Aortic dissection (AD), is a hazardous aortic disease with high mortality. The formation of AD is commonly initiated by the dilatation of the aorta or high blood pressures that tear the intima, allowing blood to flow into the aortic wall. The pulsatile pressure of the circulation then drives the blood. It separates the layers of the aortic wall, resulting in the formation of a true lumen and a false lumen [1] (figure 1.a). The false lumen represents the blood-filled space between the dissected layers of the aortic wall, while the true lumen is the usual passageway of blood.
The ADs are classified as Stanford type A (proximal) or B (distal) in the Stanford system (figure 1.b). If the ascending aorta is involved (Stanford type A), an acute condition with a high mortality rate within a few hours occurs in most cases due to the high blood pressure right after the aortic heart valve. On the other hand, Stanford type B cases (in the descending aorta) may become chronic, which means that the onset of the dissection dates back more than 14 days and patients can often be treated with medical therapy. In both cases, the symptoms of AD patients are sudden severe chest or upper back pain, which are not easily assignable to this disease.
Detecting an AD can be difficult because the symptoms are similar to those of a variety of health problems. Ultrasound Scanning (sonography), Magnetic Resonance Imaging (MRI) and Computerized Tomography (CT) are expensive techniques currently used for this purpose, with experts needed to read and interpret the images. Nevertheless, an easy to use and still reliable method for pre-identification of AD would be beneficial. Furthermore, tracking the development of the disease, such as false lumen expansion and false lumen thrombosis can be very helpful for the medical management of AD.
The presence of a false lumen alters the aortic haemodynamics and also changes the tissue distribution in the thorax. These changes can be identified and quantified by bioimpedance techniques such as impedance cardiography (ICG). In ICG, a current field longitudinally across a segment of the thorax is applied using a constant low magnitude and high-frequency alternating current. It is a non-invasive, safe, easy to use and low-cost method for measuring several cardiodynamic parameters (e.g. the Stroke Volume (SV) and the Cardiac Output (CO)) continuously [4]. Besides, this method is portable, and the analysis could be automated.
By injecting a low-amplitude alternating current into the thorax and measuring the voltage drop Δ
A 3D numerical simulation model is used to compute the impedance changes on the thorax surface in case of the type B aortic dissection. A sensitivity analysis through the Global Sensitivity Analysis (GSA) technique is applied to investigate different electrode configurations in the simulation model with different input parameters to cover as many patient-specific cases as the dimension of the input space. The final aim would be finding the desired electrode configuration, which gives the highest difference between the impedance cardiograms of the healthy condition and the ones with the AD.
The measured electrical impedance without respiratory or cardiac activity is known as static thoracic base impedance
By eliminating the oscillating cardiac-asynchronous respiratory component,
The volumetric expansion of the blood-filled aorta changes corresponding to the cardiac pulse wave. For the sake of simplicity, a spatial average time-dependent cross-sectional radius of the aorta has been used in the simulation model for two sections separately, the aortic arch and the descending aorta, see figure 2. The data are based on measurements provided in [11] from a young, healthy male volunteer at rest.
The electrical properties of resting blood mainly depend on the volume fraction of red blood cells (RBCs) called haematocrit, the temperature, and cell shape. However, the electrical properties of flowing blood are found to be influenced by the flow rate [12].
A spatial average time-dependent velocity of the blood flowing inside the aorta, taken from the experimental data provided in [11], has been taken into account for the aortic arch and the descending aorta (figure 3). During the systolic phase of a cardiac cycle, the heart contracts to pump blood into the aorta, and in the diastolic phase, the heart relaxes after contraction. This pulsatile blood flow causes the variation of blood conductivity inside the aorta. The reason is the orientation and deformation of the RBCs in case of flowing blood. At higher velocities, the shear stress increases, which consequently deforms the RBCs in the layer with the highest stress close to the vessel wall and also aligns them throughout the vessel. Both effects lead to a higher conductivity than the resting blood (figure 4) [13,14].
The Maxwell–Fricke equation for the conductivity of blood reads [13]:
In [15,16], it is shown that the blood conductivity during pulsatile blood flow is not the same at any given velocity during acceleration and deceleration. This disparity is a consequence of the RBCs inability to achieve complete randomization at end-systole, which leads to less but still considerable conductivity changes during the cardiac cycle. However, for simplicity, conductivity changes which are shown in figure 5 have been assumed in the simulation model.
