactivation (hNaP; see Eq. 5). Specifically, an increase in drive allows escape from inhibition to occur at a significantly lower level of hNaP, allowing for a much shorter expiratory phase (for more details see also Daun et al. 2009). Once the drive to the pre-I cell becomes sufficiently large, this effect saturates, leading to fairly constant TE and T. Eventually, the extra drive to pre-I can become strong enough that it prolongs the inspiratory phase via indirect inhibitory effects on the aug-E cell, mediated by the early-I cell that it excites, and T can increase slightly as a result.
Control of the oscillation period and phase durations in the 2-phase rhythm-generating state. Changes of the oscillation period (T) and the durations of inspiration (TI) and expiration (TE) in the medullary model were produced by the changes in total...
An increase in total drive to the early-I neuron (D2) from about 0.06 to 0.4 causes a balanced increase of TI and reduction of TE without significant changes in T (Fig. 7B). These changes are expected from a half-center adaptation-based oscillator, comprised here by the early-I and aug-E neurons, coupled with mutual inhibition (see also Daun et al. 2009). Note that the effects of varying D2 are different here from the three-phase case (Fig. 4B), particularly with respect to the expiratory phase, due to the difference in expiration-to-inspiration transition mechanisms across these cases.
An initial increase in total drive to the aug-E neuron (D4) from 2.29 to about 3.7 causes a balanced increase of TE and decrease of TI with only small changes in T (Fig. 7C). These changes are opposite to those produced by an increase in tonic drive to the early-I neuron (Fig. 7B), corresponding to their opposite roles in the oscillations, and are typical for a half-center adaptation-based oscillator, as mentioned earlier. In contrast, with a further increase of D4, the duration of expiration and the period increase drastically (Fig. 7C). This steep increase occurs because of two mechanisms. First, with an increase in inhibition from aug-E, the early-I neuron is no longer able to make the jump to the inspiratory phase without the “help” of (excitatory input from) the pre-I neuron. Second, the increasing aug-E inhibition to pre-I reduces the excitability of the latter, necessitating significantly greater deinactivation of INaP (increase in hNaP) for the transition to inspiration to occur.
In summary, changes in period and phase durations with changes in drive fall into two regimes: one in which the pre-I cell dominates the transition from expiration to inspiration and drives act primarily though effects on INaP and another in which the early-I cell leads this transition and thus the aug-E and early-I cells behave as a typical adaptation-based half-center oscillator.
To further understand the role of INaP in the two-phase oscillations generated by the medullary model and predict possible effects of INaP blockers on two-phase oscillations, we investigated how period and amplitude of the output (pre-I) activity change with the reduction of the maximal conductance of the persistent sodium channels (g¯NaP). A reduction of g¯NaP in the pre-I neuron all the way down to zero does not abolish two-phase oscillations in the network (Fig. 8). Instead, oscillations in the network persist, with the amplitude and duration of inspiratory bursts falling, and burst period increasing, as g¯NaP is reduced. At g¯NaP = 0, burst amplitude, duration, and period are changed by about −80, −50, and +45%, respectively (see Fig. 8, A–C). Interestingly, these effects are different from those seen by reducing the drive D1 to the pre-I cell and keeping g¯NaP intact. This difference arises because, unlike reductions in D1, decreases in g¯NaP can switch control of the onset of inspiration from the pre-I to the early-I cell. That is, the initial increase of burst period results from reducing the availability of INaP at the onset of inspiration, necessitating additional deinactivation for the transition to occur. When g¯NaP becomes sufficiently small, the early-I cell takes over the transition to inspiration, and therefore the burst period becomes stabilized at some higher duration, independent of g¯NaP.
Role of INaP in the generation of the 2-phase oscillations. A: output activity of all neurons at the basic value of g¯NaP = 5.0 nS. B: output activity of all neurons with fully suppressed INaP, i.e., at g¯NaP = 0. C: relative...
D) Explain the need to hold the warfarin prior to surgery.Anticoagulants increase the risk for bleeding during surgery and the postoperative period, so the nurse must explain the need to hold the warfarin prior to surgery and instruct the client to contact the surgeon to determine how long before surgery the medication should be stopped.The nurse then reviews Ms. Jackson's preoperative lab test results, drawn earlier in the week.3. Which serum lab value requires follow-up by the nurse?A) Sodium of 135 mEq/L.B) WBC of 14,000/mm3.C) Creatinine of 0.8 mg/dl.D) Hemoglobin of 14 g/dl.B) WBC of 14,000/mm3.The normal WBC count is 5,000 to 10,000/mm3. An increase may indicate the onset of an infection, which may be a contraindication to surgery. The nurse should notify the surgeon of this abnormal lab value.The nurse talks with Ms. Jackson about what to expect the day of surgery and during the immediate postoperative period. The nurse provides instructions regarding cough and deep breathing exercises. Ms. Jackson performs a return demonstration by breathing in through her mouth deeply and exhaling through pursed lips forcefully and rapidly.4. What action should the nurse implement?A) Advise the client to avoid pursing her lips when exhaling.B) Remind the client to cough after taking two to three breaths.C) Demonstrate the deep breathing and coughing technique again.D) Document successful completion of the return demonstration.C) Demonstrate the deep breathing and coughing technique again.Ms. Jackson has demonstrated incorrect technique. When performing deep breathing exercises, the client should inhale through the nose and exhale slowly through the mouth without pursing the lips. The nurse should demonstrate the entire procedure again for best learning by the client.