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Pulmonary Artery Viscoelastic Properties:
Buffering Function Characterization

Bia Daniel1, Gamero Lucas2, Grignola Juan C.1,
Rodríguez Muriel1, Núñez Luis1,
Armentano Ricardo L. 1,2, Ginés Fernando1

1 Dpto. de Fisiología, Facultad de Medicina, Montevideo, Uruguay.
2
Universidad Favaloro, Bs. As., Argentina

SUMMARY
Introduction: Large arterial buffering function (BF) can be estimated by arterial wall mechanical properties: elasticity (E), viscosity (h), and inertia (M) and by the harmonic content of their frequency response (Dw). To our knowledge, no study regarding the assessment of the pulmonary artery (PA) BF has been reported.
Objective: Our aim was to characterized the PA BF by estimating its E, h, M and Dw.
Material and methods: Pulmonary pressure (Konigsberg) and external diameter (sonomicrometer) were measured in six anesthetized (pentobarbital 35 mg/kg i.v.) sheep. A linear autoregressive moving average (ARMA) model was applied to the input-output (pressure-diameter) data in order to estimate E, h y M and Dw.
Results: Grouped data (mean±SD) obtained from a series of 20 beats averaged of each animal is showed in the following Table 1

Conclusions: The PA wall is a viscoelastic material with no despreciable mass. The PA frequency response showed a low pass filter performance, more selective than the aortic and carotid arteries previously reported. Considering a mean heart rate of 2 Hz, a significant number of 8 harmonics are involve in the pulmonary low pass filtering performance. The PA BF characterization could be useful to characterize right ventricular hydraulic load and its ventricular-vascular coupling.

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INTRODUCTION
   It is know that the large arteries have two distinct interrelated major functions: a) to be a low resistance blood distribution conduits to the peripheral organs, named conduit function, and b) to smooth the pressure and flow pulsatility, in order to transform it into an almost continuous arteriolo-capilary flow and pressure, named the buffer function (BF) [1, 2, 3, 7]. The latter has benefits to the heart as well as to the arterial system itself: a) it decreases heart work and the developed myocardial tension during systole; b) it decreases the arterial wall pulsatile stress, since it decreases flow and pressure systolic-diastolic changes; c) it allows to obtain an almost continuous capillary blood flow during the cardiac cycle [1, 3, 4]. Therefore, the BF exerts a protective cardiovascular action [1, 2, 3, 7]. It can be characterized by the arterial wall viscoelastic properties: elasticity (E), viscosity (h), and inertia (M) [3, 5, 6] and by the harmonic content of their band width (Dw) (its frequency response) [14], and can be modeled by studying the wall arterial system transfer function as a filter device [14].

   Today there is a growing interest in the physical properties of larges arteries, because an accurate characterization of these arteries behavior could contribute to a better understanding of the hemodynamic alterations accompanying cardiovascular diseases [4]. To evaluate the physiology and pathophysiology of the large arteries BF, a complete characterization of the arterial wall mechanical is necessary [5, 6, 8, 9]. The adaptative modeling has been used to the systemic arteries dynamic characterization in several animals models [13, 14]. Like the systemic circulation, the pulmonary circulation receives the same blood flow from the heart with the same periodicity [3]. However, there are many structural and physiological differences between both vascular beds (higher pulmonary arterial distensibility, less wall thickness, no-well developed arterioles, lower peripheral reflection coefficient, absence of increasing stiffness between central and peripheral sites, shorter path lengths along vascular segments) that impedes the extrapolation of the systemic wall arteries mechanical properties to the pulmonary artery (PA) [3].

    To our knowledge, no study regarding the assessment of PA BF in vivo using a frequency analysis has been reported.

OBJECTIVE
   Our aim was to characterize the PA mechanical properties by estimating the arterial wall E, h, M, and to determine its BF by the Dw and the natural frequency (wn).

MATERIAL AND METHODS
   Pulmonary pressure (Konigsberg) and external diameter (Sonomicrometer) were measured in six anesthetized sheep (25-38 kg) (pentobarbital 35 mg/kg i.v.). All data were digitized at 200 Hz by a burst sampling and filtered by a 50 Hz low-pass filter by means of a hardware developed in our laboratory. The delay between the signals was only 50 µsec. The linear autoregressive moving average (ARMA) discrete time model was applied to the input-output (pressure-diameter) data in order to assess the arterial wall dynamics [13, 14]. The model was evaluated using the mean of best-fit order ARMA models over all the cases considered [10, 11, 12, 13, 14]. The inverse bilinear transformation was applied to in order to obtain a continuous transfer function [10, 11, 12,13, 14]. E, h and M indexes were obtained by using bilinear transformation [13, 14]. The arterial wall natural frequency (wn) was estimated by a second order continuous model approximation of the pressure-diameter relationship, using these mechanical parameters [13, 14]. The PA band width (Dw) was estimated using the general third order ARMA model structure since it determines the system frequency response more exactly. The cutting frequency was defined at a 70,7% decrease of the initial transfer function value. Grouped data was expressed as mean±SD [13, 14].