A 3D numerical simulation model is used to investigate the changes in the electric potential and the impedance changes on the thorax surface. The model has been set up in COMSOL Multiphysics [17] for the underlying time-harmonic current flow problem. Since the duration of the cardiac cycle is much higher than the period of the injecting current, simulations can be performed in the frequency domain. The electric potential drop is evaluated between the measuring electrodes by solving the Laplace equation for the electric potential
The model consists of a simplified geometry, as shown in figure 6. Three pairs of source (injection) electrodes are placed on the surface of the thorax (each pair in one vertical line) and inject an alternating current with a magnitude of 5 mA and a frequency of 100 kHz asynchronously. For each injection, the electric potential drop is evaluated between five measurement electrode pairs (each pair in one vertical line) which leads to the thoracic impedance
The boundary conditions are:
∫
where
It has been shown in the literature [21, 22] that the blood flow is highly disturbed locally inside the aorta and changes to turbulent flow with strong recirculation. As depicted in figure 7, flow disturbances occur around the dissection, which inhibits the deformation and orientation of the RBCs. Thus, the flow shear rate and, consequently, the electrical properties of blood are altered. At the highest blood flow velocity and consequently the highest deformation and orientation rate of the RBCs, a remarkable difference in the electrical conductivity between the healthy (non-disturbed flow) and the aortic dissection conditions can be expected [6]. Since no experimental or simulation data exist regarding conductivity changes of blood in this kind of disturbed flow, it is assumed that with a radially growing false lumen also the blood flow disturbances increase and the conductivity changes decrease. To quantify this assumption, a damage factor
The damage factor
The aim of a Global Sensitivity Analysis (GSA) is to quantify the connection between the variance of the model output given the variability of its input. GSA is distinguished from a local sensitivity analysis since it investigates the whole input space of each random variable. This study aims to use a GSA technique to identify which electrode configuration has significant changes in the impedance cardiogram −|
One of the most known techniques in GSA is the variance-based method. Here, the output variance is portioned in the sum of the contributions of each random variable. Consider a mathematical model output
A random variable
In this application, only the first-order and the total-order indices are considered. Any interaction between the input random variable can be derived by subtracting the first index to the total. Consequently, the difference will result in the amount of interaction present in the model.
The Sobol’ indices are computed from a Polynomial Chaos Expansion (PCE) of the model [24], which also represents a valid mathematical metamodel. PCE consists of the sum of orthogonal, multivariate polynomials
The PCE is computed through the UQLab toolbox for Matlab [28,29]. However, the time-dependent indices are developed manually from the extrapolation of the PCE coefficients.
To assess the sensitivity analysis, the input and output spaces together with the numerical models, have to be established. Since the aim of the study is to catch the difference between different health conditions, two numerical models are set. The first one refers to the healthy condition and the second one to the dissected condition. As described in section 2–2, the latter differs from the first one in the presence of the false lumen and another blood flow profile. Therefore, different input spaces are produced for each model. Besides, introducing variability in the input space of the models will guarantee the realization of as many patient-specific cases as the dimension of the input sample. Thus, a deeper understanding of the impedance cardiography for a human thorax can be revealed. From the models’ evaluations, the PCEs for the healthy and dissected conditions are constructed, and analyzing the differences between them will guide toward the choice of the best electrode configuration.
The input space of the healthy case is composed of only two random variables, namely the maximum radius of the true lumen
The blood conductivity changes as a function of the reduced average velocity 〈
The dissected condition includes both the random variables of the healthy condition plus the radius of the false lumen
Input space description for the healthy and dissected study cases.
Cases | Variable | Distribution | Moments | Unit |
---|---|---|---|---|
Healthy | Uniform | [1.35 1.95] | cm | |
Uniform | [1.0 1.1] | - | ||
Dissected | Uniform | [1.35 1.95] | cm | |
Uniform | [1.0 1.1] | - | ||
Uniform | [0.3 1.5] | cm | ||
Uniform | [2.9 3.65] | rad |
The two models produce a measurement of the impedance cardiograms for each source electrode pairs
Two PCE functions
Informed consent has been obtained from all individuals included in this study.
The conducted research is not related to either human or animal use.
Three source electrode pairs (A, B, and C) and five measurement electrode pairs (
Each simulation contains an injection from one of the source electrode pairs and measuring from all the five measurement electrode pairs. For each simulation, the impedance cardiogram − |
Combinations of injections have been applied, and the results of calculating
Thus, the
In figure 12, the results of the sensitivity analysis on
From the sensitivity analysis in the dissected case in figure 12.b,
In figure 13,
To summarize, in the first stages of the AD in which the existence of the false lumen does not make apparent changes to the rheology of the blood flow, the presence of the disease by impedance cardiography might not be noticeable. However, as soon as the dissection creates remarkable pathological changes in the cardiovascular system, the changes in the measured impedance cardiogram due to the development of the disease such as false lumen expansion and false lumen thrombosis, might be trackable.
This study aims to investigate different electrodes configurations concerning the discrepancy between the healthy case and type B aortic dissection case. For this purpose, a numerical simulation model using a simplified geometry of the thorax has been set up. Since there are many uncertainties regarding the parameters that affect the results, a Global Sensitivity Analysis (GSA) has been implemented to quantify the relation of the variance of the model output (impedance cardiogram − |
It has been shown that the size of the false lumen has a tremendous effect on the impedance cardiogram of the dissected condition. This effect shows that in some cases, the pathological changes caused by false lumen might end up in different calculated haemodynamic parameters by impedance cardiography in comparison to other methods. Furthermore, the development of the aortic dissection disease such as false lumen expansion and false lumen thrombosis cause some pathological changes which will alter the measured impedance cardiogram. Thus, applying impedance cardiography to track these changes can be helpful for the medical management of AD.
For future works, the electrical conductivity changes of the blood in case of disturbed aortic flow by setting up simulation models and experiments, and also the possibility of tracking false lumen thrombosis by impedance cardiography, will be investigated.