Neural control hierarchy of the heart has not evolved to deal with myocardial ischemia.

The consequences of myocardial ischemia are examined from the standpoint of the neural control system of the heart, a hierarchy of three neuronal centers residing in central command, intrathoracic ganglia, and intrinsic cardiac ganglia. The basis of the investigation is the premise that while this hierarchical control system has evolved to deal with "normal" physiological circumstances, its response in the event of myocardial ischemia is unpredictable because the singular circumstances of this event are as yet not part of its evolutionary repertoire. The results indicate that the harmonious relationship between the three levels of control breaks down, because of a conflict between the priorities that they have evolved to deal with. Essentially, while the main priority in central command is blood demand, the priority at the intrathoracic and cardiac levels is heart rate. As a result of this breakdown, heart rate becomes less predictable and therefore less reliable as a diagnostic guide as to the traumatic state of the heart, which it is commonly used as such following an ischemic event. On the basis of these results it is proposed that under the singular conditions of myocardial ischemia a determination of neural control indexes in addition to cardiovascular indexes has the potential of enhancing clinical outcome.

Dynamic neural networking as a basis for plasticity in the control of heart rate.

A model is proposed in which the relationship between individual neurons within a neural network is dynamically changing to the effect of providing a measure of "plasticity" in the control of heart rate. The neural network on which the model is based consists of three populations of neurons residing in the central nervous system, the intrathoracic extracardiac nervous system, and the intrinsic cardiac nervous system. This hierarchy of neural centers is used to challenge the classical view that the control of heart rate, a key clinical index, resides entirely in central neuronal command (spinal cord, medulla oblongata, and higher centers). Our results indicate that dynamic networking allows for the possibility of an interplay among the three populations of neurons to the effect of altering the order of control of heart rate among them. This interplay among the three levels of control allows for different neural pathways for the control of heart rate to emerge under different blood flow demands or disease conditions and, as such, it has significant clinical implications because current understanding and treatment of heart rate anomalies are based largely on a single level of control and on neurons acting in unison as a single entity rather than individually within a (plastically) interconnected network.

Neural control of heart rate: the role of neuronal networking.

Neural control of heart rate, particularly its sympathetic component, is generally thought to reside primarily in the central nervous system, though accumulating evidence suggests that intrathoracic extracardiac and intrinsic cardiac ganglia are also involved. We propose an integrated model in which the control of heart rate is achieved via three neuronal "levels" representing three control centers instead of the conventional one. Most importantly, in this model control is effected through networking between neuronal populations within and among these layers. The results obtained indicate that networking serves to process demands for systemic blood flow before transducing them to cardiac motor neurons. This provides the heart with a measure of protection against the possibility of "overdrive" implied by the currently held centrally driven system. The results also show that localized networking instabilities can lead to sporadic low frequency oscillations that have the characteristics of the well-known Mayer waves. The sporadic nature of Mayer waves has been unexplained so far and is of particular interest in clinical diagnosis.

A continuous analysis of multi-input, multi-output predictive control.

A continuous formulation and method of analysis is constructed for multi-input, multi-output (MIMO) predictive control and used to compare Dynamic Matrix Control (DMC) with Simplified Predictive Control (SPC). Approximate characteristic equations are derived for each of DMC and SPC and these are used to determine, and thus compare, the closed-loop control behaviour of these methods at times long compared with the sampling time. The MIMO control problem considered is the general case of control over two coupled zones of a first order, linear process where a single control move is simultaneously input into each zone and a single output or measurement, is made from within each zone. The analytical results are illustrated through MIMO control of the terminal composition of a binary distillation column. A practically important result is an analytic basis to understand previous experimental observations that, for a wide range of processes, SPC appears to be as capable as the more sophisticated DMC. Furthermore, it is also shown here that SPC is well-conditioned over its entire parameter range in contrast to DMC. This well-conditioned behaviour makes it especially suitable for remote applications where unknown, and variable timing of future moves may be a significant issue.

Risk aversion predictive control.

A quality-controlled predictive control method, suitable for control of fast, remote systems subject to significant communication delays, is developed. Each move is quality controlled in that it independently satisfies a risk-based control performance criterion. The method is found to be capable of mitigating the ill effects of highly nonstationary delay distributions while providing good control performance for milder nonstationarity. It is demonstrated on simplified predictive control (SPC) of a single-input, single-output process. SPC is preferred here due to its simplicity and well-conditioned dependence of both the sampling time and its single parameter.

Mechanism of smart baroreception in the aortic arch.

