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J Appl Physiol 97: 984-990, 2004. First published May 7, 2004; doi:10.1152/japplphysiol.00162.2004
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Bionic epidural stimulation restores arterial pressure regulation during orthostasis

Yusuke Yanagiya,1,2 Takayuki Sato,1,3 Toru Kawada,1 Masashi Inagaki,1 Teiji Tatewaki,1,4 Can Zheng,1,2 Atsunori Kamiya,1 Hiroshi Takaki,1 Masaru Sugimachi,1 and Kenji Sunagawa1

1Department of Cardiovascular Dynamics, National Cardiovascular Center Research Institute, Suita, Osaka 565-8565; 2Pharmaceuticals and Medical Devices Agency, Chiyoda-ku, Tokyo 100-0013; 3Department of Cardiovascular Control, Kochi Medical School, Nankoku, Kochi 783-8505; and 4Japan Association for the Advancement of Medical Equipment, Bunkyo-ku, Tokyo 113-0033, Japan

Submitted 13 February 2004 ; accepted in final form 30 April 2004


   ABSTRACT
TOP
 ABSTRACT
MATERIALS AND METHODS
 RESULTS
 DISCUSSION
 APPENDIX
 GRANTS
 REFERENCES
 
A bionic baroreflex system (BBS) is a computer-assisted intelligent feedback system to control arterial pressure (AP) for the treatment of baroreflex failure. To apply this system clinically, an appropriate efferent neural (sympathetic vasomotor) interface has to be explored. We examined whether the spinal cord is a candidate site for such interface. In six anesthetized and baroreflex-deafferentiated cats, a multielectrode catheter was inserted into the epidural space to deliver epidural spinal cord stimulation (ESCS). Stepwise changes in ESCS rate revealed a linear correlation between ESCS rate and AP for ESCS rates of 2 pulses/s and above (r2, 0.876–0.979; slope, 14.3 ± 5.8 mmHg·pulses–1·s; pressure axis intercept, 35.7 ± 25.9 mmHg). Random changes in ESCS rate with a white noise sequence revealed dynamic transfer function of peripheral effectors. The transfer function resembled a second-order, low-pass filter with a lag time (gain, 16.7 ± 8.3 mmHg·pulses–1·s; natural frequency, 0.022 ± 0.007 Hz; damping coefficient, 2.40 ± 1.07; lag time, 1.06 ± 0.41 s). On the basis of the transfer function, we designed an artificial vasomotor center to attenuate hypotension. We evaluated the performance of the BBS against hypotension induced by 60° head-up tilt. In the cats with baroreflex failure, head-up tilt dropped AP by 37 ± 5 mmHg in 5 s and 59 ± 11 mmHg in 30 s. BBS with optimized feedback parameters attenuated hypotension to 21 ± 2 mmHg in 5 s (P < 0.05) and 8 ± 4 mmHg in 30 s (P < 0.05). These results indicate that ESCS-mediated BBS prevents orthostatic hypotension. Because epidural stimulation is a clinically feasible procedure, this BBS can be applied clinically to combat hypotension associated with various pathophysiologies.

baroreceptors; blood pressure; autonomic nervous system; Shy-Drager syndrome; orthostatic hypotension

THE ARTERIAL BAROREFLEX SYSTEM configures a negative feedback system and reduces arterial pressure (AP) disturbances from external influences (9, 15, 22, 23). Sudden onset of hypotension by orthostatic change occurs as a result of baroreflex failure, despite normal functioning of the cardiovascular system and efferent sympathetic nervous system. This condition is seen in multiple-system atrophy (Shy-Drager syndrome) (21, 22, 30) as well as spinal cord injuries (7, 17). Current treatments, such as salt loading (19, 33), cardiac pacing (1, 14), and pharmacological interventions (2, 3, 12, 20), fail to prevent the orthostatic hypotension. These therapies often result in an unwanted increase in AP in the supine position and neither restore nor reproduce the function of the feedback system that forms the basis of AP control (See DISCUSSION).

