Quantification of Stent Deformation from 2D Xray Images

Our goal is to develop robust methods to quantify geometric deformations of implanted SFA stents between supine and flexed positions with 2D Xray images.  Modes of deformation include: Axial, Bending, Twisting, and Cross-sectional.

It is not feasible to quantify twisting deformation using Xray images because of insufficient fiducial markers and the lack of 3D information.  Twisting can only be quantified if you can identify circumferentially-resolved fiducial markers, such as branch vessels.  However, since Xray imaging cannot resolve soft tissue, and the pattern of stent struts are essentially axisymmetric, we have no such fiducial markers.  Hence, we will focus on quantifying axial, bending, and cross-sectional deformation modes.  Note that severe axial, bending, cross-sectional deformations can cause stent buckling.

Below is a diagram of anatomic directions and views.

The basic method will be to divide the stent into segments defined by a certain number of z-rings in the supine position, and then compare the corresponding segments in the flexed position.  A segment length can be defined as the absolute arc length of the segment centerline path, probably defined as the centerline between the two borders of the stent segment.  The view that exhibits the maximum length, and hence most accurate length, is observed with a zero-obliquity view.  Note that a view with zero obliquity for a particular stent segment may exhibit obliquity for another segment because the stent may not be straight.

If obliquity is identical for corresponding segments between two body positions, there is no error in the deformation measurement because percent change is conserved.  However, if the obliquity differs between two body positions, as can be expected, a correction factor should be implemented.  Without a correction factor, we can expect the following estimation errors assuming shortening from supine to flexed position: 1) a more oblique view in the supine position will cause an underestimation of shortening, or 2) a more oblique view in the flexed position will cause an overestimation in shortening.  This is simply a result of obliquity causing an underestimation of linear dimension.

A correction factor can be derived from two 2D views.  Assuming the two views are perpendicular, you can closely estimate the length of a relatively straight segment by finding the distance based on X, Y, and Z projections of the segment.  In other words, using the two perpendicular views, apply the Pythagorean theorem to a particular segment for each body position, and then calculate percent shortening of the segment using the corrected arc lengths.  Single and double oblique cases are illustrated below.

Single oblique case

Again, the stent will be divided into segments that are defined by a particular number of z-rings in the supine position.  These segments will be compared to the corresponding segments in the flexed position to quantify the change in curvature to define bending.  The segments may be different from those of the axial analysis since longer segments may be required to capture bending.  The stent segments will be compared by the centerline paths just as for the axial deformation method.

Different from the length measurements, we now have to consider two angles of obliquity.  We define two axes of obliquity for a curve shown below.  Axial obliquity refers to rotation about the long axis of an arc.  Bend Axis obliquity refers to rotation about the axis of curvature.

Hence, assuming increased curvature from supine to flexed position, greater axial and lower bend axis obliquity for the supine position as compared to the flexed position will cause an overestimation in bending, while greater axial and lower bend axis obliquity for the flexed position will cause an underestimation in bending.

In order to derive a correction strategy for estimating bending for oblique views of curved stents, we must first make a couple of assumptions.  First, we assume that the axis of the vessel of interest is predominantly in the Superior-Inferior (SI) axis.  This is certainly the case for the SFA, as it travels down the length of the thigh.  Next, we assume that we will acquire two perpendicular views (coronal and sagittal) of the patient.  Without these assumptions, it would be possible to acquire two perpendicular views of a curved stent without capturing any of the curvature.

Case 2.

In this situation, the coronal view captures the curvature completely, with no obliquity.  You know the coronal view captures the curvature completely because the axial dimension of the stent segment as seen in the sagittal view is exactly the same as the axial dimension as seen in the coronal view.  Note that the curvature for the stent segment is highly exaggerated.

Case 3.

This is the opposite situation of the figure above.  This time, the sagittal view completely captures the curvature, while the coronal view confirms that the axial dimension of the segment is the same as that seen in the sagittal view.

Case 4. 

The sagittal view has 45 degrees of bend axis obliquity, and thus overestimates the curvature of the segment.  We can correct for this overestimation by information provided by the coronal view, which shows the true axial dimension of the segment.  By using the diagonal axial dimension, we correct the curved segment in the sagittal view by stretching it in the axial dimension.

Case 5.

This is the opposite situation of the figure above.  This time, the sagittal view contains the diagonal, true axial dimension of the curved segment, which can be used to correct the overestimation of curvature shown in the coronal view (45 degree bend axis obliquity).