A mechanism is proposed by which the patch of baroreceptors along the inner curvature of the arch of the aorta can sense hemodynamic events occurring downstream from the aortic arch, in the periphery of the arterial tree. Based on a solution of equations governing the elastic movements of the aortic wall, it is shown that the pressure distribution along the patch of baroreceptors has the same functional form as the distribution of strain along the patch. The significance of these findings are discussed, particularly as they relate to the possibility of a neuromechanical basis of essential hypertension.

SISO extended predictive control: implementation and robust stability analysis.

The proposed algorithm of extended predictive control (EPC) represents an exact method for removing the ill-conditioning in the system matrix by developing a unique weighting structure for any control horizon. The main feature of the EPC algorithm is that it uses the condition number of the system matrix to evaluate a single tuning parameter that provides a specified closed-loop response. Robust analysis demonstrated that EPC is more robust in comparison with move-suppressed and m-shifted predictive controllers in all aspects of process variation in gain, delay, and time-constant ratios. Tuning of EPC is effective and simple since there is a direct relationship between closed-loop performance and its tuning parameter.

Stochastic behavior of atrial and ventricular intrinsic cardiac neurons.

To quantify the concurrent transduction capabilities of spatially distributed intrinsic cardiac neurons, the activities generated by atrial vs. ventricular intrinsic cardiac neurons were recorded simultaneously in 12 anesthetized dogs at baseline and during alterations in the cardiac milieu. Few (3%) identified atrial and ventricular neurons (2 of 72 characterized neurons) responded solely to regional mechanical deformation, doing so in a tightly coupled fashion (cross-correlation coefficient r = 0.63). The remaining (97%) atrial and ventricular neurons transduced multimodal stimuli to display stochastic behavior. Specifically, ventricular chemosensory inputs modified these populations such that they generated no short-term coherence among their activities (cross-correlation coefficient r = 0.21 +/- 0.07). Regional ventricular ischemia activated most atrial and ventricular neurons in a noncoupled fashion. Nicotinic activation of atrial neurons enhanced ventricular neuronal activity. Acute decentralization of the intrinsic cardiac nervous system obtunded its neuron responsiveness to cardiac sensory stimuli. Most atrial and ventricular intrinsic cardiac neurons generate concurrent stochastic activity that is predicated primarily upon their cardiac chemotransduction. As a consequence, they display relative independent short-term (beat-to-beat) control over regional cardiac indexes. Over longer time scales, their functional interdependence is manifest as the result of interganglionic interconnections and descending inputs.

SISO extended predictive control-formulation and the basic algorithm.

A new predictive controller is developed that represents a significant change from conventional model predictive control. The method termed extended predictive control (EPC) uses one tuning parameter, the condition number of the system matrix to provide an easy-to-follow tuning procedure. EPC drastically improves the system matrix conditionality resulting in faster closed-loop response without oscillatory transients. The control performance of EPC is compared with the original move suppressed and recently derived shifted predictive controllers, with improved results.

Development of characteristic equations and robust stability analysis for SISO move suppressed and shifted DMC.

New controller and closed loop transfer functions for move suppressed and shifted dynamic matrix control were derived in order to compare the controller robustness on several plants as a function of tuning parameters lambda and m. The derivation of these transfer functions are for any order plant requiring its open loop step or impulse response. A generic control design algorithm was developed for selecting the controller tuning parameters using controller robustness as a performance index, in the presence of plant parameter variations and uncertainties. Shifted dynamic matrix control (DMC) was found to be more robust with respect to all plant parameter variations, and therefore more suited than move suppressed DMC to control plants with wide ranging parameters. This result was demonstrated on an experimental direct current servomotor system, and further verified on a plant having a cascade control structure with the (m , m) being the most robust to plant variations.

Development of characteristic equations and robust stability analysis for MIMO move suppressed and shifted DMC.

Discrete-time controller and closed-loop transfer functions were developed for move suppressed lambda and the recently formulated m-shifted multiple-input-multiple-output (MIMO) dynamic matrix control (DMC). Using these transfer functions, robust analyses were conducted for MIMO plants by varying corresponding delay and gain ratios of the system. In all instances, robust plots indicate that the shifted DMC is less sensitive and hence more robust to variations in the plant parameters than move suppressed DMC. It was shown that the design of these MIMO DMC controllers depends on the plant closed-loop performance and overall stability, since the selection of lambda and m directly influences the plant robustness and closed-loop dynamics.

On simplified predictive control as a generalization of least-squares dynamic matrix control.

