Interventional Quantification of Cerebral Blood Flow

CHAPTER 13

Interventional Quantification of Cerebral Blood Flow S. Demirci* , M. Kowarschik† * †

Technical University of Munich, Munich, Germany Siemens Healthineers, Forchheim, Germany

Chapter Outline 1. Introduction to the Clinical Value of Blood Flow Quantification 1.1 Blood Flow and Perfusion 1.2 Selected Diseases Related to Abnormal Flow and Perfusion Patterns in the Brain 2. Blood Flow Assessment Using Angiographic X-Ray Imaging 2.1 Overview of Angiographic X-Ray Imaging 2.2 Blood Flow Assessment in 2D 2.3 Blood Flow Assessment in 3D References

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Chapter points

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This chapter gives an insight into the medical relevance of blood flow quantification. It provides an overview of the state-of-the-art in cerebral blood flow assessment and introduces several novel concepts of flow quantification using angiographic imaging in 2D and 3D.

1. INTRODUCTION TO THE CLINICAL VALUE OF BLOOD FLOW QUANTIFICATION 1.1 Blood Flow and Perfusion A major purpose of blood flow is to transport both oxygen and nutrients to tissue of various types (e.g., organ tissue, muscle tissue). A variety of diseases are thus related to abnormal flow of blood in vessels or abnormal perfusion of capillary tissue. Potentially, such diseases can be related to all regions of the human body. For example, the blood flow in coronary arteries and the corresponding myocardial perfusion play an important role in the assessment of a patient’s cardiac condition. As another example, a malignant tumor in a patient’s liver is typically characterized by enhanced perfusion due to hypervascularization. Finally, elderly patients with a relevant Computing and Visualization for Intravascular Imaging and Computer-Assisted Stenting http://dx.doi.org/10.1016/B978-0-12-811018-8.00013-8

© 2017 Elsevier Ltd. All rights reserved.

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cardiovascular risk profile often have blood flow and perfusion deficits in their periphery, i.e., their legs and feet. Generally speaking, the treatment of all of these pathologies can benefit from accurate measurements of blood flow and tissue perfusion. Minimally invasive procedures are gaining importance due to shorter patient recovery times and lower complication rates, enhanced clinical workflows, and cost reductions. Such procedures cover endovascular treatments, where interventional devices such as guidewires and catheters are advanced through the patient’s vasculature to the lesion to be treated, e.g., via the transfemoral route. We refer to Refs. [1, 2] for detailed overviews of the growing field of image-guided interventions and minimally invasive therapies. The clinical focus of this chapter is on brain imaging and thus on applications in interventional neuroradiology. Therefore, our primary motivation for the assessment of blood flow and perfusion is based on patients suffering from cerebral vascular disorders. In particular, these pathologies cover ischemic and hemorrhagic strokes, arteriovenous malformations (AVMs), dural arteriovenous fistulas (DAVFs), and aneurysms, which will be described briefly in the following section.

1.2 Selected Diseases Related to Abnormal Flow and Perfusion Patterns in the Brain Stroke. According to the World Health Organization (WHO), stroke is the second leading cause of death, behind ischemic heart disease. In 2012, 11.9% of all deaths worldwide were caused by stroke.1 It is worth noting that there are two types of stroke: ischemic and hemorrhagic [3]. An ischemic stroke is caused by an occlusion of a cerebral artery by an embolus, whereas a hemorrhagic stroke is related to the spontaneous rupture of an aneurysm or an AVM, for instance. Ischemic strokes account for approximately 85% of all strokes. An overview of today’s imaging strategies for assessing stroke patients is given in Ref. [4]. Generally speaking, the high morbidity of stroke results from the interplay between neurological impairment, the emotional and also the social consequences of that neurological impairment, and the additional high recurrence risk of stroke [5]. In patients experiencing a typical large vessel acute ischemic stroke, 120 million neurons, 830 billion synapses, and 714 km (447 miles) of myelinated fibers are lost each hour. In each minute, 1.9 million neurons, 14 billion synapses, and 12 km (7.5 miles) of myelinated fibers are destroyed.

This quotation by Saver [6] highlights several impressive quantities regarding the impact of ischemic stroke events. It thus motivates the need for the fastest, most appropriate treatment. In patients suffering from acute ischemic stroke, the assessment of blood flow and brain tissue perfusion can help to identify both the infarct core and the so-called penumbra region (i.e., the tissue at risk) that may benefit from revascularization. 1 See http://www.who.int.