Case 6.

This scenario exhibits 45 degree axial obliquity in both the coronal and sagittal views, so both views exhibit underestimated curvature.  If these two views are reasonably perpendicular, however, we can correct the curvature underestimation by using the Pythagorean theorem to stretch the bend dimension (perpendicular to the axial dimension) of the curve.

What about mixed obliquity?  It turns out there is a general, and very simple, rule that can be applied to all obliquity problems.  Assuming simple, homogeneous curvature in a segment of interest, curvature can be estimated with only the axial and bend dimensions of a curve.  Assuming that the coronal and sagittal views are reasonably normal to each other, we can measure the X, Y, and Z projections of the axial and bend dimensions of the segment.  The true dimensions can then be calculated by the Pythogorean theorem, as described in the axial deformation section, and the curvature can subsequently be estimated.  Note that curvature and segment lengths are greatly exaggerated in the figures below.

Recall that the method described in the axial deformation section to estimate arc length of a stent segment requires essentially straight segments.  The method described here can be used to address segments that have simple curvature as well.

Cross-sectional Deformation

Cross-sectional deformations will be estimated from the same segments defined for the axial deformation analysis.  Recall that the two borders and centerline paths of the stent segments were already defined for the axial analysis.  Perdicular lines can be drawn along the centerline path and local stent diameters can be measured between the two stent borders.  Averaging these perpendicular lines for a segment would give a mean diameter for that particular view.  With two perpendicular views (coronal and sagittal), effective average diameter, eccentricity, and cross-sectional area can all be roughly approximated.

Applying Deformation Data to Device Design

Cardiovascular device designers have near complete control over the architecture, dimensions, materials, and surfaces of the implants they develop. These inputs are necessary but insufficient for accurately predicting durability performance of these devices. Rather, the implant must be analyzed in context of the anatomy and biomechanics of the setting in which it is placed. It is the combination of the anatomy plus the implant that ultimately drives the cyclic deformations experienced by the device, and it is this combined in-situ loading that determines the resulting cyclic strains and fatigue performance of the implant. It is simple to apply arbitrary deformations to a stent in benchtop experiments, and deduce strains from the resulting macro and micro deformations of the structure. It is somewhat more difficult, but still quite feasible, to directly observe deformations of native or diseased arteries as a function of limb flexion. Combining these two, however, is not at all simple. One can not simply apply the deformations observed in the unstented vessel directly to the stent. The stent is designed to exert outward forces on the vessel, and thus, by definition, changes the compliance and deformation characteristics of the vessel. Therefore, simply mapping the unstented deformations directly to the stent would significantly overstate the amount of strain experienced by the implant. Further, it is impossible to deduce the forces exerted by the flexing vessel simply by observing its deformation state in a straight and flexed position. Because of these limitations, it is quite difficult to ascertain in advance the cyclic forces or deformations experienced by a stent in the setting of a flexed vessel.

The ASPECT study is designed to address the limitations described above. In this study, stents will be thoroughly studied in a benchtop setting to understand the relationship between applied forces and observed deformations. These stents will be implanted in subjects with diseased superficial femoral arteries. Per the protocol, the limbs will be flexed and the stents will be imaged as described above. The deformations observed in a realistic clinical setting can now be related to corresponding forces exerted by the surrounding anatomy under these conditions. In this sense, the implanted stent is acting as a force measurement device: the deformations observed in situ are related to anatomical forces by means of a "calibration" between deformation and force that is established with benchtop testing. Virtually any type of stent can be used for this approach, but for simplicity it is advisable to focus the efforts of the study on a single stent architecture.

Once the force data is extracted using the above described technique, it can be applied to new or different stents of any architecture. For example, let's assume that the stent selected for this study is known to have some rate of fracture in clinical practice. For this hypothetical stent, we may find that a axial compressive load of 1 newton occurs in the 15 millimeter region where the stent crosses the adductor hiatus. In this hypothetical stent, this 1 newton load results in macroscopic local axial compression of 10%, which in turn causes individual stents to flex causing a cyclic strain amplitude of 0.5%, which is predictive of fatigue fracture. Now, knowing that an axial compressive load of 1 newton is applied to a region 15 millimeters in length, one can use standard computational simulation techniques (such as finite element analysis) to study an alternative stent design, applying the same 1 newton load on a 15 millimeter segment of a new design. In the case of this new design, the 1 newton load results in perhaps 8% macroscopic axial compression, and the improved design better distributes deformation throughout the structure such that predicted cyclic strain amplitudes are reduced to 0.2%, and the structure is predicted to have infinite fatigue life. This is a simplified example intended to highlight some of the possible applications of the data collected in this study; much more sophisticated load cases and simulations are also possible, provided the relevant deformation data is collected in a relevant clinical setting.

