title: A mathematical model of coronary blood flow control: simulation of patient-specific three-dimensional hemodynamics during exercise.
abstract: This work presents a mathematical model of the metabolic feedback and adrenergic feedforward control of coronary blood flow that occur during variations in the cardiac workload. It is based on the physiological observations that coronary blood flow closely follows myocardial oxygen demand, that myocardial oxygen debts are repaid, and that control oscillations occur when the system is perturbed and so are phenomenological in nature. Using clinical data, we demonstrate that the model can provide patient-specific estimates of coronary blood flow changes between rest and exercise, requiring only the patient's heart rate and peak aortic pressure as input. The model can be used in zero-dimensional lumped parameter network studies or as a boundary condition for three-dimensional multidomain Navier-Stokes blood flow simulations. For the first time, this model provides feedback control of the coronary vascular resistance, which can be used to enhance the physiological accuracy of any hemodynamic simulation, which includes both a heart model and coronary arteries. This has particular relevance to patient-specific simulation for which heart rate and aortic pressure recordings are available. In addition to providing a simulation tool, under our assumptions, the derivation of our model shows that β-feedforward control of the coronary microvascular resistance is a mathematical necessity and that the metabolic feedback control must be dependent on two error signals: the historical myocardial oxygen debt, and the instantaneous myocardial oxygen deficit.
authors.affiliation: Division of Imaging Sciences and Biomedical Engineering, King's College London, King's Health Partners, St. Thomas' Hospital, London, United Kingdom; christopher.arthurs@kcl.ac.uk.
authors.forename: Christopher J
authors.identifier: 0000-0002-0448-6146
authors.initials: CJ
authors.lastname: Arthurs
authors.affiliation: Division of Imaging Sciences and Biomedical Engineering, King's College London, King's Health Partners, St. Thomas' Hospital, London, United Kingdom; Departments of Surgery and Biomedical Engineering, University of Michigan, Ann Arbor, Michigan.
authors.forename: Kevin D
authors.initials: KD
authors.lastname: Lau
authors.affiliation: King's College London British Heart Foundation Centre of Excellence, The Rayne Institute, St. Thomas' Hospital Campus, London, United Kingdom; and.
authors.forename: Kaleab N
authors.initials: KN
authors.lastname: Asrress
authors.affiliation: King's College London British Heart Foundation Centre of Excellence, The Rayne Institute, St. Thomas' Hospital Campus, London, United Kingdom; and.
authors.forename: Simon R
authors.initials: SR
authors.lastname: Redwood
authors.affiliation: Division of Imaging Sciences and Biomedical Engineering, King's College London, King's Health Partners, St. Thomas' Hospital, London, United Kingdom; Departments of Surgery and Biomedical Engineering, University of Michigan, Ann Arbor, Michigan.
authors.forename: C Alberto
authors.initials: CA
authors.lastname: Figueroa
mesh_terms: D000222:Adaptation, Physiological; D062186:Arterial Pressure; D001341:Autonomic Nervous System / Q000502:physiology; D003198:Computer Simulation; D003326:Coronary Circulation; D003331:Coronary Vessels / Q000294:innervation / Q000502:physiology*; D015444:Exercise; D006339:Heart Rate; D006439:Hemodynamics; D006801:Humans; D008955:Models, Cardiovascular; D009119:Muscle Contraction; D018482:Muscle, Skeletal / Q000378:metabolism / Q000502:physiology*; D009206:Myocardium / Q000378:metabolism; D010100:Oxygen / Q000097:blood; D010101:Oxygen Consumption; D013997:Time Factors; D014655:Vascular Resistance
chemical_list: D010100:Oxygen
keywords: autonomic control; coronary flow; exercise; mathematical model; metabolic control