Interventional Quantification of Blood Flow

Since ischemic stroke is caused by vessel occlusion, its therapy is based on systemic intravenous thrombolysis and—for improved revascularization rates—on catheter-based procedures comprising both intra-arterial thrombolysis and mechanical recanalization of the occluded vessel, e.g., using clot-retrieving devices. Mechanical recanalization of a blocked vessel is also referred to as thrombectomy. We refer to Refs. [3, 4, 7–9] and the references to additional clinical publications provided therein for more detailed information. Therefore, the assessment of blood flow and cerebral perfusion can support risk stratification and help the interventionalist to decide upon the appropriate treatment strategy, which ranges from leaving the patient untreated to drug-based or mechanical recanalization of the blocked artery, also beyond the established time window. For a comprehensive definition and classification of ischemic stroke events and for a list of respective treatment recommendations, we refer to the latest release of the stroke prevention and treatment guidelines by the American Heart Association/American Stroke Association [5]. Arteriovenous Malformation (AVM). A cerebral AVM is characterized by an abnormal network of blood vessels that commonly do not supply any capillary bed. This network is typically referred to as the nidus of the AVM. The nidus is supplied by a number of arteries (feeders) and drained by a number of veins. AVMs exhibit a high morphologic variety. So far, the causes of such malformations are not well understood. They are assumed to be based on head injuries or genetic disorders. The point prevalence of AVMs in adults is reported to be about 18 in 100,000. A comprehensive discussion of brain AVMs including a review of their frequency and their prognosis can be found in Ref. [10]; a clinically widespread classification of AVMs was proposed by Spetzler and Martin [11]. Cerebral AVMs may cause various symptoms and issues, ranging from neurological disorders to bleedings, i.e., hemorrhagic strokes. For the case of an unruptured AVM, it is essential to assess its risk of rupture by analyzing the number of feeding arteries and the blood flow therein, the angioarchitecture of its nidus, as well as the number and the structure of its draining veins and the blood flow therein. A common treatment approach of AVMs covers embolization using endovascular techniques and their successive resection, based on either open surgery or radiosurgery [12, 13]. Dural Arteriovenous Fistula (DAVF). The general term “fistula” refers to an abnormal connection, e.g., between organs or vessels. DAVFs are fistulas connecting the branches of dural arteries to dural veins or a venous sinus. In particular, AVMs may contain DAVFs. According to Ref. [14], the incidence of DAVFs is unknown. While many DAVFs remain clinically silent, some of them may cause symptoms similar to AVMs, including neurological disorder or hemorrhage, among others. Similar to AVMs, the treatment of DAVFs is based on endovascular embolization or surgical clipping.

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We refer to Ref. [15] for a widely established classification of DAVFs and again to Ref. [14] for details on DAVFs and their medical management. Aneurysm. Cerebral aneurysms are balloon-like dilatations of arterial vessel walls and may occur at a variety of different locations in the brain. Their reported incidence rates in the adult population range from 1% to 5% [16]. According to configuration, size, and location, aneurysms may cause various clinical symptoms. Aneurysmal rupture represents the most severe event and causes subarachnoid hemorrhage, which corresponds to a hemorrhagic stroke and represents a major cause of morbidity and mortality throughout the world [17]. However, most brain aneurysms will remain asymptomatic. Today’s options of treating both ruptured and unruptured aneurysms cover surgical as well as endovascular therapies [18–20]. In either case, it is important to assess cerebral flow before, during, and after the treatment in order to protect the parent artery and to react to periprocedural complications.

2. BLOOD FLOW ASSESSMENT USING ANGIOGRAPHIC X-RAY IMAGING 2.1 Overview of Angiographic X-Ray Imaging Due to their flexibility, angiographic C-arm devices represent today’s most commonly used systems in interventional imaging. Their name is derived from their architecture, which is characterized by a C-shaped arm that has an X-ray source mounted on one end and a flat-panel detector attached to the other. Meanwhile, C-arm systems based on image intensifier technology have been widely replaced by devices using flat-panel detectors, primarily due to the resulting improvements in image quality and the less bulky design of the latter. C-arm systems primarily perform a wide spectrum of endovascular diagnostic and therapeutic procedures. Today’s scanners can be used to perform both 2D and 3D imaging. When referring to 3D imaging using C-arm systems, the term “cone-beam CT (CBCT) imaging” is often used in order to emphasize the cone-shaped geometry of the X-ray beam that is emitted by the X-ray source. We refer to Ref. [21] for an introduction to angiographic C-arm systems. Compared to a mono-plane system consisting of just one single C-arm, a biplane system comprises of two independent C-arms such that two views of the patient’s anatomy and the interventional procedure can be acquired simultaneously. Such biplane systems are used in interventional neuroradiology, for instance, due to the geometric complexity of the cerebral vasculature. Radio-opaque X-ray contrast agents (also referred to as dye) are commonly based on iodine and need to be used since the X-ray attenuation of blood is too low to enable the identification of blood vessels in native X-ray images. We refer to Ref. [21] for discussions of contrast agents for X-ray, MR, and ultrasound imaging. Due to the