RESULTS
   Mean pulmonary arterial pressure was 13.1±5.7 mmHg, and heart rate was closed to 2 Hz. Grouped data obtained from a series of 20 beats averaged of each animal is showed in the table 1. When the pressure-diameter relation is evaluated in the frequency domain, the complex elastic modulus (1/E(jw)) obtained from the ARMA model is shown to be frequency dependent. Its modulus derived from the simplified second order model. Figure 1 shows the frequency response averaged derived from the simplified second order model (E, h and M). The band width obtained from the third order ARMA model, was 17±4 Hz and wn was 8±2.1 Hz. (Table 1) (Figure 1)

DISCUSSION
   This work provides a complete in vivo characterization of the PA mechanical properties, by means of a lineal discrete time parametric model (ARMA), from the pressure-diameter measured. The model parameters, elasticity, viscosity and inertia, characterize the mechanical behavior of the studied system. The PA wall is a viscoelastic material of not negligible mass. The frequency response characterizes the PA BF and corresponds of a low pass filter with a natural frequency of 8 Hz and a band width of 17±4 Hz, which are more selective than previously reported for aorta and carotid arteries [14]. Considering a mean heart rate of 2 Hz, in a optimal performance a significant number of 8 harmonics are involve in the PA low pass filtering performance.

   The PA higher BF than systemic arteries secondary to its more selective band width, could be an adaptative feature to counterbalance its no-well developed arterioles and its shorter vascular length in order to maintain a relative low capillary pulsatility and an optimal respiratory gases exchange. Also, taking into account the direct relation between the filter bandwidth and its temporal response (the higher band width, the faster temporal response), the PA narrow band width could determine a slow temporal response.

CONCLUSIONS
   Since PA represents the right ventricular hydraulic load, its dynamic characterization (given by E, h, M and BF), will contribute to a better understanding of the right ventricular-arterial coupling and several clinical situations that modify the PA wall structure and function (pulmonary thromboembolism, congenital heart disease, postoperative heart surgery, orthotopic heart transplant).

REFERENCES

1. Yin CPF, 1987. Ventricular/Vascular Coupling: Clinical, physiological and engineering aspects. New York, Springer-Verlag, 1987.

2. LondonGM, 1997.Large arteries haemodynamics:conduit versus cushioning function.Blood Press Suppl 1997;2:48-51

3. Wilmer W. Nichols, Michael F O`Rourke. McDonald`s Blood Flow in Arteries. Theoretical, experimental and clinical principles. Fourth Edition. 1998.

4. Simon A, Levenson J, 1986. La compliance artèrielle joue-t-elle un ròle dans la physiopathologie de l'hypertension artérielle? [Does arterial compliance play a role in the physiopathology of hypertension]? La Presse Médicale, 20 décembre 1986, 15(45):2243-6

5. Armentano RL, Barra JG., Levenson J, Simon A, Pichel RH: Arterial wall mechanics in conscious dogs: assessment of viscous, inertial, and elastic moduli to characterize the aortic wall behavior. Circ Res 1995;76:468-478)

6. J.G. Barra, R.L. Armentano, J.Levenson, E. Cabrera Fischer, R.Pichel, A.Simon, 1993. "Assessment of smooth muscle contribution to descending thoracic aortic elastic mechanics in conscious dogs", Circ. Research, vol. 73, pp. 1040-1050, 1993.

7. M. F. O'Rourke, 1995. "Second workshop on structure and function of large arteries. Part I. Mechanical principles in arterial disease", Hypertension, vol. 26, pp. 2- 9, 1995.

8. Armentano RL, Megnien LJ, Simon A, Bellenfant F, Barra JG, Levenson J. Effects of hypertension on viscoelasticity of carotid and femoral arteries in humans. Hypertension 1995; 26:48-54

9. Gamero LG, Armentano RL, Barra JG, Levenson J, Pichel H. Non-invasive Single Beat Modeling of Human Carotid Properties in Hypertension. Computers in Cardiology, IEEE Press, 1987; 24:449-452

10. Ljung L. System Identification. Theory for the user. Prentice Hall, 1987.

11. Akaike H. Fitting autoregressive models for prediction. Ann. Inst. Stat. Math, 1969; 21:243-247

12. R.L. Armentano, M Risk, J. Fochesatto. Análisis de Señales y Sistemas: Tomo II : Fundamentos y Aplicaciones. Ed. Rocamora. Buenos Aires. Argentina. 1997

13. L. G. Gamero, R. L. Armentano, J. G. Barra, J. Levenson.1999. Modelado e identificación adaptativa para la evaluación del filtrado hidráulico aórtico: efecto de la activación y de la hipertensión renovascular. Anales del XII Congreso Argentino de Bioingeniería, Buenos Aires. Argentina. 1999.

14. Ricardo Armentano. Tesis de Doctor de l'Université de Paris VII. Denis Diderot. Doctorat de Biomecanique: Mecanique de systèmes biologiques. Détermination in vivo des caractéristiques hémodynamiques artérielles, application a l'hypertension Noviembre de 1999.

 

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2nd Virtual Congress of Cardiology

Dr. Florencio Garófalo
Steering Committee
President
Dr. Raúl Bretal
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President
Dr. Armando Pacher
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President
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Copyright© 1999-2001 Argentine Federation of Cardiology
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