Previously, our laboratory developed a bionic baroreflex system (BBS) that substitutes the defective vasomotor center with an artificial controller (i.e., an artificial vasomotor center) to restore the native baroreflex function (24, 26). In these animal studies, the celiac ganglion was exposed by laparotomy and stimulated directly as the efferent neural interface in the BBS. However, for clinical application of the BBS, a less invasive and more stable electrical stimulation method is required.

In the present study, we examined the hypothesis that the spinal cord is a candidate site for the efferent neural interface in our bionic strategy. Epidural spinal cord stimulation (ESCS) has been used for the management of patients with malignant neoplasm, angina pectoris, and peripheral ischemia (6, 29). Stimulating the dorsal part of the spinal cord changes sympathetic nerve activity, AP in animals (11, 32) and heart rate in humans (18). If we can delineate how ESCS affects AP quantitatively, then this may lead to clinical application of the BBS. We studied the feasibility of ESCS-mediated BBS using an animal model of central baroreflex failure.


   MATERIALS AND METHODS
TOP
 ABSTRACT
 MATERIALS AND METHODS
RESULTS
 DISCUSSION
 APPENDIX
 GRANTS
 REFERENCES
 
Study design.   BBS is a negative feedback system and consists of two components: peripheral effectors and the artificial vasomotor center (Fig. 1). Peripheral effectors change AP in response to ESCS. The artificial vasomotor center (controller) determines the ESCS rate in response to changes in AP. Using BBS, we computer programmed the artificial vasomotor center and substituted the defective vasomotor center with an artificial vasomotor center.



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  		Fig. 1. Simplified diagram of bionic baroreflex system (BBS) using epidural spinal cord stimulation (ESCS). Peripheral effectors change arterial pressure (AP) in response to ESCS. The artificial vasomotor center determines ESCS rate in response to changes in AP. Transfer function of the peripheral effectors (Gp) cannot be controlled, but the vasomotor center transfer function (Gc) can be computer programmed as needed. Pd, pressure disturbance to AP.

 
For this purpose, we first characterized the static as well as dynamic responses of the peripheral effectors. With this knowledge, we then designed an artificial vasomotor center using simulation to delineate the parameters for obtaining optimal AP response. Finally, we evaluated the performance of the ESCS-mediated BBS in cats during orthostatic AP changes.

Animals and surgical procedures.   Animals were cared for in strict accordance with the "Guiding Principles for the Care and Use of Animals in the Field of Physiological Sciences," approved by the Physiological Society of Japan. Six adult cats of either sex, weighing 1.6–3.7 kg, were premedicated with ketamine (5 mg/kg im) and then anesthetized by intraperitoneal injection (1.0 ml/kg) of a mixture of urethane (250 mg/ml) and {alpha}-chloralose (40 mg/ml).

For AP measurement, a high-fidelity pressure transducer (SPC-320, Millar Instruments, Houston, TX) was placed in the aortic arch via the right femoral artery. Pancronium bromide (0.3 mg/kg) was administered to prevent muscular activity. The cats were mechanically ventilated with oxygen-enriched room air. Body temperature was maintained at around 38°C with a heating pad. To produce the baroreflex failure model, the carotid sinus, aortic depressor, and vagal nerves were sectioned bilaterally. The rationale for using baroreceptor-deafferentiated animals as the baroreflex failure model is that, in patients with multiple-system atrophy, the reason for sudden hypotension induced by orthostatic change is a lack of reflex control of AP sensed at the baroreceptors.

A partial laminectomy was performed in the L3 vertebra to expose the dura mater. A multielectrode catheter with interelectrode distance of 10 mm was introduced rostrally ~7 cm into the epidural space. The stimulating electrodes were positioned on the dorsal surface of the spinal cord within T12, T13, and L1. These spinal levels were selected because our preliminary studies showed that ESCS to these levels produced greater AP response compared with other spinal levels. The catheter was connected to an isolated electric stimulator (SS-102J and SEN7203, Nihon Kohden, Tokyo, Japan) via a custom-made, constant-voltage amplifier. The stimulator was controlled with a laboratory computer (PC9801FA, NEC, Tokyo, Japan).