Interventional Quantification of Blood Flow

nephrotoxicity of iodine- and gadolinium-based contrast media, a general objective is to keep the contrast agent load as low as reasonable, particularly in patients with renal insufficiency.2 The assessment of blood flow in arterial and venous vessels plays an important role in the diagnosis and treatment of vascular disorders. The term “blood flow assessment” is rather general and refers to the determination of physical parameters that govern the flow. These parameters include temporal quantities, flow velocities, and volumetric flow rates, among others. While some of these quantities can be obtained in vivo by measurements (e.g., image- or catheter-based), others require physiological flow models to be parameterized properly and simulated numerically. In diagnostic imaging, a variety of modalities are clinically established to evaluate a patient’s blood flow. These methods range from ultrasound examinations to more sophisticated imaging techniques such as time-resolved computed tomography angiography (CTA), time-resolved magnetic resonance angiography (MRA), and phase-contrast magnetic resonance imaging (pcMRI) for directly estimating blood flow velocities, among others [21]. These methods either work without the administration of a contrast agent, or some modality-specific contrast agent is injected intravenously. The previously mentioned imaging techniques are thus considered to be noninvasive. In contrast, approaches toward the interventional (i.e., peritherapeutic) assessment of blood flow primarily cover angiographic imaging using C-arm devices. Additionally, flow catheters and percutaneous Doppler ultrasound measurements are used in clinical practice. Again, we refer to Ref. [21] for a comprehensive overview. Aside from percutaneous Doppler ultrasound, these methods are considered invasive. The acquisition of conventional time-resolved 2D digital subtraction angiography (DSA) image series is based on an intra-arterial injection of contrast agent, which means that a catheter needs to be inserted into the patient’s body and advanced to the target region to be examined. Likewise, the use of flow catheters requires the positioning of the device in the vessel segment to be interrogated. Flow catheters are primarily used in cardiology and interventional radiology, and make use of Doppler ultrasound or the physical principle of thermodilution. The thermodilution method is based on measuring the temperature drop of the bloodstream distal to the injection location of a given amount of a cool fluid such as saline, for instance. See, e.g., the early publication by Ganz and Swan [22] and also Kramme et al. [23]. Due to the requirements of flow catheters regarding the vessel lumen, they are not commonly used in brain vessels. Instead, less invasive image-based methods for assessing cerebral blood flow are desirable. The Doppler ultrasound in general exploits the fact that the flow velocity of the blood causes a Doppler shift in the frequency of the reflected ultrasound waves. This

2 As an alternative to iodinated dye in X-ray imaging, CO -based contrast media may be used for certain 2

examinations.

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shift can be determined and used to estimate the velocity of the blood flow, which may of course be time-varying. Besides its applications in cardiology, percutaneous Doppler ultrasound can also be used to assess the flow in some major cerebral vessel. In this case, it is referred to as a transcranial Doppler (TCD) ultrasound [24]. However, due to the high acoustic impedance of the patient’s skull, the appropriate use of TCD is limited to basal intracerebral vessels. Subsequent sections will concern blood flow measurement and the assessment of cerebral hemodynamics based on angiographic X-ray imagery using C-arm scanners.

2.2 Blood Flow Assessment in 2D 2.2.1 Analysis of Vascular Flow Generally speaking, the determination of blood flow parameters based on 2D angiographic image series (e.g., 2D DSA series) is a difficult task. 2D X-ray images are projections of the 3D subject onto a plane, i.e., the X-ray detector [21]. Consequently, the 2D images lack depth information and, hence, their interpretation requires both general anatomical knowledge and good 3D understanding of the patient’s vascular structures. This interpretation becomes even more complicated if patient motion occurs during the acquisition of the image series. In this case, the subtraction of the mask image from a fill image may lead to an inaccurate result. Since our major focus is on brain imaging, however, patient motion is commonly less pronounced than it is in cardiac and abdominal imaging. Therefore, algorithmic approaches toward motion artifact correction are not discussed here and we refer to the available literature, cf. [25, 26], for example. In the following, we distinguish between methods that aim at quantitative flow evaluation in vessels and—as a particular clinical application—approaches that focus on the estimation of flow patterns in cerebral aneurysms in order to assess the efficacy of flow-diverting stents that are deployed to recanalize the bloodstream. The methods presented in this section have in common that they are all based on 2D DSA image series. Each pixel of a frame of a 2D DSA series is characterized by a time-contrast curve (TCC). For the case of a pixel that corresponds to a blood vessel, its TCC essentially looks like the example curve depicted in Fig. 13.1. The contrast increases until the peak of the curve is reached. The length of the respective time period from the defined starting point until this peak is reached is named time to peak (TTP) opacification. For example, this starting point may correspond to the time point at which the X-ray acquisition starts or at which the TCC reaches a given threshold (e.g., 10% of its peak value). Afterwards, the contrast washes out again. Various curve parameters may be extracted, such as its average wash-in gradient, its average wash-out gradient, and its full width at half maximum (FWHM) [27].

