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Models for Closed-Loop Cardiac Control Using Vagal Nerve Stimulation

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Handbook of Neuroengineering

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.

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References

  1. 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)

    Google Scholar 

  2. 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)

    Google Scholar 

  3. 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)

    Google Scholar 

  4. 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)

    Google Scholar 

  5. 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)

    Google Scholar 

  6. 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)

    Google Scholar 

  7. 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)

    Google Scholar 

  8. 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)

    Google Scholar 

  9. 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)

    Google Scholar 

  10. 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)

    Google Scholar 

  11. Mudd, J.O., Kass, D.A.: Tackling heart failure in the twenty-first century. Nature 451(7181), 919–928 (2008)

    Google Scholar 

  12. 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)

    Google Scholar 

  13. 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)

    Google Scholar 

  14. 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)

    Google Scholar 

  15. 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)

    Google Scholar 

  16. 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)

    Google Scholar 

  17. 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)

    Google Scholar 

  18. Bilbao, A., Escobar, A., García-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)

    Google Scholar 

  19. 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)

    Google Scholar 

  20. 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)

    Google Scholar 

  21. 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)

    Google Scholar 

  22. 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)

    Google Scholar 

  23. 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)

    Google Scholar 

  24. 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)

    Google Scholar 

  25. 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)

    Google Scholar 

  26. 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)

    Google Scholar 

  27. Bequette, B.W.: Challenges and recent progress in the development of a closed-loop artificial pancreas. Annu. Rev. Control 36(2), 255–266 (2012)

    Google Scholar 

  28. Robert, R.: Model–based development of neuroprostheses for paraplegic patients. Philos. Trans. R. Soc. Lond. Ser. B: Biol. Sci. 354(1385), 877–894 (1999)

    Google Scholar 

  29. 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)

    Google Scholar 

  30. Noble, D.: A modification of the hodgkin-huxley equations applicable to purkinje fibre action and pacemaker potentials. J. Physiol. 160(2), 317–352 (1962)

    Article  Google Scholar 

  31. 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)

    Google Scholar 

  32. Beeler, G.W., Reuter, H.: Reconstruction of the action potential of ventricular myocardial fibres. J. Physiol. 268(1), 177–210 (1977)

    Google Scholar 

  33. 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)

    Google Scholar 

  34. Priebe, L., Beuckelmann, D.J.: Simulation study of cellular electric properties in heart failure. Circ. Res. 82(11), 1206–1223 (1998)

    Google Scholar 

  35. 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)

    Google Scholar 

  36. 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)

    Google Scholar 

  37. 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)

    Google Scholar 

  38. 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)

    Google Scholar 

  39. 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)

    Google Scholar 

  40. 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)

    Google Scholar 

  41. 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)

    Google Scholar 

  42. FitzHugh, R.: Impulses and physiological states in theoretical models of nerve membrane. Biophys. J. 1(6), 445 (1961)

    Google Scholar 

  43. 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)

    MATH  Google Scholar 

  44. 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)

    Google Scholar 

  45. 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)

    Google Scholar 

  46. El Houari, K.: Modeling and Imaging of Electrocardiographic Activity. PhD thesis (2018)

    Google Scholar 

  47. Panfilov, A., Keener, J.: Re-entry in an anatomical model of the heart. Chaos Solitons Fractals 5(3–4), 681–689 (1995)

    MATH  Google Scholar 

  48. Gray, R., Jalife, J.: Ventricular fibrillation and atrial fibrillation are two different beasts. Chaos: Interdiscip. J. Nonlinear Sci. 8(1), 65–78 (1998)

    MATH  Google Scholar 

  49. Miller, W.T., Geselowitz, D.B.: Simulation studies of the electrocardiogram. I. The normal heart. Circ. Res. 43(2), 301–315 (1978)

    Google Scholar 

  50. 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)

    Google Scholar 

  51. 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)

    Google Scholar 

  52. 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)

    Google Scholar 

  53. Ursino, M.: Interaction between carotid baroregulation and the pulsating heart: a mathematical model. Am. J. Physiol.-Heart Circ. Physiol. 275(5), H1733–H1747 (1998)

    Google Scholar 

  54. Ursino, M.: A mathematical model of the carotid baroregulation in pulsating conditions. IEEE Trans. Biomed. Eng. 46(4), 382–392 (1999)

    Google Scholar 

  55. 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)

    Google Scholar 

  56. 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)

    Google Scholar 

  57. Li, J.K.: The Arterial Circulation: Physical Principles and Clinical Applications. Springer Science & Business Media, Totowa, Humana Press (2000)