Data recording for characterizing AP response to ESCS.   To characterize the static as well as dynamic AP responses to ESCS, we measured AP responses while changing ESCS rate. To estimate static response, we changed the ESCS rate sequentially in stepwise increments and decrements. Each stimulation step was maintained for 90 s. To estimate dynamic response, we randomly changed the ESCS rate, according to a binary white noise sequence with a minimum sequence length of 1 s. In both protocols, the stimulation voltage was fixed at 5 V, and the pulse width of the stimulus was 1 ms. While the stimulation was given, ESCS rate and AP were digitized at a rate of 200 Hz with a 12-bit resolution analog-to-digital converter [AD12–8 (PM), Contec, Osaka, Japan] and stored in another laboratory computer (PC98-NX VA70J, NEC). In this study, "ESCS rate" is defined as the number of stimulation pulses per second and is distinguished from the term "frequency," which refers to how frequently ESCS rate changes.

Estimation of static AP response parameters.   We parameterized the static AP response to ESCS. Each steady-state AP value was obtained by averaging the AP during the last 10 s of each ESCS step. Stimulation at low-ESCS rate decreased AP, but stimulation at higher rates increased AP. We fit both responses together to a linear regression model of AP vs. ESCS rate. We determined the rate at which the pressor and depressor effects balanced and designated it the offset stimulation rate (so).

Estimation of peripheral effector transfer function.   The transfer function of the peripheral effector was estimated by using a white noise method described in detail elsewhere (10, 13, 16, 24–26, 31). Briefly, on the basis of the resampled data at 10 Hz, the linear transfer function from ESCS rate to AP was calculated as a quotient of the ensemble average of cross-power between the two and that of ESCS rate power. The transfer function was calculated up to 0.5 Hz with a resolution of 0.0098 Hz. We parameterized the transfer function by using an iterative, nonlinear, least squares fitting technique (10).

Design of central characteristics and implementation by the artificial vasomotor center.   Based on the parameterized effector transfer function, we designed the vasomotor center transfer function using computer simulation. The characteristics of the vasomotor center have been identified as derivative characteristics in rabbits and rats (10, 13, 25). We did not have the corresponding data for cats but assumed that they resembled those in rabbits and rats. We adjusted the parameters by simulation, aiming to attenuate hypotension to ~20 mmHg within 5 s and to ≤10 mmHg at 30 s. We implemented designed transfer function by the artificial vasomotor center with convolution algorithm (see APPENDIX).

Head-up tilt tests.   The efficacy of the BBS against orthostatic stress was evaluated in each animal by the head-up tilt (HUT) test. We placed baroreflex failure animals in a prone position on a custom-made tilt table and measured AP responses to 60° HUT, with or without BBS activation. In the absence of BBS control, we fixed the ESCS rate at so, irrespective of AP changes. The BBS was activated by sending ESCS command to the stimulator, as calculated by the artificial vasomotor center in response to AP change. Tilt angle, ESCS rate, and AP were stored in a laboratory computer.

Statistical analysis.   All data are presented as means ± SD. We analyzed AP responses at 5 and 30 s after HUT. AP changes from control value were compared among protocols by using repeated-measures analysis of variance followed by Dunnett's multiple-comparison procedure (8). Differences were considered significant when P < 0.05.