Interventional Quantification of Blood Flow

Fig. 13.1 Idealized time-contrast curve (TCC) of a vascular pixel in a 2D DSA image series: once the contrast agent is being injected into the vessel, the contrast in one single vascular pixel increases until the peak of the curve is reached. Afterwards the contrast washes out again until the original pixel intensity value is reached. The length of the respective time period from the defined starting point until the curve’s peak is reached is named time to peak (TTP) opacification. Various curve parameters may be extracted such as its average wash-in gradient, its average wash-out gradient, and its full width at half maximum (FWHM).

These curve parameters can be used immediately to quantify temporal characteristics of the patient’s blood flow. Color coding may be applied in addition in order to represent these pixel-specific quantities in a single 2D image. Several manufacturers of angiographic C-arm systems offer corresponding software products that generate parametric color images from 2D DSA series, cf. [28]. An example of how TTP measurements may be employed to assess the changes in a patient’s cerebral blood flow before and after stenting of his left internal carotid artery (ICA), may be found in Ref. [29]. A similar application of TTP measurements based on 2D DSA image series was presented in Ref. [30]. In this chapter, we focused on the assessment of embolization procedures in patients with carotid-cavernous fistulas (CCFs), which represent a particular form of DAVFs. It was demonstrated that the embolization of these fistulas generally led to normal cerebral circulation times and that TTP measurement tools might therefore be applicable to support the determination of endpoints during embolization procedures. In order to estimate the velocity of the contrast agent bolus, it is necessary to determine both spatial distances as well as temporal differences. The average velocity v¯ of the bolus within a given vessel segment can then be computed as v¯ =

s , t

(13.1)

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where s denotes the length of the vessel segment and t represents the time the bolus needs to pass through the vessel segment. Unfortunately, the estimation of both s and t can be difficult and thus errorprone. Since 2D DSA images generally lack depth information, s can only be approximated, since the 3D structure of the vessel segment under consideration may lead to severe inaccuracies due to foreshortening. Furthermore, the shape of the contrast agent bolus becomes wider as it travels through the patient’s vasculature. There are two major reasons for this bolus widening effect: the dispersion of the contrast agent in blood and the dilution of the mixture of contrast agent and blood due to collateral flows of nonenhanced blood. We refer to Ref. [31] for a comprehensive discussion of these issues and a variety of approaches toward estimating bolus arrival times from 2D DSA series. In order to overcome the lack of in-depth information and therefore to improve the estimation of s, some researchers proposed to use additional vascular 3D images in order to measure the length of the vascular segment under consideration more precisely. For the sake of simplicity, we generally assume that the intra-arterial injection of the contrast agent does not significantly change the physiological flow of blood in terms of velocity and volumetric flow rate. This may lead to inaccuracies if the location of the injection (i.e., the catheter tip) is close to the locations of the measurements. A physical model of contrast injection into an arterial bloodstream can be found in Ref. [32]. An evaluation of the impact of contrast injection parameters on the resulting TCCs in a canine model was presented in Ref. [33]. Besides velocity estimates, the determination of volumetric flow rates further requires the knowledge of a vessel’s cross-sectional area. The volumetric flow rate Q(l, t) at location l along the vessel’s centerline and time t is then given by  v(x, t) × n(l)dx, (13.2) Q(l, t) = A(l)

where A(l) denotes the cross-sectional area of the vessel at location l along its centerline, v(x, t) is the flow velocity field, n(l) represents the normal vector of A(l), and × denotes the cross product (vector product) as usual. This situation is illustrated in Fig. 13.2. Eq. (13.2) can alternatively be written as Q(l, t) = A(l)v(l, t),

(13.3)

where v(l, t) represents the spatially averaged velocity magnitude of the flow at location l perpendicular to A(l) at time t, i.e.,  1 v(x, t) × n(l)dx. (13.4) v(l, t) = A(l) A(l)

Interventional Quantification of Blood Flow

Flow Centerline

A(l )

n(l)

l

Fig. 13.2 For the calculation of the volumetric flow rate at location l along the vessel’s centerline, it is crucial to have knowledge about the cross-sectional area A(l) of the vessel at location l along its centerline and the normal vector of A(l) denoted as n (l).

