SLIDE 1 Lesson 12b 1
Aortic stiffness: reconstruction of the compliance profile from TAC images acquired over the cardiac cycle.
Ettore Lanzarone April 15, 2020
MEDICAL SUPPORT SYSTEMS FOR CHRONIC DISEASES
Engineering and Management for Health University of Bergamo
LESSON 12B
Motivation
The degeneration of the vascular wall tissue induces a change of the arterial stiffness, i.e., the capability
- f the vessel to distend under the pulsatile hemodynamic load.
In the literature, the aortic stiffness is usually computed following a simple approach, in which only the maximum and the minimum values of both arterial diameter and blood pressure over the cardiac cycle are considered. However, this is not directly related to the stiffness. In these two lessons, we will develop an approach to estimate the stiffness, and its spatial variation, of a given arterial region exploiting:
- patient-specific geometrical data derived from computed tomography angiography (CTA);
- pressure waveforms generated using a lumped parameter model of the arterial circulation.
The arterial stiffness is computed linking the kinematic information derived from CTA with pressure waveforms. The final objective is to create a decision support tool non-invasive diagnosis of arterial (aortic) diseases.
SLIDE 2 Lesson 12b 2
Structure
The proposed methodology includes:
- 1. medical imaging analysis;
- 2. generation of aortic blood pressure waveforms;
- 3. estimation of the aortic stiffness.
Medical imaging analysis
The aim is to acquire the aortic diameter evolution along with the cardiac cycle. Thus, the information is anatomo-functional and not only anatomic. It requires several images and the comparison between them. In a formal way, the cardiac cycle T is discretized considering I+1 equally spaced time instants ti with:
and ti = i T / I
and tI = T Due to the cyclic behavior, the image at tI is actually not acquired (the image at t0 is used twice: at the beginning and the ending of the cardiac cycle) Thus I images are acquired; they are CTA images.
SLIDE 3
Lesson 12b 3
Medical imaging analysis
Computed Tomography Angiography (CTA) is a computed tomography technique used to visualize arterial and venous vessels throughout the body. Using a contrast injected into the blood vessels, images highlight the volume occupied by blood. Thus, they can be used to visualize the vessels of the heart, the aorta and other large blood vessels, the lungs, and the kidneys. CTA is typically used to search for blockages, aneurysms (dilations of walls), dissections (tearing of walls), and stenosis (narrowing of vessel).
Medical imaging analysis
The patient receives an intravenous injection of contrast and then the heart or the vessel is scanned using a high speed CT scanner. The contrast material is radiodense, which causes it to light up brightly within the blood vessels of interest. This method displays the anatomical detail of blood vessels more precisely than MRI or ultrasound. After the scan is completed the images are post-processed to better visualize the vessels and can even be created in the 3D images.
SLIDE 4 Lesson 12b 4
Medical imaging analysis
In our problem, each acquired CTA image is used to reconstruct a 3D model of the considered aortic segment through an image segmentation processing. The adopted imaging analysis develops in the following three steps: 1) acquisition of patient-specific medical images; 2) segmentation and anatomical reconstruction of the lumen profile; 3) virtual slicing of the 3-D reconstruction to assess cross-sectional contours at different sites. ACQUISITION Image are obtained via 4D electrocardiography (ECG)-gated CT. The ECG technique allows synchronizing a series of CT scans with the cardiac cycle through the ECG signal, to obtaining different snapshots of the vascular district as function of time (commonly expressed as percentage of the R-R interval). In our data, the 4D CT scans are acquired every 5% of the R–R interval (20 CTA images + last image at 100% assumed to be equal to the initial one at 0%).
Medical imaging analysis
RECONSTRUCTION Medical images used are in DICOM format. In our data, the anatomical reconstruction of the descending aorta lumen profile is performed, for each CTA image, through a semiautomatic segmentation process [1], using the open source software ITK-Snap [2] based on a 3-D active contour segmentation method [3].
- 1. F. Auricchio, M. Conti, S. Marconi, A. Reali, J. L. Tolenaar, and S. Trimarchi, “Patient-specific aortic endografting
simulation: From diagnosis to prediction,” Comput. Biol. Med., vol. 43, pp. 386–394, 2013.
- 2. www.itksnap.org
- 3. P. A. Yushkevich, J. Piven, H. Hazlett, R. Smith, J. G. S. Ho, and G. Gerig, “User-guided 3D active contour
segmentation of anatomical structures: Significantly improved efficiency and reliability,” Neuroimage, vol. 31, pp. 1116–1128, 2006.
SLIDE 5
Lesson 12b 5
Medical imaging analysis
SLICING The slicing procedure is performed through the following steps: 1. definition of the aortic centerline; 2. definition of n cutting planes normal to the centerline and equally spaced along the centerline; 3. detection of the cross-sectional contour points in each plane and spline interpolation; 4. 4) calculation of the center of mass for each cross-sectional contour and computation of the mean radius as the mean value of distances between the center of mass and contour points. In our data, silicing is implemented through a python-script exploring and combining modules of VTK library (www.vtk.org) and of VMTK library (www.vmtk.org). It is worth noting that the same cutting planes are usually kept for all images. Such an approximation is reasonable only under the working hypothesis that the movement of the considered tract of the aorta is negligible (descending tract of the thoracic aorta, which is bounded by the surrounding tissue).
Medical imaging analysis
Image processing will be addressed in one of the Labs you will follow. Here we focus on the decision support tool.
