- Email: [email protected]
Response from Dr. Giller
Letters to the Editor-in-Chief Noninvasive method for determination of arterial compliance using doppler echocardiography and subclavian pulse tracings. Circulation 1994;89:2688 –2699. Nichols WW, O’Rourke MF. McDonald’s blood flow in arteries. 3rd ed. London: Edward Arnold, 1990. Riley WA, Barnes RW, Evans GW, Burke GL. Ultrasonic measurement of the elastic modulus of the common carotid artery. Stroke 1992;23:952–956. Tortoli P, Guidi G, Guidi F, Menicucci C, Atzeni C, Muchada R. Detection of vascular haemodynamics through a high speed velocity profiler. Eur J Ultrasound 1999;9:231–244. Yates FE. Good manners in good modeling: mathematical models and
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computer simulations of physiological systems. Am J Physiol 1978; R159 –R160. Yoshigi M, Keller BB. Characterization of embryonic aortic impedance with lumped parameter models. Am J Physiol 1997;273:H19 –H27.
ROBERTO BURATTINI Department of Electronics and Automatics University of Ancona Via Brecce Bianche 60131 Ancona, Italy Received 7 April 2000
PII: S0301-5629(00)00257-X
RESPONSE FROM DR. GILLER To the Editor-in-Chief: We appreciate the keen interest that Dr. Burattini has shown our article regarding development of an impedance index for the cerebral circulation. Unfortunately, we feel that he has chosen to misunderstand many points of this work. In this article, we proposed that an “impedance index” could be calculated using TCD signals in place of flow and noninvasive carotid pressures in place of arterial line pressures in the calculations. We established the shape of the impedance curve for healthy subjects, and showed that the shape changed, developing a peak at the second or third harmonic, for patients with significant vasospasm. As is true for extracranial sites, the origin of these peaks in impedance curves is of great interest because they can indicate the presence of reflected waves from the periphery. Calculations of distances, however, argued against this being the origin of the peaks in the impedance curves. When we looked at a simple model of the cerebral circulation, we found that peaks could be recreated by weighting the inductance term, and showed that this weighting, in fact, occurred in vasospasm. The model then showed that peaks could occur because of a “tuning” between the capacitative and inductive components of the circulation, rather than from reflections from the periphery. The model was not developed to make quantitative clinical predictions, but was extremely helpful in understanding the dynamic aspects of our data.
Dr. Burattini suggests that the only useful models are those that are strictly quantitative. However, some of the more useful models developed recently are qualitative in nature (for example, those dealing with chaotic behavior and oscillations), and many quantitative models lead to hopeless confusion in understanding complex data. We feel that adherence to Dr. Burattini’s rigid restriction of what constitutes a useful model is harmful and would lead to a loss of valuable insights. We also do not agree with Dr. Burattini’s interpretation of the various pressures calculated from the model. It is wellknown that the pressure drop across the more distal arteriolar bed is greater than the drop across the more proximal larger vessels. Furthermore, we interpret these pressure drops as the pressure drop across the vascular system, rather than transmural pressure. In any case, we disagree that these correspondences are one-to-one because it is only the resemblance of the linearized version of the Navier–Stokes equations to the electrical analogs that allows the pressure and flow data to be compared with the voltage and current.
PII: S0301-5629(00)00258-1
COLE A. GILLER University of Texas Southwestern Medical Center Department of Neurosurgery 5323 Harry Hines Blvd Dallas, TX 75235-8855, USA
1201
computer simulations of physiological systems. Am J Physiol 1978; R159 –R160. Yoshigi M, Keller BB. Characterization of embryonic aortic impedance with lumped parameter models. Am J Physiol 1997;273:H19 –H27.
ROBERTO BURATTINI Department of Electronics and Automatics University of Ancona Via Brecce Bianche 60131 Ancona, Italy Received 7 April 2000
PII: S0301-5629(00)00257-X
RESPONSE FROM DR. GILLER To the Editor-in-Chief: We appreciate the keen interest that Dr. Burattini has shown our article regarding development of an impedance index for the cerebral circulation. Unfortunately, we feel that he has chosen to misunderstand many points of this work. In this article, we proposed that an “impedance index” could be calculated using TCD signals in place of flow and noninvasive carotid pressures in place of arterial line pressures in the calculations. We established the shape of the impedance curve for healthy subjects, and showed that the shape changed, developing a peak at the second or third harmonic, for patients with significant vasospasm. As is true for extracranial sites, the origin of these peaks in impedance curves is of great interest because they can indicate the presence of reflected waves from the periphery. Calculations of distances, however, argued against this being the origin of the peaks in the impedance curves. When we looked at a simple model of the cerebral circulation, we found that peaks could be recreated by weighting the inductance term, and showed that this weighting, in fact, occurred in vasospasm. The model then showed that peaks could occur because of a “tuning” between the capacitative and inductive components of the circulation, rather than from reflections from the periphery. The model was not developed to make quantitative clinical predictions, but was extremely helpful in understanding the dynamic aspects of our data.
Dr. Burattini suggests that the only useful models are those that are strictly quantitative. However, some of the more useful models developed recently are qualitative in nature (for example, those dealing with chaotic behavior and oscillations), and many quantitative models lead to hopeless confusion in understanding complex data. We feel that adherence to Dr. Burattini’s rigid restriction of what constitutes a useful model is harmful and would lead to a loss of valuable insights. We also do not agree with Dr. Burattini’s interpretation of the various pressures calculated from the model. It is wellknown that the pressure drop across the more distal arteriolar bed is greater than the drop across the more proximal larger vessels. Furthermore, we interpret these pressure drops as the pressure drop across the vascular system, rather than transmural pressure. In any case, we disagree that these correspondences are one-to-one because it is only the resemblance of the linearized version of the Navier–Stokes equations to the electrical analogs that allows the pressure and flow data to be compared with the voltage and current.
PII: S0301-5629(00)00258-1
COLE A. GILLER University of Texas Southwestern Medical Center Department of Neurosurgery 5323 Harry Hines Blvd Dallas, TX 75235-8855, USA