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# Baroreceptor_Lu_et_al_2001

The model simulates baroreceptor function by changing heart rate, ventricular contractility, and arterial resistance in response to an input aortic pressure signal.

Model number: 0075

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## Description

  The model simulates baroreceptor function by changing heart rate, ventricular
contractility, and arterial resistance in response to an input aortic pressure
signal. No circulatory model is present, and the input aortic pressure curve is
taken from the literature (Stergiopulos 1999). An aortic pressure curve follower
variable (PaopFOL) is used to set the aortic pressure time-derivative.

The model was first implemented by Lu et al. (2001) and was based on work by
Wesseling and Settles (1992). An aortic pressure waveform from Stergiopulos et al.
(1999) is used as input to the baroreceptor pathway.  There is no circulatory
model present, and the aortic waveform remains unchanged by the resulting heart
rate, ventricular contractility and arterial resistance values.



## Equations

$\large \frac{dP_{AOP_{FOL}}}{dt} = \frac{(P_{AOP}-P_{AOP_{FOL}})}{\tau_{FOL}}$

$\large a2 \cdot a \cdot \frac{ddNbr}{dt} + (a2+a)\cdot\frac{dNbr}{dt} + Nbr = K \cdot (P_{AOP} + a1 \cdot \frac{dP_{AOP_{FOL}}}{dt})$

$\large \frac{N_{HRV}}{dt} = \{{ \frac{-N_{HRV} + [K_{HRV} \cdot Nbr(t-L_{HRV})]}{T_{HRV}} \text if t>L_{HRV} \atop 0 \text if t\leq L_{HRV}}$

$\large F_{HRV} = a_{HRV} + \frac{b_{HRV}}{e^{\tau_{HRV} \cdot (N_{HRV}-No_{HRV})}+1.0}$

$\large \frac{N_{HRS}}{dt} = \{{ \frac{-N_{HRS} + [K_{HRS} \cdot Nbr(t-L_{HRS})]}{T_{HRS}} \text if t>L_{HRS} \atop 0 \text if t\leq L_{HRS}}$

$\large F_{HRS} = a_{HRS} + \frac{b_{HRS}}{e^{\tau_{HRS} \cdot (N_{HRS}-No_{HRS})}+1.0}$

$\large \frac{N_{CON}}{dt} = \{{ \frac{-N_{CON} + [K_{CON} \cdot Nbr(t-L_{CON})]}{T_{CON}} \text if t>L_{CON} \atop 0 \text if t\leq L_{CON}}$

$\large F_{CON} = a_{CON} + \frac{b_{CON}}{e^{\tau_{CON} \cdot (N_{CON}-No_{CON})}+1.0}$

$\large \frac{N_{VASO}}{dt} = \{{ \frac{-N_{VASO} + [K_{VASO} \cdot Nbr(t-L_{VASO})]}{T_{VASO}} \text if t>L_{VASO} \atop 0 \text if t\leq L_{VASO}}$

$\large F_{VASO} = a_{VASO} + \frac{b_{VASO}}{e^{\tau_{VASO} \cdot (N_{VASO}-No_{VASO})}+1.0}$

$\large HR = h1 + (h2 \cdot F_{HRS})-(h3 \cdot F_{HRS}^{2})-(h4 \cdot F_{HRV}) + (h5 \cdot F_{HRV}^2)-(h6 \cdot F_{HRV} \cdot F_{HRS})$

$\large aF_{CON} = a_{MIN} + (Ka \cdot F_{CON})$

$\large bF_{CON} = b_{MIN} + (Kb \cdot F_{CON})$

$\large R_{SA} = Kr \cdot e^{4 \cdot F_{VASO}} + Kr \cdot (\frac{V_{SA,MAX}}{V_{SA}})^2$

The equations for this model may be viewed by running the JSim model applet and clicking on the Source tab at the bottom left of JSim's Run Time graphical user interface. The equations are written in JSim's Mathematical Modeling Language (MML). See the Introduction to MML and the MML Reference Manual. Additional documentation for MML can be found by using the search option at the Physiome home page.

## References

  Lu K, Clark JW, Ghorbel FH, Ware DL, Bidani A.,
A human cardiopulmonary system model applied to the analysis
of the Valsalva maneuver.  Am J Physiol Heart Circ Physiol.
281: H2661-H2679, 2001.

Stergiopulos N, Westerhof BE, Westerhof N., Total arterial
inertance as the fourth element of the windkessel model.
Am J Physiol 276: H81-H88, 1999.

Wesseling KH and Settels JJ. Circulatory model of baro- and cardio-pulmonary reflexes.
In: Blood Pressure and Heart Rate Variability, edited by Di Rienzo M.
IOS Press, 1992, p. 56-67.

The governing equations for Nbr is adopted from Spickler JW, Kezdi P, and Geller E.
Transfer characteristics of the carotid sinus pressure control system. In: Baroreceptors and
Hypertension, edited by Kezdi P. Pergamon, Dayton, OH, 1665, pp. 31-40.



## Key Terms

baroreceptor, heart rate control, cardiovascular system, sympathetic control, parasympathetic control, arterial resistance, contractility, Lu, afferent pathway, efferent pathway, Publication, data, Nervous system, autonomic system

## Model History

Get Model history in CVS.

Posted by: BEJ

## Acknowledgements

Please cite www.physiome.org in any publication for which this software is used and send an email with the citation and, if possible, a PDF file of the paper to: staff@physiome.org.
Or send a copy to:
The National Simulation Resource, Director J. B. Bassingthwaighte, Department of Bioengineering, University of Washington, Seattle WA 98195-5061.