In today’s practice, neither v(x, t) nor v(l, t) can be measured exactly and, therefore, v(l, t) needs to be approximated by an estimate of the temporal and spatial average velocity v¯ in the respective vessel segment, see Eq. (13.1). If 2D images are used solely, vascular crosssections may be estimated based on the assumption of cylindrical vessels [31]. However, if 3D information of the vascular geometry is available as well, cross-sectional areas may be determined more accurately.3 The extraction of quantitative flow parameters from 2D DSA image series is highly attractive from a clinical perspective. This is true despite the previously mentioned limitations that may drastically compromise the accuracy of the estimates. The relevant arguments from a practical standpoint are that the acquisition of 2D DSA series is already part of today’s clinical routine and that rough estimates of flow parameters or their relative changes may already be sufficient. Hence, the application of flow assessment methods based on such 2D image series fits well into the current clinical workflows and might require neither increased X-ray dose nor increased contrast agent load for the patient. In contrast, flow assessment techniques that raise the need for additional 3D scans will only be used in practice, if the added clinical value justifies the more complicated and time-consuming workflow as well as—potentially—the additional amounts of X-ray dose and contrast agent. 2.2.2 Analysis of Flow Patterns in Cerebral Aneurysms Image-Based Metrics for Assessing Flow Diverter Efficacy. A particular application of flow pattern analysis based on 2D DSA refers to the question of efficacy of

3 Note that the cross-sectional area of a vessel may be time-varying due to cardiac pulsation. Yet, this

behavior is difficult to observe using today’s medical imaging technology because of limitations in temporal and spatial resolution. This effect is therefore ignored for the sake of simplicity.

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flow-diverting devices (also named flow diverters), which represent an endovascular treatment option for cerebral aneurysms [16]. The term “flow diverter” refers to a special stent device with a dense mesh structure that is deployed in the parent artery and placed across the orifice of the aneurysm. Its purpose is to redirect blood flow away from the aneurysm, which physiologically leads to blood clotting and the formation of a thrombus within the aneurysm sac. The flow diverter might further provide a scaffold for neointimal and endothelial tissue overgrowth that eventually separates the aneurysm from the parent vessel and thus restores the original vessel topology. Ideally, the aneurysm finally degenerates completely. We refer to the clinical publications [19, 34–36] for details on endovascular aneurysm treatment using flow diverters. In some patients, several flow diverters need to be deployed in order to treat the aneurysm successfully. An important property of flow diverters is that they can preserve relevant arterial branches that they may cover, instead of blocking them, which might cause severe perfusion deficits in the supplied brain territories [20]. During the endovascular treatment of the aneurysm using flow-diverting stents, the interventionalist needs to decide whether the deployed device (or devices) already redirects the bloodstream sufficiently or whether further measures need to be taken. One further option is the placement of additional coils within the aneurysm sac, for instance. So far, this decision is based on the visual inspection of 2D DSA series that are acquired peritherapeutically. This evaluation step is highly subjective and depends on the experience of the physician. The physician’s decision is thus hard to reproduce, it is not quantifiable, and its predictive value cannot be validated easily. Therefore, the development of imagebased quantitative metrics that capture hemodynamic modifications induced by the deployment of flow-diverting stents is desirable for advancing evidence-based medicine and implementing standard clinical guidelines. Several quantitative metrics for the angiographic assessment of flow diverter efficacy have been proposed so far. They cover visual grading schemes and the extraction of characteristic parameters from TCCs that correspond to user-defined regions of interest (ROIs) placed within the aneurysm, among others. Yet none of these metrics that have been proposed so far can be considered clinically established. Rather, these approaches represent suggestions toward supporting the clinical community with image-based analysis tools that require future in-depth evaluation to determine whether they can add value to peritherapeutic decision making [37]. We refer the reader to Ref. [38], which covers a comprehensive survey of algorithmic approaches that have been proposed so far in order to assess quantitatively the efficacy of flow-diverting stents using angiographic imaging. In the following, we will present two image-based approaches that aim at quantifying the changes in flow patterns after the endovascular treatment of cerebral aneurysms using flow diverters.

Interventional Quantification of Blood Flow

Assessment of Hemodynamics Using Optical Flow. This first approach is motivated by the clinical hypothesis that flow diversion leads to reduced intraaneurysmal velocity magnitudes. The following description of our method follows the more detailed discussion in Ref. [38]. The fundamental technical idea behind this algorithmic approach is to recover flow patterns in a cerebral aneurysm before and after flow diverter deployment by tracking the motion of a contrast agent. Given a moderate injection rate of iodinated dye into the bloodstream as well as a sufficiently high DSA acquisition frame rate (e.g., 15 frames per second), the resulting mixture exhibits local contrast patterns that can be monitored, e.g., using optical flow methods. The term “optical flow” refers to a family of methods used in computer vision. These algorithms were introduced about 30 years ago in order to recover the motion of rigid objects from sequences of optical camera images [39]. The aim of optical flow estimators is to determine time-dependent displacement fields, i.e., to estimate the 2D displacement field u(x, ti ) between any two temporally adjacent 2D frames I(x, ti ) and I(x, ti+1 ) of the given image series. The original formulation of the optical flow method is characterized by the assumption of constant brightness of corresponding image pixels, i.e., I(x, ti ) = I(x + u(x, ti ), ti+1 ).