   RESULTS
TOP
 ABSTRACT
 MATERIALS AND METHODS
 RESULTS
DISCUSSION
 APPENDIX
 GRANTS
 REFERENCES
 
Figure 2A is a representative example of static AP response to stepwise ESCS changes. Stepwise increases of ESCS rate produced a depressor response initially at low-ESCS rate and a pressor response at higher rates, and subsequent decreases of ESCS rate produced almost perfect reversal of AP changes. The relationship between AP and ESCS rate appeared nonlinear as a whole (Fig. 2B, top). However, for ESCS rates of 2 pulses/s and above, there is a linear relationship (r2 = 0.964, AP = 16.0 x ESCS + 44.0, so = 3.2 pulses/s; Fig. 2B). A linear relationship during ESCS was found in all animals [r2, 0.876–0.979 (median, 0.959) slope, 14.3 ± 5.8 mmHg·pulses–1·s; pressure axis intercept, 35.7 ± 25.6 mmHg; so, 4.9 ± 2.5 pulses/s]. The following protocols were performed by using this linear ESCS range.



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  		Fig. 2. A: representative time series of static AP response to ESCS. Stepwise increases of ESCS rate produced a depressor response initially at low-ESCS rate and a pressor response at higher rates, and subsequent decreases of ESCS rate produced almost perfect reversal of AP changes. B: procedures to estimate steady-state relationship between AP and ESCS rate. Each steady-state AP value was plotted against ESCS rate (top). Although the relationship between AP and ESCS rate appears nonlinear as a whole, linear regression analysis was conducted for the data obtained during ESCS (2, 4, 6, and 8 Hz), omitting the values before and after ESCS (0 Hz). A linear relationship is obtained. The value so represents the stimulation rate where pressor and depressor responses balance.

 
Figure 3A is a representative example of dynamic AP response to ESCS. We selected low- and high-stimulation rates that produced depressor and pressor responses, respectively, and stimulated the spinal cord, according to a binary white noise sequence. AP did not respond to fast changes in ESCS rate, but appeared to respond to slower changes, increasing with high-rate stimulation and decreasing with low-rate stimulation. The estimated transfer function indicated low-pass filter characteristics. Figure 3B shows the averaged transfer function from ESCS rate to AP in six animals. The gain decreased as the frequency increased and was attenuated to one-tenth of the lowest frequency at 0.1 Hz. The phase approached zero radian at the lowest frequency, reflecting in-phase changes of ESCS rate and AP. The parameters obtained by the least squares fitting to the second-order, low-pass filter model are as follows: dynamic gain = 16.7 ± 8.3 mmHg·pulses–1·s, natural frequency = 0.022 ± 0.007 Hz, damping coefficient = 2.40 ± 1.07, and lag time = 1.06 ± 0.41 s. The dynamic gain was much higher than the gain at the lowest frequency in the transfer function (Fig. 3A) but comparable to the slope obtained in the static protocol. The coherence function was close to unity between 0.01 and 0.4 Hz, indicating that the input-output relation was governed by almost linear dynamics in this range. To facilitate better understanding of the dynamic AP response to ESCS, the step functions were calculated by time integral of the inverse Fourier transform of the transfer functions. The estimated step functions are averaged and shown in Fig. 3C. An initial time lag and overdamped slow AP response to unit step ESCS are evident. The time courses of the estimated step functions were almost identical to but smoother than those of the actually observed AP responses to stepwise ESCS changes, indicating the ability to cancel out noises by the white noise method.



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  		Fig. 3. A: representative example of dynamic AP response to ESCS. B: averaged transfer functions from ESCS rate to AP, i.e., Gp (gain and phase) and coherence function (Coh). C: estimated step response (resp) computed from the transfer function. Data are expressed as means ± SD for 6 cats.

 
Figure 4 is a representative example of how we designed the vasomotor center transfer function. The steady-state gain is determined simply to match a total baroreflex loop gain of 5. This setting ensures that the steady-state AP fall will be attenuated to 10 mmHg in the case of a depressor stimulus of 60 mmHg. By changing the derivative corner frequency (fc), we simulated various transient AP responses to orthostatic depressor stimulation. Lower fc causes unstable oscillation in AP (Fig. 4B, left), and higher fc slows AP restoration (Fig. 4B, right). On the basis of these simulations, fc = 0.02 Hz was selected in this example (Fig. 4B, middle, 0.018 ± 0.008 Hz in 6 cats).



