Abstract
Vagal nerve stimulation has shown beneficial effects in treating cardiovascular diseases. However, the lack of clinical efficacy, as well as differences in stimulation parameters due to patient variability, indicates the necessity to integrate an automatic closed-loop control method, enabling subject-specific, optimal VNS parameter updates in real time. A mathematical model to predict subject-specific cardiovascular response to vagal nerve stimulation is required for validating the efficacy and safety of the closed-loop VNS device, as well as to explore more advanced control algorithms. This chapter provides a brief review of published mathematical models involved in predicting short-term cardiovascular response to vagal nerve stimulation. The entire system is discussed by separating it into four subsystems, representing the cardiac electrophysiology, the circulation system, the regulation mechanisms, and the electrical stimulation. The physiological issues involved in each subsystem and how these issues have been handled in published models are investigated. This chapter provides a framework for future efforts in mathematical modeling of the entire closed-loop cardiac control system using vagal nerve stimulation.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Similar content being viewed by others
References
Ben-Menachem, E., Revesz, D., Simon, B., Silberstein, S.: Surgically implanted and non-invasive vagus nerve stimulation: a review of efficacy, safety and tolerability. Eur. J. Neurol. 22(9), 1260–1268 (2015)
Kawada, T., Yamazaki, T., Akiyama, T., Li, M., Ariumi, H., Mori, H., Sunagawa, K., Sugimachi, M.: Vagal stimulation suppresses ischemia-induced myocardial interstitial norepinephrine release. Life Sci. 78(8), 882–887 (2006)
Arimura, T., Saku, K., Kakino, T., Nishikawa, T., Tohyama, T., Sakamoto, T., Sakamoto, K., Kishi, T., Ide, T., Sunagawa, K.: Intravenous electrical vagal nerve stimulation prior to coronary reperfusion in a canine ischemia-reperfusion model markedly reduces infarct size and prevents subsequent heart failure. Int. J. Cardiol. 227, 704–710 (2017)
Li, M., Zheng, C., Sato, T., Kawada, T., Sugimachi, M., Sunagawa, K.: Vagal nerve stimulation markedly improves long-term survival after chronic heart failure in rats. Circulation 109(1), 120–124 (2004)
De Ferrari, G.M., Crijns, H.J., Borggrefe, M., Milasinovic, G., Smid, J., Zabel, M., Gavazzi, A., Sanzo, A., Dennert, R., Kuschyk, J., et al.: Chronic vagus nerve stimulation: a new and promising therapeutic approach for chronic heart failure. Eur. Heart J. 32(7), 847–855 (2011)
Hamann, J.J., Ruble, S.B., Stolen, C., Wang, M., Gupta, R.C., Rastogi, S., Sabbah, H.N.: Vagus nerve stimulation improves left ventricular function in a canine model of chronic heart failure. Eur. J. Heart Fail. 15(12), 1319–1326 (2013)
Inagaki, M., Kawada, T., Lie, M., Zheng, C., Sunagawa, K., Sugimachi, M.: Intravascular parasympathetic cardiac nerve stimulation prevents ventricular arrhythmias during acute myocardial ischemia. In: 2005 IEEE Engineering in Medicine and Biology 27th Annual Conference, pp. 7076–7079. IEEE (2006)
Zheng, C., Li, M., Inagaki, M., Kawada, T., Sunagawa, K., Sugimachi, M.: Vagal stimulation markedly suppresses arrhythmias in conscious rats with chronic heart failure after myocardial infarction. In: 2005 IEEE Engineering in Medicine and Biology 27th Annual Conference, pp. 7072–7075. IEEE (2006)
Li, D.-J., Evans, R.G., Yang, Z.-W., Song, S.-W., Wang, P., Ma, X.-J., Liu, C., Xi, T., Su, D.-F., Shen, F.-M.: Dysfunction of the cholinergic anti-inflammatory pathway mediates organ damage in hypertension. Hypertension 57(2), 298–307 (2011)