Simplified predictive control (SPC) of a single-input single-output control scheme is compared to the more sophisticated, least-squares formulation of dynamic matrix control (DMC) and its move-suppressed variant (move-suppressed DMC) for a typical two time-step control horizon. A closed-loop, continuous analysis shows that the discrete form of SPC generalizes the discrete DMC algorithm, and its variants, to control responses faster than one-half the process response time while remaining well conditioned.

Online optimization of fuzzy-PID control of a thermal process.

A constrained optimization of a simple fuzzy-PID (PID-proportional integral derivative) system is designed for the online improvement of PID control performance during productive control runs. The cost function design yields a desirable balance between rise time, setpoint overshoot, and settling time to the setpoint. The constraints determined by simulation yield control performance no worse than the existing control performance during online optimization. The optimized fuzzy-PID system is compared to a similarly optimized PID controller and a benchmark model predictive controller.

Continuous analysis of move suppressed and shifted DMC.

"Shifted DMC" (shifted dynamic matrix control) has been empirically shown to have significant improved closed-loop control characteristics over "move-suppressed DMC" where, in the latter, diagonal terms of the dynamic matrix DMC prediction model are augmented to reduce numerical ill conditioning. An added benefit of shifted DMC was that the so-called "shifting parameter," replacing the move suppression parameter, was easily found from the open-loop response. Therefore a novel analytical method, based on a closed form, continuous approximation to closed-loop DMC control, is introduced here and used to quantify the previous empirical results. The dependence of slow and fast time scales of the closed-loop response on the parameters is examined for move-suppressed and shifted DMC methods. It is found that in move-suppressed DMC the slow control time scale is sharply dependent upon the sampling time and move-suppression parameter and that these difficulties are eliminated in shifted DMC.

"Smart" baroreception along the aortic arch, with reference to essential hypertension.

Beat-to-beat regulation of heart rate is dependent upon sensing of local stretching or local "disortion" by aortic baroreceptors. Distortions of the aortic wall are due mainly to left ventricular output and to reflected waves arising from the arterial tree. Distortions are generally believed to be useful in cardiac control since stretch receptors or aortic baroreceptors embedded in the adventitia of the aortic wall, transduce the distortions to cardiovascular neural reflex pathways responsible for beat-to-beat regulation of heart rate. Aortic neuroanatomy studies have also found a continuous strip of mechanosensory neurites spread along the aortic inner arch. Although their purpose is now unknown, such a combined sensing capacity would allow measurement of the space and time dependence of inner arch wall distortions due, among other things, to traveling waves associated with pulsatile flow in an elastic tube. We call this sensing capability--"smart baroreception." In this paper we use an arterial tree model to show that the cumulative effects of wave reflections, from many sites far downstream, have a surprisingly pronounced effect on the pressure distribution in the root segment of the tree. By this mechanism global hemodynamics can be focused by wave reflections back to the aortic arch, where they can rapidly impact cardiac control via smart baroreception. Such sensing is likely important to maintain efficient heart function. However, alterations in the arterial tree due to aging and other natural processes can lead in such a system to altered cardiac control and essential hypertension.

Control of cardiac function and noise from a decaying power spectrum.

Evidence is presented that adds to the debate surrounding the question: To what extent does neural control of cardiac output exploit noise? The transduction capability of cardiac afferent neurons, situated in and adjacent to the heart, is vital to feedback in control of cardiac function. An analysis of in situ cardiac afferent activity shows evidence of independent and exponentially distributed interspike intervals. An anatomical basis for such memoryless interspike intervals ultimately derives from the fact that each afferent neuron is associated with a field of sensory neurites, or bare nerve endings, that transduce local chemical and mechanical stimuli in a many-to-one fashion. As such, cardiac afferent neurons and their sensory neurite inputs are respectively modeled here by the Hodgkin-Huxley equations forced by "red" noise (decaying power spectrum) perturbing an otherwise constant subthreshold input. A variable barrier competition model is derived from these equations in order to address the question: How are noisy inputs being processed by sensory neurons to cause each spike? It is found that ion channels are responsible for significant input "whitening" (increased spectral power at higher frequency) through differentiation of the inputs. Such whitening is a means to distinguish low-frequency control signals from otherwise red noise fluctuations. Furthermore, spiking occurs when backward moving averages of the whitened inputs, over a window of the order of the sodium activation time scale, exceed an approximately constant barrier.

Competition model for aperiodic stochastic resonance in a Fitzhugh-Nagumo model of cardiac sensory neurons.