(13.5)

Introducing a first-order Taylor series approximation of the image intensities, we obtain δI (13.6) (x, ti ), δt where ∇ represents the gradient operator with respect to the spatial dimensions, i.e.,   ∂I ∂I T , (13.7) , ∇I = ∂x ∂y I(x + u(x, ti ), ti+1 ) ≈ I(x, ti ) + (∇I)(x, ti ), u(x, ti ) +

and ., . denotes the scalar product (inner product). Hence, Eq. (13.5) can be approximated by ∂I + (∇I) · u = 0, (13.8) ∂t where we dropped the parameters for the ease of notation. For the case of motion recovery from X-ray image series, the assumption of constant image brightness is easily violated. Therefore, Wildes et al. proposed replacing Eq. (13.8) with the continuity equation ∂I + ∇(Iu) = 0, ∂t

(13.9)

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which represents the conservation of mass of contrast agent across the images of the DSA series [40]. A comprehensive discussion of the link between the physical properties of fluid flows and their image-based restoration using optical flow methods is given in Ref. [41]. Eq. (13.9) can be shown to be ill-posed. Consequently, further constraints on the estimated displacement fields u(x, ti ) need to be set. For this purpose, various regularization methods have been proposed [38]. In our approach, we use the second-order div-curl regularizer proposed in Ref. [42]. This means that we compute the solution u = u(x, t) of Eq. (13.9) that minimizes the functional  (13.10) Ju (t) = ∇div(u(x, t))2 + ∇curl(u(x, t))2 dx 

on the image domain  for all time instances t. A particular advantage of this regularization approach is that it enforces spatial coherence (i.e., neighboring image pixels will be characterized by similar displacements), while not penalizing nonlaminar flows, which are likely to appear in the context of brain aneurysms. This second property is ensured by considering the gradients of the divergence and curl operators instead of the operators themselves. Note that Eqs. (13.9), (13.10) are continuous representations of the problem that need to be discretized properly for the sake of their numerical solution. Our implementation uses the numerical scheme proposed in Ref. [42], which is based on a multiresolution finite-difference approximation of the problem. Proper boundary conditions are derived from the physically motivated assumption that there is no flow across the boundaries of the vasculature. As soon as the time-dependent displacement fields u(x, ti ) have been computed, various quantities can be derived [38]. One option could be to determine time-averaged magnitudes of projected velocities within user-defined regions of interest (ROIs). In order to account for variations in the patient’s cardiac activity during the treatment, the estimated intra-aneurysmal velocities can be normalized by estimated velocities in the parent artery proximal to the flow-diverting device or devices. We refer to this additional correction step as inflow normalization. Fig. 13.3 shows color-coded (gray scale) representations of the magnitudes of the projected velocities pre- and postflow diverter implantation. The scaling of the left image is the same as the scaling of the right image. Both images were normalized with respect to respective ROIs on the parent artery located proximal to the aneurysm. In this case, the resulting inflow-normalized average velocity magnitude within the aneurysm was reduced by 26% due to flow diverter deployment. Hence, the deployment of flowdiverting stents indeed led to reductions in the estimated velocity magnitudes. Obviously, such considerations require that the injection and imaging parameters remain constant from pre to post. Injection parameters cover the initial concentration

Interventional Quantification of Blood Flow

Fig. 13.3 The color-coding (gray scaling) of time-averaged magnitudes of estimated velocities pre- (left) and postflow (right) diverter treatment reveals that the resulting inflow-normalized average velocity magnitude within the aneurysm was significantly reduced after flow diverter deployment.

of iodinated contrast agent, the amount of contrast agent, and the injection rate, as well as the location of the catheter tip. Imaging parameters cover the angulation of the Carm, the position of the table and the patient, and the X-ray dose settings, as well as the acquisition frame rate of the DSA series. In addition, the viewing direction (i.e., the angulation of the C-arm) should exhibit as little vascular overlap as possible in order that the projected intra-aneurysmal displacement fields can be estimated as accurately as possible. A similar method was proposed by Pereira et al. [43], where the induced flow changes in the aneurysm were reduced to a single scalar value that the researchers denoted MAFA (mean aneurysmal flow amplitude) ratio. They also took into account potential flow changes in the parent artery before and after the implantation of the flow diverter. However, their estimation of the volumetric flow rates in the parent artery required 3D vascular datasets, which rendered the clinical workflow more complicated and timeconsuming, and potentially led to an increased radiation dose as well as contrast agent load due to the additional scans. In summary, it needs to be evaluated thoroughly how far the optical flow analysis of 2D DSA image series can be applied in order to assess complicated intraaneurysmal flow changes in 3D that are caused by the deployment of flow-diverting stents. Different angulations of the C-arm device might lead to different estimates of flow patterns. However, the analysis of 2D DSA image series yields quantifiable and reproducible quantities. Therefore, this approach already represents an advantage over the current clinical practice, which is only based on the subjective visual inspection of image data.