Plachta, D.T., Gierthmuehlen, M., Cota, O., Espinosa, N., Boeser, F., Herrera, T.C., Stieglitz, T., Zentner, J.: Blood pressure control with selective vagal nerve stimulation and minimal side effects. J. Neural Eng. 11(3), 036011 (2014)
Mudd, J.O., Kass, D.A.: Tackling heart failure in the twenty-first century. Nature 451(7181), 919–928 (2008)
Brandt, E.B., Bashar, S.J., Mahmoud, A.I.: Stimulating ideas for heart regeneration: the future of nerve-directed heart therapy. Bioelectron. Med. 5(1), 8 (2019)
Sharma, K., Premchand, R.K., Mittal, S., Monteiro, R., Libbus, I., DiCarlo, L.A., Ardell, J.L., Amurthur, B., KenKnight, B.H., Anand, I.S.: Long-term follow-up of patients with heart failure and reduced ejection fraction receiving autonomic regulation therapy in the ANTHEM-HF pilot study. Int. J. Cardiol. 323, 175–178 (2021)
Yuan, H., Silberstein, S.D.: Vagus nerve and vagus nerve stimulation, a comprehensive review: part II. Headache: J. Head Face Pain 56(2), 259–266 (2016)
Premchand, R.K., Sharma, K., Mittal, S., Monteiro, R., Dixit, S., Libbus, I., DiCarlo, L.A., Ardell, J.L., Rector, T.S., Amurthur, B., et al.: Autonomic regulation therapy via left or right cervical vagus nerve stimulation in patients with chronic heart failure: results of the ANTHEM-HF trial. J. Card. Fail. 20(11), 808–816 (2014)
Zannad, F., De Ferrari, G.M., Tuinenburg, A.E., Wright, D., Brugada, J., Butter, C., Klein, H., Stolen, C., Meyer, S., Stein, K.M., et al.: Chronic vagal stimulation for the treatment of low ejection fraction heart failure: results of the neural cardiac therapy for heart failure (NECTAR-HF) randomized controlled trial. Eur. Heart J. 36(7), 425–433 (2015)
Gold, M.R., Van Veldhuisen, D.J., Hauptman, P.J., Borggrefe, M., Kubo, S.H., Lieberman, R.A., Milasinovic, G., Berman, B.J., Djordjevic, S., Neelagaru, S., et al.: Vagus nerve stimulation for the treatment of heart failure: the INOVATE-HF trial. J. Am. Coll. Cardiol. 68(2), 149–158 (2016)
Bilbao, A., Escobar, A., GarcÃa-Perez, L., Navarro, G., Quirós, R.: The Minnesota living with heart failure questionnaire: comparison of different factor structures. Health Qual. Life Outcomes 14(1), 23 (2016)
Chen, C.-A., Chang, C.-H., Lin, M.-T., Hua, Y.-C., Fang, W.-Q., Wu, M.-H., Lue, H.-C., Wang, J.-K.: Six-minute walking test: normal reference values for taiwanese children and adolescents. Acta Cardiol. Sin. 31(3), 193 (2015)
Waninger, M.S., Bourland, J.D., Geddes, L.A., Schoenlein, W.E., Graber, G., Weirich, W.E., Wodigka, G.R.: Electrophysiological control of ventricular rate during atrial fibrillation. Pacing Clin. Electrophysiol. 23(8), 1239–1244 (2000)
Zhang, Y., Mowrey, K.A., Zhuang, S., Wallick, D.W., Popović, Z.B., Mazgalev, T.N.: Optimal ventricular rate slowing during atrial fibrillation by feedback AV nodal-selective vagal stimulation. Am. J. Physiol.-Heart Circ. Physiol. 282(3), H1102–H1110 (2002)
Tosato, M., Yoshida, K., Toft, E., Nekrasas, V., Struijk, J.J.: Closed-loop control of the heart rate by electrical stimulation of the vagus nerve. Med. Biol. Eng. Comput. 44(3), 161–169 (2006)
Ugalde, H.M.R., Ojeda, D., Le Rolle, V., Andreu, D., Guiraud, D., Bonnet, J.-L., Henry, C., Karam, N., Hagege, A., Mabo, P., et al.: Model-based design and experimental validation of control modules for neuromodulation devices. IEEE Trans. Biomed. Eng. 63(7), 1551–1558 (2015)
Greenwald, E., So, E., Wang, Q., Mollazadeh, M., Maier, C., Etienne-Cummings, R., Cauwenberghs, G., Thakor, N.: A bidirectional neural interface IC with chopper stabilized BioADC array and charge balanced stimulator. IEEE Trans. Biomed. Circuits Syst. 10(5), 990–1002 (2016)
