On the clinical estimation of the hemodynamical and mechanical properties of the arterial tree

Cardiovascular diseases are the major cause of death globally, thus, a reliable estimation of the risk on cardiovascular diseases is essential. Arterial stiffness is an independent predictor of cardiovascular risk. It can be assessed in clinical practice either locally, from arterial distensibility, or globally (averaged over an arterial segment), from the velocity of the blood pressure wave. However, arterial stiffness differs between arteries and increases towards the peripheries. Furthermore, the current methods neglect the complex hemo-dynamic phenomena governing the blood pressure and blood volume flow in the arterial system. The aim of the present research is to develop a strategy to estimate distributed arterial mechanical properties for (parts of) the arterial tree. For that purpose, ultrasound measurements of blood velocity and change in vessel wall diameter at multiple locations are combined with the results of subject specific computational fluid dynamics simulations to compose a comprehensive model of the hemodynamics, e.g. in a limb. Lumped parameter or one dimensional wave propagation models are applied to study the complex wave propagation phenomena in the arterial system. However, since the mechanical properties of the arterial wall are required as model input, these models cannot be used to directly estimate arterial stiffness. Nevertheless, the arterial mechanical properties can be estimated in a reverse process, in which the model output, expressed by the blood volume flow and blood pressure waveforms, is compared with the corresponding measurements. Input parameters are then optimized until the best fit is obtained between measured and simulated blood volume flow and blood pressure waveforms. This approach yields a distributed arterial stiffness along the arterial tree. In this research the approach described above is applied to the arm arterial tree. The model input consists of the blood volume flow waveform in the brachial artery. To obtain the required model input and initial parameter values as well as the measurements needed in the fitting process, accurate estimates of the arterial wall distension and blood volume flow are required at a limited number of locations along the arterial tree. Blood volume flow can be estimated from measured blood velocity and lumen diameter. In Chapter 2, the blood volume flow estimation methods based on Poiseuille (parabolic profile) and Womersley were compared. It is shown that, compared with Womersley, blood volume flow estimation assuming Poiseuille profiles significantly underestimates the dynamical properties of the blood volume flow waveform. However, Womersley profiles are only valid for long and straight arteries with a symmetric velocity distribution across the lumen. Therefore, in Chapter 3 an alternative method for blood volume flow estimation is presented, which can also deal with an asymmetric velocity distribution and, hence, can be applied in curved arteries. The new method is based on the integration of the axial velocity distribution across an artery. It is demonstrated that this method gives a better approximation of the blood volume flow waveform than methods based on Poiseuille or Womersley profiles. Based on multiple ultrasound measurements and a subject specific wave propagation model, an optimization scheme was developed to estimate the distributed arterial mechanical properties in the arm. A fitting procedure, based on local sensitivity indexes, has been developed in Chapter 4. The estimated arterial Young’s moduli, for 6 volunteers, range from 1.0 to 6.0 MPa with an average of (3.8 ± 1.7) MPa for the brachial artery and from 1.2 to 7.8 MPa with an average of (4.8 ± 2.2) MPa for the radial artery. The good match between measured and simulated waveforms and the realistic stiffness parameters indicate good in-vivo suitability. The proposed patient-specific modelling requires many in-vivo measurements implying long measurement times. It would be of great interest to identify those input parameters that have the largest impact on the optimization protocol. For that purpose, in Chapter 5 a Monte-Carlo study, constructed with 3000 model evaluations, has been performed. This resulted in estimates for the global sensitivity indices of a large number of parameters in a wide range of input and output values. The sensitivity indices suggest that the majority of the input parameters are significantly influencing the output, with the Young modulus (E) having the largest influence and the arterial lengths the lowest. The results suggest that imaging techniques with high temporal and spacial resolution should be preferred. We can conclude that the reverse modelling method, employing a combination of a wave propagation model and specific ultrasound measurements, is suitable to estimate the distributed arterial mechanical properties. However, to achieve clinical applicability, the optimization scheme needs some improvement by a further reduction of measurement uncertainties or the inclusion of measurement uncertainty in the fitting procedure. We can conclude that the reverse modelling method, employing a combination of a wave propagation model and specific ultrasound measurements, is suitable to estimate the distributed arterial mechanical properties. However, to achieve clinical applicability, the optimization scheme needs some improvement by a further reduction of measurement uncertainties or the inclusion of measurement uncertainty in the fitting procedure.