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Fourier-Based Evaluation of Hemodynamics. Due to the patient’s cardiac cycle, the physiological blood flow velocities in arteries vary periodically.4 Consequently, a constant rate of contrast medium injection into the parent artery of the aneurysm leads to periodic brightness patterns in the DSA images, which can also be observed within the aneurysm. A second approach toward assessing flow diverter efficacy is motivated by the clinical hypothesis that these stents lead to a decoupling of the aneurysm from the bloodstream in the parent artery and therefore to reduced pulsatility patterns of contrast agent within the aneurysm sac. The approach we proposed recently therefore aims at the quantification of pulsatility of intra-aneurysmal hemodynamic brightness patterns. The subsequent summary of this method follows the more detailed presentation in Ref. [38]. In order to quantify the pulsatility exhibited by the intra-aneurysmal flow, a ROI was placed on top of the aneurysm in each frame of the DSA series. The resulting TCC was then transformed into Fourier space by computing its discrete Fourier transform (DFT). After that, its power spectral density (PSD [44]) within a properly selected frequency band around the patient’s heart rate was estimated. In other words, the method is based on determining the energy of the signal given by the TCC that corresponds to a frequency range located around the patient’s heart rate. We refer to Ref. [38] for a discussion of appropriate DSA acquisition rates based on the patient’s heart rate and Nyquist’s sampling theorem [44]. We applied the periodogram estimator [44] to determine the energy of the TCC within the selected frequency range and declared its pulsatility P = P(fl , fh ) with respect to this range as average quantity as follows: f

 fh + 12

P(fl , fh ) =



f k= fl

ˆ P (fk ), 

(13.11)

+ 12

where fl and fh denote the lower and upper bounds of the selected frequency range, respectively, f represents the bin width of the DFT (i.e., f = Fs /N, where Fs is the temporal sampling frequency of the TCC and N + 1 is the number of equidistant sampling points of the TCC along its time axis), and fk = kf . ˆ P refers to the periodogram estimator of the TCC given by  N 2  1   ˆ P (f ) = TCCn e−2π ifn  , (13.12)     N n=1 see Ref. [44].

4 Venous blood flow is typically much slower due to the significantly lower venous pressure gradients and

the relatively large calibers of veins.

Interventional Quantification of Blood Flow

Finally, the pulsatility ratio RP was defined as the ratio of the pulsatility P after (i.e., P post ) and before (i.e., P pre ) flow diverter deployment, i.e., P post . (13.13) P pre Hence, RP < 1 indicated a decrease in pulsatility. Note that the bounds fl and fh of the frequency range were omitted in Eq. (13.13). In our experiments [38], they were chosen to be the same for determining P pre and P post . In general, however, they may vary to account for a change in the patient’s heart rate during the intervention.5 In order to compute the pulsatility ratio RP according to Eq. (13.13), appropriate ROIs need to be selected in the DSA series acquired before and after flow diverter implantation. Fig. 13.4 illustrates the steps of the proposed method. Note that the TCCs depicted in Fig. 13.4 were preprocessed properly. This means that the baselines—obtained by low-pass filtering the original TCCs—were subtracted such that only those frequencies attributed to the patient’s cardiac cycle were left. Besides, the resulting curves were divided by the mean of the original TCC to account for variations in the amount of dye injected into the parent artery, and a Hamming window function was applied to mitigate spectral leakage effects. Fig. 13.4 illustrates the idealized situation that the frequency components around the patient’s heart rate are reduced considerably by the deployment of one or more flow-diverting stents. RP =

Fig. 13.4 Fourier-based analysis of intra-aneurysmal pulsatility patterns: two regions of interest (ROIs) are delineated in DSA image series acquired pre- and postflow diverter treatment. Time-contrast curves (TCCs) are extracted from both ROIs and preprocessed (1). The power spectral density (PSD) is estimated for each TCC (2). PSD estimates are compared within a certain frequency range around the heart rate (3).

5 This would require the heart rates to be stored with the DSA series, which is typically not the case in

today’s clinical practice.

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The same process of estimating a pulsatility ratio can be repeated for corresponding ROIs on the parent artery in the pre- and post-DSA series, which should be located proximal to the aneurysm. In order to enhance the accuracy and the predictive value of the proposed method, this proximal pulsatility ratio can then be incorporated into the comparison as a normalization factor to account for variations in the injection profile or the patient’s physiological blood flow. Furthermore, the aneurysmal ROIs may be rasterized in order to eliminate global averaging effects which are caused by phase differences of TCCs corresponding to individual pixels of the selected ROI [38]. As is the case for the optical flow approach, the injection and imaging parameters should of course also remain constant from pre to post. The pulsatility-based metric for the assessment of flow diverter efficacy was evaluated using 13 pairs of pre-/post-DSA series. The aneurysms that were treated using flowdiverting stents were characterized by a variety of locations, types, and sizes. The results were presented and discussed in detail [38]. In summary, they support the clinical hypothesis that flow diversion leads to a reduction of pulsatility of intra-aneurysmal hemodynamics. However, it could be observed that these results may be drastically compromised by vascular overlap. Therefore, analogous to the optical flow approach, properly chosen C-arm angulations are mandatory in order to achieve meaningful pulsatility ratio estimates. Likewise, further clinical studies are required in order to determine whether the proposed pulsatility metric can reliably support clinical decision making during endovascular aneurysm treatment.