Romero-Ugalde, H.M., Le Rolle, V., Bonnet, J.-L., Henry, C., Bel, A., Mabo, P., Carrault, G., Hernández, A.I.: A novel controller based on state-transition models for closed-loop vagus nerve stimulation: application to heart rate regulation. PloS One 12(10), e0186068 (2017)
Méry, D., Singh, N.K.: Closed-loop modeling of cardiac pacemaker and heart. In: International Symposium on Foundations of Health Informatics Engineering and Systems, pp. 151–166. Springer (2012)
Bequette, B.W.: Challenges and recent progress in the development of a closed-loop artificial pancreas. Annu. Rev. Control 36(2), 255–266 (2012)
Robert, R.: Model–based development of neuroprostheses for paraplegic patients. Philos. Trans. R. Soc. Lond. Ser. B: Biol. Sci. 354(1385), 877–894 (1999)
Hodgkin, A.L., Huxley, A.F.: A quantitative description of membrane current and its application to conduction and excitation in nerve. J. Physiol. 117(4), 500–544 (1952)
Noble, D.: A modification of the hodgkin-huxley equations applicable to purkinje fibre action and pacemaker potentials. J. Physiol. 160(2), 317–352 (1962)
Di Francesco, D., Noble, D.: A model of cardiac electrical activity incorporating ionic pumps and concentration changes. Philos. Trans. R. Soc. Lond. B Biol. Sci. 307(1133), 353–398 (1985)
Beeler, G.W., Reuter, H.: Reconstruction of the action potential of ventricular myocardial fibres. J. Physiol. 268(1), 177–210 (1977)
Luo, C.-H., Rudy, Y.: A dynamic model of the cardiac ventricular action potential. II. Afterdepolarizations, triggered activity, and potentiation. Circ. Res. 74(6), 1097–1113 (1994)
Priebe, L., Beuckelmann, D.J.: Simulation study of cellular electric properties in heart failure. Circ. Res. 82(11), 1206–1223 (1998)
ten Tusscher, K.H., Noble, D., Noble, P.-J., Panfilov, A.V.: A model for human ventricular tissue. Am. J. Physiol.-Heart Circ. Physiol. 286(4), H1573–H1589 (2004)
Winslow, R.L., Rice, J., Jafri, S., Marban, E., O?Rourke, B.: Mechanisms of altered excitation-contraction coupling in canine tachycardia-induced heart failure, II: Model studies. Circ. Res. 84(5), 571–586 (1999)
Puglisi, J.L., Bers, D.M.: Labheart: an interactive computer model of rabbit ventricular myocyte ion channels and Ca transport. Am. J. Physiol.-Cell Physiol. 281(6), C2049–C2060 (2001)
Nygren, A., Fiset, C., Firek, L., Clark, J.W., Lindblad, D.S., Clark, R.B., Giles, W.R.: Mathematical model of an adult human atrial cell: the role of K+ currents in repolarization. Circ. Res. 82(1), 63–81 (1998)
Courtemanche, M., Ramirez, R.J., Nattel, S.: Ionic mechanisms underlying human atrial action potential properties: insights from a mathematical model. Am. J. Physiol.-Heart Circ. Physiol. 275(1), H301–H321 (1998)
Sarai, N., Matsuoka, S., Kuratomi, S., Ono, K., Noma, A.: Role of individual ionic current systems in the sa node hypothesized by a model study. Jpn. J. Physiol. 53(2), 125–134 (2003)
Mangoni, M.E., Traboulsie, A., Leoni, A.-L., Couette, B., Marger, L., Le Quang, K., Kupfer, E., Cohen-Solal, A., Vilar, J., Shin, H.-S., et al.: Bradycardia and slowing of the atrioventricular conduction in mice lacking cav3. 1/α1g t-type calcium channels. Circ. Res. 98(11), 1422–1430 (2006)
FitzHugh, R.: Impulses and physiological states in theoretical models of nerve membrane. Biophys. J. 1(6), 445 (1961)
Sovilj, S., Magjarević, R., Al Abed, A., Lovell, N.H., Dokos, S.: Simplified 2d bidomain model of whole heart electrical activity and ecg generation. Meas. Sci. Rev. 14(3), 136–143 (2014)