SLIDE 6
Lesson 12b 6
Medical imaging analysis
In this study, we consider the case of a 74-year-old female patient, who presents an asymptomatic 5.5-cm pseudo-aneurysm at the level of the distal anastomosis (eight years after ascending aortic repair for aneurysm) and whose medical history includes hypertension and atrial fibrillation.
Because the patient declined a new sternotomy and the anatomy of the lesion was suitable, endovascular exclusion of the pseudo-aneurysm was planned using a custom-made stent graft (Bolton Medical, Inc., Sunrise, FL, USA). The core of the graft scaffold is composed of three self-expanding nitinol rings, having a 0.5 mm thickness, sutured on the polyester vascular fabric; a slender nitinol ring is sutured inside the fabric tube at each end. The proximal landing zone is composed of a surgical graft, 30 mm in diameter, which shows an elliptic shape with a maximum diameter of 37 mm. For such a reason, the part of ascending aorta targeted by the endovascular treatment is neglected in this study, so that the vascular region of our interest reduces to part of descending aorta.
Medical imaging analysis
The first figure shows the vascular region of our interest (i.e., descending aorta between the left subclavian and the diaphragm). The second figure shows different views of one of the 4D CTA scans: images highlight the region of interest clearly showing the contrasted descending aortic lumen.
SLIDE 7 Lesson 12b 7
Medical imaging analysis
The fourth figure shows the 3D reconstruction
- f the descending aorta lumen for one of the
images, virtually sliced in eight sections. The third figure shows the results
Medical imaging analysis
Image processing will be addressed in one of the Labs you will follow. Here we focus on the decision support tool. Thus, I provide you the radii measured on the considered patient.
SLIDE 8 Lesson 12b 8
Generation of aortic pressure waveforms
The absence of noninvasive methods for directly measuring pressure waveforms in the aorta motivates their generation by means of a mathematical model. We refer to the lumped parameter model of the arterial tree already considered in one of the previous examples. The original model has been modified the existing lumped parameter model to increase the number segments in the observed aortic region. Hence, the same tract is modeled by a higher number
- f segments in series, each one with a reduced length.
The aim is to obtain as many segments in the observed aortic piece as the number
- f the sections, to get an univocal correspondence between the segments of lumped parameter
model and the considered sections.
Generation of aortic pressure waveforms
Lumped parameter model of the circulation: division of the segments to exactly match the position of the 8 sections.
SLIDE 9 Lesson 12b 9
Generation of aortic pressure waveforms
The parameters of the new segments can be determined by scaling those that depend on the length of the segment, according to this table.
Generation of aortic pressure waveforms
Simulation to get the pressures are conducted considering:
- physiological hematic parameters
- inlet aortic flow, average flow, the pulse period tuned to accomplish a reference literature value of 5
L/min and a duration of one cardiac cycle equal to 0.8 s (as indicated by the metadata of the adopted CTA dataset).
- tuning of the peripheral resistances in order to simulate hypertensive conditions (in the considered
example, where a relevant hypertension is observed, resistances are increased by 40% to generate pressure waveforms between about 90 and 140 mmHg). Values are generated by the model every 0.002 seconds whereas values used for the estimation are those at time instants corresponding to the CTA trigger, i.e., every 0.04 seconds.
SLIDE 10
Lesson 12b 10
Estimation of the aortic stiffness
SIMPLER APPROACH Stiffness is usually defined in terms of the maximum change in cross-sectional diameter at section i and the corresponding maximum change in blood pressure during the cardiac cycle at the same section. Then, the Young modulus E is defined as the ratio between the stress increment Δσ and the strain increment Δε. Assuming the arterial wall as a thin-walled tubes and following the Laplace law for thin-walled tubes subjected to an internal pressure, the Young modulus Ei at section i assumes the following form: hi is the thickness of the arterial wall at section i
Generation of aortic pressure waveforms
This approach neglects the dynamics within the cardiac cycle and only takes the maximum variations into account.
SLIDE 11 Lesson 12b 11
Practical lesson
MORE SOPHISTICATED APPROACH The procedure assumes a constitutive law between the aortic radius ri(t) and the blood pressure Pi(t) waveforms for each cross-sectional area i (with i = 1, ..., 8). Assuming each aortic segment i as a thin-walled circular tube, having luminal radius ri and thickness hi, under the hypothesis of cylindrical vessel made up of isotropic linear elastic material model with Young modulus Ei, it is possible to derive from the Laplace law the relation between ri and the internal tube pressure Pi:
Practical lesson
The quantities ri(t) and Pi(t) are state variables, whose values are provided by the noninvasive measurements. The derivatives are obtained considering the current value and the previous one. The term Eihi is the unknown quantity given by the product of two terms, i.e., the Young modulus Ei and the thickness hi. Unfortunately, given the physics of the problem, it is not possible to separate the two contributions based on the observations of ri(t) and Pi(t); to overcome such a limitation, we can provide an estimation of the product Eihi;
- nce such term is be estimated,
the Young modulus will be provided assuming a constant thickness value.
SLIDE 12
Lesson 12b 12
Practical lesson
Tasks: 1. To derive the pressure values to be coupled with the radius values for the 20 time instants. 2. To estimate the stiffness Ei, for each section i, with the simpler approach 3. To estimate the stiffness Ei, for each section i, with the more complex approach
Practical lesson
Estimate the radii. For now, I am not providing suggestions about the technique. Feel free to choose the most suitable one.