Regional cardiac control depends upon feedback of the status of the heart from afferent neurons responding to chemical and mechanical stimuli as transduced by an array of sensory neurites. Emerging experimental evidence shows that neural control in the heart may be partially exerted using subthreshold inputs that are amplified by noisy mechanical fluctuations. This amplification is known as aperiodic stochastic resonance (ASR). Neural control in the noisy, subthreshold regime is difficult to see since there is a near absence of any correlation between input and the output, the latter being the average firing (spiking) rate of the neuron. This lack of correlation is unresolved by traditional energy models of ASR since these models are unsuitable for identifying "cause and effect" between such inputs and outputs. In this paper, the "competition between averages" model is used to determine what portion of a noisy, subthreshold input is responsible, on average, for the output of sensory neurons as represented by the Fitzhugh-Nagumo equations. A physiologically relevant conclusion of this analysis is that a nearly constant amount of input is responsible for a spike, on average, and this amount is approximately independent of the firing rate. Hence, correlation measures are generally reduced as the firing rate is lowered even though neural control under this model is actually unaffected.

Functional interdependence of neurons in a single canine intrinsic cardiac ganglionated plexus.

To determine the activity characteristics displayed by different subpopulations of neurons in a single intrinsic cardiac ganglionated plexus, the behaviour and co-ordination of activity generated by neurons in two loci of the right atrial ganglionated plexus (RAGP) were evaluated in 16 anaesthetized dogs during basal states as well as in response to increasing inputs from ventricular sensory neurites. These sub-populations of right atrial neurons received afferent inputs from sensory neurites in both ventricles that were responsive to local mechanical stimuli and the nitric oxide donor nitroprusside. Neurons in at least one RAGP locus were activated by epicardial application of veratridine, bradykinin, the beta1-adrenoceptor agonist prenaterol or glutamate. Epicardial application of angiotensin II, the selective beta2-adrenoceptor agonist terbutaline and selective alpha-adrenoceptor agonists elicited inconsistent neuronal responses. The activity generated by both populations of atrial neurons studied over 5 min periods during basal states displayed periodic coupled behaviour (cross-correlation coefficients of activities that reached, on average, 0.88 +/- 0.03; range 0.71-1) for 15-30 s periods of time. These periods of coupled activity occurred every 30-50 s during basal states, as well as when neuronal activity was enhanced by chemical activation of their ventricular sensory inputs. These results indicate that neurons throughout one intrinsic cardiac ganglionated plexus receive inputs from mechano- and chemosensory neurites located in both ventricles. That such neurons respond to multiple chemical stimuli, including those liberated from adjacent adrenergic efferent nerve terminals, indicates the complexity of the integrative processing of information that occurs within the intrinsic cardiac nervous system. It is proposed that the interdependent activity displayed by populations of neurons in different regions of one intrinsic cardiac ganglionated plexus, responding as they do to multiple cardiac sensory inputs, forms the basis for integrated regional cardiac control.

Aperiodic stochastic resonance in a hysteretic population of cardiac neurons.

Aperiodic stochastic resonance (ASR) is studied for a densely interconnected population of excitatory and inhibitory neurons that exhibit hysteresis. Switching between states in the presence of noisy external forcing is represented as a "competition between averages" and this is further explained through a semianalytical model. In contrast to energy-based approaches where only the timing of a switch between states is represented, the competition between averages also identifies the input history responsible for a switch. This last point leads to some interesting conclusions regarding cause and effect in the presence of noisy forcing of a hysteretic system. For example, at subthreshold inputs, it is found that the input history causing a switch between states is primarily dependent upon the noise level even though the corresponding time to switch is sensitive to both the distance from the threshold and the noise level. Since the application considered here is to cardiac neuronal control, control performance is considered over the full input range. Noise tuning for adequate control performance is found to be unnecessary if the noise level is high enough. This is consistent with studies of ASR for sensory neurons. Another observation made here that may be of clinical significance is that at higher noise levels, constraints placed upon inputs to ensure adequate control performance are likely to depend upon the switching direction.

PID gain scheduling using fuzzy logic.

A simple, yet robust and stable alternative to proportional, integral, derivative (PID) gain scheduling is developed using fuzzy logic. This fuzzy gain scheduling allows simple online duplication of PID control and the online improvement of PID control performance. The method is demonstrated with a physical model where PID control performance is improved to levels comparable to model predictive control. The fuzzy formulation is uniquely characterized by; (i) one fuzzy input variable involving the PID manipulated variable, (ii) two parameters to be tuned, while previously tuned PID parameters are retained, and (iii) a gain scheduling differential equation which relates the fuzzy and conventional PID manipulated variables and enables fuzzy gain scheduling.