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  		Fig. 4. Representative example of designing the Gc. A: schematic diagram of the method of designing the Gc. AP changes in the presence of Pd were simulated by changing the corner frequency (fc) for derivative characteristic in the Gc. B: simulation results of this example. A vasomotor center with fc of 0.02 Hz restores AP with sufficient speed and stability (center).

 
Figure 5 shows a representative example of real-time application of BBS to a cat. In the control cat with baroreflex failure, abrupt HUT produced a rapid and then progressive fall in AP by 44 mmHg in 30 s (Fig. 5, left). Activation of the simulation-based BBS attenuated the AP fall (Fig. 5, middle; AP fall, 25 mmHg in 5 s and 19 mmHg in 30 s) but did not attain the predetermined target (gaps indicated by vertical bars in Fig. 5, middle and right). If the total loop gain of 5 were preserved, the AP fall should theoretically be attenuated to 44/(1 + 5), or ~7 mmHg, according to the linear control theory. The observed attenuation of 19/44 (=1/2.3) indicated that the actual gain was 1.3 (1 + 1.3 = 2.3). To achieve a total loop gain of 5, we increased the gain of the vasomotor center transfer function by 3.8-fold and reassessed the efficacy of BBS. As a result, AP returned to the predetermined target (Fig. 5, right; AP fall, 19 mmHg in 5 s, 7 mmHg in 30 s).



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  		Fig. 5. Representative example of real-time application of the BBS during head-up tilt (HUT). Left: in the cat with baroreflex failure, ESCS rate was fixed at 5.0 pulse/s. HUT produced a rapid and then progressive fall in AP. Middle: simulation-based BBS (BBS-sim) attenuated the AP fall but did not attain the predetermined target. Right: gain adjustment of the vasomotor center (BBS-adj) resulted in quick and sufficient attenuation of AP fall (see text for detail). Vertical bars indicate the ranges of predetermined targets.

 
Figure 6 summarizes the results obtained from six cats, demonstrating the effectiveness of the BBS performance. In the cat model of baroreflex failure, HUT decreased AP by 37 ± 5 mmHg in 5 s and by 59 ± 11 mmHg in 30 s. In animals with simulation-based vasomotor center, the initial attenuation (AP fall: 32 ± 7 mmHg in 5 s) was not significant, and the steady-state attenuation (17 ± 8 mmHg in 30 s) did not satisfy the predetermined target. On the other hand, in animals with gain-adjusted vasomotor center (2.4 ± 1.1-fold increase), the BBS achieved both initial and the steady-state targets (21 ± 2 mmHg in 5 s, P < 0.05; 8 ± 4 mmHg in 30 s, P < 0.05).



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  		Fig. 6. Summarized results of HUT obtained from 6 cats. A: averaged time courses of AP responses to HUT in cats with baroreflex failure (top) and with BBS (middle and bottom). Using the parameters determined from simulation, we found that the BBS (BBS-sim) did not adequately attenuate hypotension in all cats (middle). Appropriate gain increase (BBS-adj) was necessary for quick and sufficient attenuation of hypotension (bottom). B: changes in AP produced by HUT. Data are expressed as means ± SD. *P < 0.05 compared with baroreflex failure.

 

   DISCUSSION
TOP
 ABSTRACT
 MATERIALS AND METHODS
 RESULTS
 DISCUSSION
APPENDIX
 GRANTS
 REFERENCES
 
The present results indicate that AP can be controlled by ESCS and that ESCS-mediated BBS prevents orthostatic hypotension in anesthetized cats. Although the BBS based on simulation alone did not work as predicted during HUT, gain adjustments of the vasomotor center achieved quick and stable restoration of AP.