Sovilj, S., Magjarević, R., Lovell, N., Dokos, S.: Realistic 3d bidomain model of whole heart electrical activity and ecg generation. In: Computing in Cardiology 2013, pp. 377–380. IEEE (2013)
Clayton, R., Bernus, O., Cherry, E., Dierckx, H., Fenton, F.H., Mirabella, L., Panfilov, A.V., Sachse, F.B., Seemann, G., Zhang, H.: Models of cardiac tissue electrophysiology: progress, challenges and open questions. Prog. Biophys. Mol. Biol. 104(1–3), 22–48 (2011)
El Houari, K.: Modeling and Imaging of Electrocardiographic Activity. PhD thesis (2018)
Panfilov, A., Keener, J.: Re-entry in an anatomical model of the heart. Chaos Solitons Fractals 5(3–4), 681–689 (1995)
Gray, R., Jalife, J.: Ventricular fibrillation and atrial fibrillation are two different beasts. Chaos: Interdiscip. J. Nonlinear Sci. 8(1), 65–78 (1998)
Miller, W.T., Geselowitz, D.B.: Simulation studies of the electrocardiogram. I. The normal heart. Circ. Res. 43(2), 301–315 (1978)
Morris, P.D., Ryan, D., Morton, A.C., Lycett, R., Lawford, P.V., Hose, D.R., Gunn, J.P.: Virtual fractional flow reserve from coronary angiography: modeling the significance of coronary lesions: results from the VIRTU-1 (VIRTUal Fractional Flow Reserve From Coronary Angiography) study. JACC: Cardiovasc. Interv. 6(2), 149–157 (2013)
Nørgaard, B.L., Leipsic, J., Gaur, S., Seneviratne, S., Ko, B.S., Ito, H., Jensen, J.M., Mauri, L., De Bruyne, B., Bezerra, H., et al.: Diagnostic performance of noninvasive fractional flow reserve derived from coronary computed tomography angiography in suspected coronary artery disease: the NXT trial (analysis of coronary blood flow using ct angiography: next steps). J. Am. Coll. Cardiol. 63(12), 1145–1155 (2014)
Radaelli, A., Augsburger, L., Cebral, J., Ohta, M., Rüfenacht, D., Balossino, R., Benndorf, G., Hose, D., Marzo, A., Metcalfe, R., et al.: Reproducibility of haemodynamical simulations in a subject-specific stented aneurysm model—a report on the Virtual Intracranial Stenting Challenge 2007. J. Biomech. 41(10), 2069–2081 (2008)
Ursino, M.: Interaction between carotid baroregulation and the pulsating heart: a mathematical model. Am. J. Physiol.-Heart Circ. Physiol. 275(5), H1733–H1747 (1998)
Ursino, M.: A mathematical model of the carotid baroregulation in pulsating conditions. IEEE Trans. Biomed. Eng. 46(4), 382–392 (1999)
Heldt, T., Shim, E.B., Kamm, R.D., Mark, R.G.: Computational modeling of cardiovascular response to orthostatic stress. J. Appl. Physiol. 92(3), 1239–1254 (2002)
Shi, Y., Lawford, P., Hose, R.: Review of zero-d and 1-d models of blood flow in the cardiovascular system. Biomed. Eng. Online 10(1), 33 (2011)
Li, J.K.: The Arterial Circulation: Physical Principles and Clinical Applications. Springer Science & Business Media, Totowa, Humana Press (2000)
Guyton, A.C., Coleman, T.G., Granger, H.J.: Circulation: overall regulation. Annu. Rev. Physiol. 34(1), 13–44 (1972)
Westerhof, N., Lankhaar, J.-W., Westerhof, B.E.: The arterial windkessel. Med. Biol. Eng. Comput. 47(2), 131–141 (2009)
Kim, H., Jansen, K., Taylor, C.: Incorporating autoregulatory mechanisms of the cardiovascular system in three-dimensional finite element models of arterial blood flow. Ann. Biomed. Eng. 38(7), 2314–2330 (2010)
Blanco, P., Trenhago, P., Fernandes, L., Feijóo, R.: On the integration of the baroreflex control mechanism in a heterogeneous model of the cardiovascular system. Int. J. Numer. Methods Biomed. Eng. 28(4), 412–433 (2012)
Lau, K.D., Figueroa, C.A.: Simulation of short-term pressure regulation during the tilt test in a coupled 3d–0d closed-loop model of the circulation. Biomech. Model. Mechanobiol. 14(4), 915–929 (2015)