    Google Scholar 

  58. Guyton, A.C., Coleman, T.G., Granger, H.J.: Circulation: overall regulation. Annu. Rev. Physiol. 34(1), 13–44 (1972)

    Google Scholar 

  59. Westerhof, N., Lankhaar, J.-W., Westerhof, B.E.: The arterial windkessel. Med. Biol. Eng. Comput. 47(2), 131–141 (2009)

    Google Scholar 

  60. 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)

    Google Scholar 

  61. 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)

    MathSciNet  Google Scholar 

  62. 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)

    Google Scholar 

  63. 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)

    MathSciNet  Google Scholar 

  64. 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)

    Google Scholar 

  65. Magosso, E., Ursino, M.: Cardiovascular response to dynamic aerobic exercise: a mathematical model. Med. Biol. Eng. Comput. 40(6), 660–674 (2002)

    Google Scholar 

  66. 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)

    Google Scholar 

  67. 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)

    Google Scholar 

  68. Barnea, O., Moore, T., Dubin, S., Jaron, D.: Cardiac energy considerations during intraaortic balloon pumping. IEEE Trans. Biomed. Eng. 37(2), 170–181 (1990)

    Google Scholar 

  69. 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)

    Google Scholar 

  70. 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)

    Google Scholar 

  71. 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)

    Google Scholar 

  72. 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)

    MathSciNet  MATH  Google Scholar 

  73. Codrean, A., Dragomir, T.-L.: Averaged modeling of the cardiovascular system. In: 52nd IEEE Conference on Decision and Control, pp. 2066–2071. IEEE (2013)

    Google Scholar 

  74. 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)

    Google Scholar 

  75. 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)

    Google Scholar 

  76. 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)

    Google Scholar 

  77. 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)

    Google Scholar 

  78. 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)

    Google Scholar 

  79. 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)

    Google Scholar 

  80. 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)

    Google Scholar 

  81. Artiles, A.D., Heldt, T., Young, L.R.: Effects of artificial gravity on the cardiovascular system: computational approach. Acta Astronaut. 126, 395–410 (2016)

    Google Scholar 

  82. 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)

    MathSciNet  MATH  Google Scholar 

  83. 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)

    Google Scholar 

  84. 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)

    Google Scholar 

  85. Lodi, C.A., Ursino, M.: Hemodynamic effect of cerebral vasospasm in humans: a modeling study. Ann. Biomed. Eng. 27(2), 257–273 (1999)

    Google Scholar 

  86. 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)

    Google Scholar 

  87. 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)

    Google Scholar 

  88. 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)

    Google Scholar 

  89. Freeman, R.: Neurogenic orthostatic hypotension. N. Engl. J. Med. 358(6), 615–624 (2008)

    Google Scholar 

  90. 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)

    MATH  Google Scholar 

  91. Molkov, Y.: Baroreflex Models, pp. 307–315. Springer, New York (2015)

    Google Scholar 

  92. Wake, E., Brack, K.: Characterization of the intrinsic cardiac nervous system. Auton. Neurosci. 199, 3–16 (2016)

    Google Scholar 

  93. 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)

    Google Scholar 

  94. 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)

    Google Scholar 

  95. 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)

    Google Scholar 

  96. 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)

    Google Scholar 

  97. 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)

    Google Scholar 

  98. Zenker, S., Rubin, J., Clermont, G.: From inverse problems in mathematical physiology to quantitative differential diagnoses. PLoS Comput. Biol. 3(11), e204 (2007)

    MathSciNet  Google Scholar 

  99. 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)

    Google Scholar 

  100. 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)

    Google Scholar 

  101. 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)

    Google Scholar 

  102. 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)

    Google Scholar 

  103. 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)

    Google Scholar 

  104. 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)

    Google Scholar 

  105. 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)

    Google Scholar 

  106. 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)

    Google Scholar 

  107. 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)

    Google Scholar 

  108. 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)

    Google Scholar 

  109. Howland, R.H.: Vagus nerve stimulation. Curr. Behav. Neurosci. Rep. 1(2), 64–73 (2014)

    Google Scholar 

  110. 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)

    Google Scholar 

  111. 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)

    Google Scholar 

  112. 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)

    Google Scholar 

  113. Kember, G., Ardell, J.L., Armour, J.A., Zamir, M.: Vagal nerve stimulation therapy: what is being stimulated? PLoS One 9(12), e114498 (2014)

    Google Scholar 

  114. 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)

    Google Scholar 

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Correspondence to Mayuresh V. Kothare .

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Table 4 List of Abbreviations

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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

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