Necessity of BBS for treatment of central baroreflex failure.   Conventional treatments for central baroreflex failure aim at increasing AP. Although they alleviate the hypotension to the extent of preventing syncope, they have adverse effects of causing supine hypertension and enhancing the risk of hypertensive organ disease. Recently, Shannon et al. (28) suggested well-timed water consumption as a treatment for orthostatic hypotension in patients with autonomic failure. Their strategy is superior to conventional treatments because it prevents AP fall if predicted in advance. However, at least a few minutes are necessary for their method to increase AP. This time lag makes it impossible to control AP against sudden or unpredictable AP fall. None of the treatments attempted so far can prevent sudden orthostatic hypotension because the dynamics of the baroreflex remain impaired.

In contrast, the BBS continuously monitors and controls AP to achieve quick restoration of AP. Because AP is increased via sympathetic pathways, the AP response to the BBS vasomotor center command is as fast as that to the native vasomotor center control. Therefore, the quick, adequate, and stable nature of the native baroreflex system can be restored by the BBS with appropriate settings of the artificial vasomotor center.

Designing the vasomotor center transfer function and parameter adjustments.   In a negative feedback system, closed-loop responses to external perturbation are dependent on the dynamic characteristics of the total open-loop transfer function. We assumed that the derivative characteristics in cats are identical to those in rabbits or rats, which have been delineated previously (10, 13, 25). We optimized gain and derivative parameters for each cat so that both speed and stability were achieved.

In animal experiments, however, the simulation results were not fully reproduced. Gain adjustments of the vasomotor center were necessary to attain quick and sufficient attenuation of the AP fall. This discrepancy cannot be explained without considering a possible slope decrease or nonlinearity in peripheral effector characteristics (AP-ESCS relationship) caused by the HUT, or both. Pooling of blood volume in the splanchnic and hindlimb circulation would be a cause for such attenuated AP response. If AP responses during posture change can be defined quantitatively, then a more elaborate artificial vasomotor center can be developed that automatically adjusts the parameters. Automated adjustments may also be accomplished with adaptive control systems that execute real-time system identification and self-tuning of controller. The present study suggests the necessity of such manipulation of the vasomotor center settings.

Pressor and depressor responses by ESCS.   We demonstrated both depressor and pressor responses in AP to ESCS with a linear range (Fig. 2). Earlier studies have shown that dorsal column stimulation produces pressor and depressor responses. Depressor response is produced by a group of dorsal column fibers that project to the dorsal nuclei at the level of C8 to L1 and transmit to the fibers that ascend through the dorsal spinocerebeller tracts (4, 27, 32). Pressor response is produced by another group of fibers that ascends or descends through the terminal zone and enter the gray matter. Some of these fibers project to the intermedial lateral columns to activate sympathetic presynaptic fibers. AP responses to ESCS observed in the present study are the results of compound responses in these multiple pathways. Nevertheless, controllability of AP by the BBS is ascertained by a clear linearity between ESCS and AP response in both static and dynamic relationships.

Although we have not confirmed it in the closed-loop condition, depressor response shown in the open-loop condition indicates that ESCS-mediated BBS can attenuate hypertension as well as hypotension. Because an offset ESCS rate (so) is applied in the absence of pressure disturbance, lowering ESCS rate would attenuate hypertension to some extent. AP in conscious animals fluctuates between hypertension and hypotension, even in a quiet position (5). The speed of AP restoration is considered sufficient to control these fluctuations.

Future step for clinical application.   Clearly, the next step toward clinical application is to demonstrate the safety and the effectiveness of the ESCS-mediated BBS during orthostasis in conscious patients and animals. To study BBS in conscious animals, we have been developing an implantable hardware that enables BBS. Elaboration of such devices is mandatory for its future clinical application by searching the optimal stimulating site and condition that do not cause uncomfortable sensation and muscle twitch. A control algorithm must be developed that overcomes the problem revealed in the present study. The developing implant would be as small and low power as a pacemaker, with the aid of recent LSI technologies, and would be telemetrically programmable. In parallel, we began collaboration with a clinical group to develop ESCS-mediated BBS to suppress sudden hypotension in anesthetized humans during surgery. This study would prove the feasibility of human BBS.