Canuto, D., Chong, K., Bowles, C., Dutson, E.P., Eldredge, J.D., Benharash, P.: A regulated multiscale closed-loop cardiovascular model, with applications to hemorrhage and hypertension. Int. J. Numer. Methods Biomed. Eng. 34(6), e2975 (2018)
Liang, F., Takagi, S., Himeno, R., Liu, H.: Multi-scale modeling of the human cardiovascular system with applications to aortic valvular and arterial stenoses. Med. Biol. Eng. Comput. 47(7), 743–755 (2009)
Magosso, E., Ursino, M.: Cardiovascular response to dynamic aerobic exercise: a mathematical model. Med. Biol. Eng. Comput. 40(6), 660–674 (2002)
Ursino, M., Fiorenzi, A., Belardinelli, E.: The role of pressure pulsatility in the carotid baroreflex control: a computer simulation study. Comput. Biol. Med. 26(4), 297–314 (1996)
Lu, K., Clark, J. Jr, Ghorbel, F., Ware, D., Bidani, A.: A human cardiopulmonary system model applied to the analysis of the valsalva maneuver. Am. J. Physiol.-Heart Circ. Physiol. 281(6), H2661–H2679 (2001)
Barnea, O., Moore, T., Dubin, S., Jaron, D.: Cardiac energy considerations during intraaortic balloon pumping. IEEE Trans. Biomed. Eng. 37(2), 170–181 (1990)
Suga, H., Sagawa, K., Shoukas, A.A.: Load independence of the instantaneous pressure-volume ratio of the canine left ventricle and effects of epinephrine and heart rate on the ratio. Circ. Res. 32(3), 314–322 (1973)
DeBoer, R., Karemaker, J.M., Strackee, J.: Hemodynamic fluctuations and baroreflex sensitivity in humans: a beat-to-beat model. Am. J. Physiol.-Heart Circ. Physiol. 253(3), H680–H689 (1987)
Heldt, T., Chang, J., Chen, J., Verghese, G., Mark, R.: Cycle-averaged dynamics of a periodically driven, closed-loop circulation model. Control Eng. Pract. 13(9), 1163–1171 (2005)
Parlikar, T.A., Heldt, T., Verghese, G.C.: Cycle-averaged models of cardiovascular dynamics. IEEE Trans. Circuits Syst. I: Reg. Pap. 53(11), 2459–2468 (2006)
Codrean, A., Dragomir, T.-L.: Averaged modeling of the cardiovascular system. In: 52nd IEEE Conference on Decision and Control, pp. 2066–2071. IEEE (2013)
Ochsner, G., Amacher, R., Daners, M.S.: A novel mean-value model of the cardiovascular system including a left ventricular assist device. Cardiovasc. Eng. Technol. 8(2), 120–130 (2017)
Korakianitis, T., Shi, Y.: Effects of atrial contraction, atrioventricular interaction and heart valve dynamics on human cardiovascular system response. Med. Eng. Phys. 28(8), 762–779 (2006)
Smith, B.W., Andreassen, S., Shaw, G.M., Jensen, P.L., Rees, S.E., Chase, J.G.: Simulation of cardiovascular system diseases by including the autonomic nervous system into a minimal model. Comput. Methods Programs Biomed. 86(2), 153–160 (2007)
Chung, D., Niranjan, S., Clark, J. Jr, Bidani, A., Johnston, W., Zwischenberger, J., Traber, D.: A dynamic model of ventricular interaction and pericardial influence. Am. J. Physiol.-Heart Circ. Physiol. 272(6), H2942–H2962 (1997)
Sun, Y., Beshara, M., Lucariello, R.J., Chiaramida, S.A.: A comprehensive model for right-left heart interaction under the influence of pericardium and baroreflex. Am. J. Physiol.-Heart Circ. Physiol. 272(3), H1499–H1515 (1997)
Magosso, E., Cavalcanti, S., Ursino, M.: Theoretical analysis of rest and exercise hemodynamics in patients with total cavopulmonary connection. Am. J. Physiol.-Heart Circ. Physiol. 282(3), H1018–H1034 (2002)
Olufsen, M.S., Ottesen, J.T., Tran, H.T., Ellwein, L.M., Lipsitz, L.A., Novak, V.: Blood pressure and blood flow variation during postural change from sitting to standing: model development and validation. J. Appl. Physiol. 99(4), 1523–1537 (2005)