In clinical practice, a variety of diagnostic imaging modalities are routinely used to assess the disease state, guide any interventional procedures, and monitor outcomes. In approximate order of increasing invasiveness, these include duplex ultrasound, magnetic resonance (MR) imaging, plain two dimensional X-ray, computed tomography (CT) three dimensional xray, intravascular ultrasound, and angiography. Several of these modalities are commonly used in conjunction with a contrast medium to enhance visibility of the vessel lumen, which is associated with elevated burden on the subject's renal system. 

• Duplex ultrasound can quantify flow volumes and patency, but does not provide spatial or geometrical data at all, so it is not useful for quantifying stent deformation.
• MR imaging with contrast media can provide calibrated three dimensional spatial data on native vessels. Typically, subjects are confined in a narrow tube, limiting the amount of limb flexion that can be studied with conventional MR. Metal creates artifacts in an MR scan, so it is not useful for quantifying deformation of vessels containing metallic stents.
• Digital plain X-ray is perhaps the most common imaging modality in radiology. It requires no contrast or intervention, and presents no limits to subject mobility, allowing for a wide range of limb flexion. Though it provides a planar 2D image, a 3D reconstruction can be created by combining data from two orthogonal projections. The resolution of these images is typically high enough to resolve individual stent struts, and the radiation burden on the subject is low relative to other X-ray modalities discussed here. While this modality can provide excellent spatial data on the stent as a function of various limb flexion positions, it does not provide data on the course of the vessel. 
• Computed tomography (CT) provides calibrated three dimensional spatial data within an anatomical region of interest, with or without contrast. CT can provide excellent data on vessel morphology (if used in contrast), as well as excellent resolution of an implanted stent (in the absence of contrast). However, like MR, the mobility of the subject is limited. Since limb flexion is limited with CT, this modality can not provide complete data to allow for quantification of stent deformation. It also exposes the subject to a relatively high amount of radiation. CT is often part of standard pre-procedural diagnosis and surveillance, and if available, can be useful for mapping the location of the vessel and branches relative to the implanted stent.
• Intravascular Ultrasound (IVUS) and related technologies such as Optical Coherence Tomography (OCT) uses sound or light waves to construct a cross sectional image of the vessel from inside the lumen.  These technologies can also be used to quantify the composition of the plaque, by discriminating between calcified regions, fibro-fatty regions, and normal luminal tissue, while identifying stent struts as distinct "shadows". As the catheter is pulled through the area of interest, it is possible to reconstruct serial cross-sectional slices into a three dimensional representation of the vessel. These three dimensional can not capture curvature of the stent, nor is the subject free to flex their limb because of the presence of the catheter.
• Angiography is commonly used throughout any interventional procedure. A C-Arm contains an X-ray source and Image Intensifier, and can be easily positioned at any angle necessary to view the region of interest during the procedure. This technology is designed to provide live, real-time images to guide the intervention, but is not well suited to capturing high resolution still images required to quantify stent deformation. Contrast angiography presents similar limits to mobility as IVUS because of the necessity of a catheter to be present in one or both limbs. Angiography without contrast does have these limitations, so it is possible to use an Angiography C-Arm to capture orthogonal X-ray images of an implanted stent.
• Finally, Dyna-CT is a technology that combines some of the advantages of CT with the convenience of a C-Arm based angiography setting. In this modality, a C-Arm is programmed to sweep through a defined range, while capturing images throughout the range of motion. The resulting images are then combined by software algorithms into a three dimensional spatial representation of the region of interest.

A combination of these modalities is required to capture all of the data required to quantify stent deformation in context with the surrounding vessel and anatomy. Ideally, a contrast CT or MR will provide spatial data on the vessel prior to intervention. Spatial information of the stent will then be captured with an orthogonal set of 2D plain X-rays with at least two states of flexion. A post-procedural CT will provide data allowing investigators to quantify the location of the stented segment relative to surrounding anatomical landmarks and branch vessels. Finally, IVUS data for the stented segment will allow for quantification of plaque composition, and potentially the relationship between plaque composition and stent flexion.