Finally, new methods for long-term manometry are definitely required. Intravascular manometry can be achieved only with long-lasting antithrombotic material. Other indirect methods should be used until we are confident in antithrombotic ability.

Conclusions.   As a step toward clinical application of BBS, we demonstrated that AP could be controlled with ESCS. We designed the artificial vasomotor center based on the dynamic characteristics of AP response to ESCS. Although there was a dissociation between the predicted and actual attenuation of AP fall, ESCS-mediated BBS with appropriate gain adjustment was capable of preventing HUT-induced hypotension rapidly, sufficiently, and stably.


   APPENDIX
TOP
 ABSTRACT
 MATERIALS AND METHODS
 RESULTS
 DISCUSSION
 APPENDIX
GRANTS
 REFERENCES
 
Simulation of AP Restoration and Implementation by the Artificial Vasomotor Center

We modeled the vasomotor center transfer function (Gc) as

(A1)
where f is frequency, Kc is the steady-state gain of the artificial vasomotor center, fc1 is fc for derivative characteristics, fc2 and fc3 are corner frequencies for high-cut characteristics, j is an imaginary unit, and Lc is a pure delay. The value fc2 was set to 10 x fc1, and fc3 was set to 1 Hz. These settings attenuate AP pulsation and preserve total baroreflex gain (13). Lc was introduced to simulate the possible time delay of 0.1 s in transforming AP to ESCS rate but was excluded in real-time application to improve AP stability.

The simulation was performed as follows. The block diagram in Fig. 4A is represented as


where Gp is transfer function of the peripheral effectors, and Pd is pressure disturbance to AP. Rearranging these formula yields

(A2)

The time domain representation of Eq. A2 is

(A3)
where {Delta}AP(t) is AP change from control value, and g({tau}) is the impulse response function of the total open-loop transfer function (Gc·Gp). To simulate orthostatic hypotension, Pd(t) is set as an exponential AP fall to –60 mmHg with a time constant of 5 s rather than a stepwise fall (see Fig. 6A, top). We simulated the transient AP response to depressor stimulus while changing fc1 in the presence of the negative feedback system.

To implement the designed vasomotor center transfer function, we programmed the artificial vasomotor center to calculate ESCS rate in response to AP changes, according to the following equation:

where h({tau}) is the impulse response function of the designed vasomotor center transfer function, {Delta}AP(t) is AP change from the control value, and so is the offset ESCS rate obtained from the static parameterization.


   GRANTS
TOP
 ABSTRACT
 MATERIALS AND METHODS
 RESULTS
 DISCUSSION
 APPENDIX
 GRANTS
REFERENCES
 
This study was supported by a Grant-in-Aid for Scientific Research (A15200040) from the Japan Society for the Promotion of Science, the Program for Promotion of Fundamental Studies in Health Science of Pharmaceuticals and Medical Devices Agency of Japan, and a Health and Labour Sciences Research Grant (Research on Advanced Medical Technology, H14-nano-002) from the Ministry of Health, Labour and Welfare of Japan.


   FOOTNOTES
 

Address for reprint requests and other correspondence: M. Sugimachi, Dept. of Cardiovascular Dynamics, National Cardiovascular Center Research Institute, 5-7-1 Fujishirodai, Suita 565–8565, Japan.

The costs of publication of this article were defrayed in part by the payment of page charges. The article must therefore be hereby marked "advertisement" in accordance with 18 U.S.C. Section 1734 solely to indicate this fact.


   REFERENCES
TOP
 ABSTRACT
 MATERIALS AND METHODS
 RESULTS
 DISCUSSION
 APPENDIX
 GRANTS
 REFERENCES
 

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