Artiles, A.D., Heldt, T., Young, L.R.: Effects of artificial gravity on the cardiovascular system: computational approach. Acta Astronaut. 126, 395–410 (2016)
Pstras, L., Thomaseth, K., Waniewski, J., Balzani, I., Bellavere, F.: Mathematical modelling of cardiovascular response to the valsalva manoeuvre. Math. Med. Biol. J. IMA 34(2), 261–292 (2017)
Williams, n.d., Brady, R., Gilmore, S., Gremaud, P., Tran, H.T., Ottesen, J.T., Mehlsen, J., Olufsen, M.S.: Cardiovascular dynamics during head-up tilt assessed via pulsatile and non-pulsatile models. J. Math. Biol. 79(3), 987–1014 (2019)
Park, J.H., Gorky, J., Ogunnaike, B., Vadigepalli, R., Schwaber, J.S.: Investigating the effects of brainstem neuronal adaptation on cardiovascular homeostasis. Front. Neurosci. 14, 470 (2020)
Lodi, C.A., Ursino, M.: Hemodynamic effect of cerebral vasospasm in humans: a modeling study. Ann. Biomed. Eng. 27(2), 257–273 (1999)
Cornelissen, A.J., Dankelman, J., VanBavel, E., Stassen, H.G., Spaan, J.A.: Myeogenic reactivity and resistance distribution in the coronary arterial tree: a model study. Am. J. Physiol.-Heart Circ. Physiol. 278(5), H1490–H1499 (2000)
Melchior, F.M., Srinivasan, R.S., Charles, J.B.: Mathematical modeling of human cardiovascular system for simulation of orthostatic response. Am. J. Physiol.-Heart Circ. Physiol. 262(6), H1920–H1933 (1992)
Ardell, J.L., Rajendran, P.S., Nier, H.A., KenKnight, B.H., Armour, J.A.: Central-peripheral neural network interactions evoked by vagus nerve stimulation: functional consequences on control of cardiac function. Am. J. Physiol.-Heart Circ. Physiol. 309(10), H1740–H1752 (2015)
Freeman, R.: Neurogenic orthostatic hypotension. N. Engl. J. Med. 358(6), 615–624 (2008)
Sturdy, J., Ottesen, J.T., Olufsen, M.S.: Modeling the differentiation of A-and C-type baroreceptor firing patterns. J. Comput. Neurosci. 42(1), 11–30 (2017)
Molkov, Y.: Baroreflex Models, pp. 307–315. Springer, New York (2015)
Wake, E., Brack, K.: Characterization of the intrinsic cardiac nervous system. Auton. Neurosci. 199, 3–16 (2016)
Djabella, K., Médigue, C., Sorine, M.: A differential model of the baroreflex control of the cardiovascular system during a tilt test. In: Proceedings of the 44th IEEE Conference on Decision and Control, pp. 903–908. IEEE (2005)
Chen, S., Ferreira, A., Simaan, M.A., Antaki, J.F.: A mathematical model of a cardiovascular system regulated by the baroreflex. In: 2006 American Control Conference, p. 6. IEEE (2006)
Ojeda, D., Le Rolle, V., Rossel, O., Karam, N., Hagège, A., Bonnet, J.-L., Mabo, P., Carrault, G., Hernández, A.I.: Analysis of a baroreflex model for the study of the chronotropic response to vagal nerve stimulation. In: 2015 7th International IEEE/EMBS Conference on Neural Engineering (NER), pp. 541–544. IEEE (2015)
Dan, A., Dragomir, T.: State feedback control models for the cardiovascular system in constant exercise scenario. In: 2018 IEEE 12th International Symposium on Applied Computational Intelligence and Informatics (SACI), pp. 000285–000290 IEEE (2018)
Berger, R.D., Saul, J.P., Cohen, R.J.: Transfer function analysis of autonomic regulation. I. Canine atrial rate response. Am. J. Physiol.-Heart Circ. Physiol. 256(1), H142–H152 (1989)
Zenker, S., Rubin, J., Clermont, G.: From inverse problems in mathematical physiology to quantitative differential diagnoses. PLoS Comput. Biol. 3(11), e204 (2007)
Johnson, J.M., Rowell, L.B., Niederberger, M., Eisman, M.M.: Human splanchnic and forearm vasoconstrictor responses to reductions of right atrial and aortic pressures. Circ. Res. 34(4), 515–524 (1974)
Mancia, G., Mark, A.L.: Arterial baroreflexes in humans. In: Shepherd JT., Abboud FM. (eds.) Handbook of physiology, Section 2: The Cardiovascular System, Bethesda. American Physiologic Society 1983, pp. 755–793 (2011)
Mark, A.L., Mancia, G.: Cardiopulmonary baroreflexes in humans. In: Shepherd JT., Abboud FM. (eds.) Handbook of physiology, Section 2: The Cardiovascular System, Bethesda. American Physiologic Society 1983, pp. 795–813 (2011)
Molkov, Y.I., Rubin, J.E., Rybak, I.A., Smith, J.C.: Computational models of the neural control of breathing. Wiley Interdiscip. Rev.: Syst. Biol. Med. 9(2), e1371 (2017)
Lin, J., Ngwompo, R.F., Tilley, D.G.: Development of a cardiopulmonary mathematical model incorporating a baro–chemoreceptor reflex control system. Proc. Inst. Mech. Eng. Part H: J. Eng. Med. 226(10), 787–803 (2012)
Seki, A., Green, H.R., Lee, T.D., Hong, L., Tan, J., Vinters, H.V., Chen, P.-S., Fishbein, M.C.: Sympathetic nerve fibers in human cervical and thoracic vagus nerves. Heart Rhythm 11(8), 1411–1417 (2014)
Noller, C.M., Levine, Y., Urakov, T., Aronson, J., Nash, M.: Vagus nerve stimulation in rodent models: an overview of technical considerations. Front. Neurosci. 13, 911 (2019)
Qing, K.Y., Wasilczuk, K.M., Ward, M.P., Phillips, E.H., Vlachos, P.P., Goergen, C.J., Irazoqui, P.P.: B fibers are the best predictors of cardiac activity during vagus nerve stimulation. Bioelectron. Med. 4(1), 5 (2018)
Krahl, S.E., Senanayake, S.S., Handforth, A.: Destruction of peripheral c-fibers does not alter subsequent vagus nerve stimulation-induced seizure suppression in rats. Epilepsia 42(5), 586–589 (2001)
Stakenborg, N., Gomez-Pinilla, P.J., Verlinden, T.J., Wolthuis, A.M., D’Hoore, A., Farré, R., Herijgers, P., Matteoli, G., Boeckxstaens, G.E.: Comparison between the cervical and abdominal vagus nerves in mice, pigs, and humans. Neurogastroenterol. Motil. 32, e13889 (2020)
Howland, R.H.: Vagus nerve stimulation. Curr. Behav. Neurosci. Rep. 1(2), 64–73 (2014)
Helmers, S., Begnaud, J., Cowley, A., Corwin, H., Edwards, J., Holder, D., Kostov, H., Larsson, P., Levisohn, P., De Menezes, M., et al.: Application of a computational model of vagus nerve stimulation. Acta Neurol. Scand. 126(5), 336–343 (2012)
Mourdoukoutas, A.P., Truong, D.Q., Adair, D.K., Simon, B.J., Bikson, M.: High-resolution multi-scale computational model for non-invasive cervical vagus nerve stimulation. Neuromodulation: Technol. Neural Interface 21(3), 261–268 (2018)
Warner, H.R., Russell R. Jr: Effect of combined sympathetic and vagal stimulation on heart rate in the dog. Circ. Res. 24(4), 567–573 (1969)
Kember, G., Ardell, J.L., Armour, J.A., Zamir, M.: Vagal nerve stimulation therapy: what is being stimulated? PLoS One 9(12), e114498 (2014)
Yao, Y., Kothare, M.V.: Model predictive control of selective vagal nerve stimulation for regulating cardiovascular system. In: 2020 American Control Conference (ACC), pp. 563–568. IEEE (2020)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Appendix
Appendix
Rights and permissions
Copyright information
© 2023 Springer Nature Singapore Pte Ltd.
About this entry
Cite this entry
Yao, Y., Kothare, M.V., Thakor, N.V. (2023). Models for Closed-Loop Cardiac Control Using Vagal Nerve Stimulation. In: Thakor, N.V. (eds) Handbook of Neuroengineering. Springer, Singapore. https://doi.org/10.1007/978-981-16-5540-1_123
Download citation
DOI: https://doi.org/10.1007/978-981-16-5540-1_123
Published:
Publisher Name: Springer, Singapore
Print ISBN: 978-981-16-5539-5
Online ISBN: 978-981-16-5540-1
eBook Packages: EngineeringReference Module Computer Science and Engineering