2.3 Blood Flow Assessment in 3D The quantitative assessment of cerebral blood flow in 3D using angiographic C-arm systems involves the tomographic reconstruction of a vascular 3D dataset. Tomographic image reconstruction has been an active field of research for more than three decades. Besides medical imaging modalities that are not based on the application of ionizing radiation (e.g., MRI scanners), a variety of modalities is based on tomographic reconstruction from X-ray projection images, such as CT and CBCT. Typical reconstruction algorithms cover analytic as well as iterative approaches, which can further be subdivided into algebraic and statistical methods. For a more detailed discussion of image reconstruction algorithms, we refer to Ref. [45]. So far, a wide variety of methods toward the interventional reconstruction and the successive assessment of blood flow in 3D using angiographic C-arm devices have been proposed. These approaches may be categorized by the number of individual scans and

Interventional Quantification of Blood Flow

contrast agent injections that are required, by the complexity of the physical models they are based on, and by the variety of physical flow parameters they can deliver. The method presented in Ref. [46] is based on the combination of a 2D DSA images series and a static 3D image of the cerebral vasculature. An optical flow algorithm was used to estimate flow velocities in the image plane from the 2D DSA series, which were then backprojected into the 3D representation of the vessel tree. Afterwards, the resulting 3D flow fields were combined with estimates of the cross-sectional areas of the vessels in order to determine volumetric flow rates. Hence, this method required two different scans (i.e., a CBCT scan for the reconstruction of the static 3D image and a 2D DSA series) as well as two contrast agent injections. In addition, an accurate 2D/3D image registration method was needed to align the datasets based on the subsequent acquisitions. A comparable algorithm was provided in Ref. [47]. This method, however, did not rely on optical flow estimates. Rather, the authors suggested reconstructing bolus arrival times in 3D by reprojecting (i.e., forward projecting) vessel segments onto the detector plane and retrieving the temporal information in 3D from the respective target pixels’ TCCs. Likewise, an efficient image registration algorithm was employed to account for inaccuracies due to patient motion. Another approach similar to the two previous ones was described in Ref. [48]. In this work, projected velocity estimates were determined along the centerlines of vessel segments that had been segmented in the 2D DSA series. A cross-correlation approach was used to robustly determine bolus transit times despite highly pulsatile flow patterns [31]. The projected velocities were then backprojected into a previously reconstructed vascular 3D dataset, where a graph-based approach was used to resolve ambiguities due to vessel overlap. The primary objective of this research on flow velocity estimation was to determine patient-specific boundary conditions for computational fluid dynamics (CFD) simulations. Another similar approach was presented in Ref. [49]. In this chapter, the authors proposed a method that was based on a 3D image of the brain vasculature as well as a biplane 2D DSA dataset, i.e., two 2D DSA series acquired simultaneously from different viewing directions. The advantage of using biplane DSA over the use of monoplane DSA was that accuracy issues due to vascular overlap could be improved. The time-dependent filling of the vasculature with contrast medium was then determined by minimizing a functional that covered the perspective mappings of the 3D vessel geometry onto the two image planes of the biplane system, along with appropriate modeling assumptions using blood flow and dye propagation. As is the case for the two aforementioned approaches outlined in Refs. [46, 47], two separate acquisitions and two separate contrast agent injections were required. Accurate 2D/3D registration was mandatory once again. Finally, the method described in Ref. [50] is characterized by a set of mathematical equations that describe the physical and physiological properties of blood flow

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and contrast agent transport. The parameters governing the underlying model were numerically optimized such that the resulting propagation of the contrast agent through the patient’s vasculature matched the acquired projection images as best as possible. The approach is based on subtracted projection images from two successive rotational scans of the C-arm scanner, i.e., two successive CBCT scans. This means that the subtracted projection images were eventually obtained by subtracting the projection images of a native mask scan from the respective projection images based on a contrast-enhanced scan; the so-called fill scan. There are two obvious advantages of this method presented in Ref. [50]. First, only one contrast injection was needed and, second, there was no 2D/3D registration step required. Clinical results based on this method were presented afterwards in Ref. [51]. In comparison to the previously mentioned approaches toward 3D flow reconstruction, the method discussed in Ref. [50] is characterized by a physically and physiologically motivated model of blood flow and dye propagation. Consequently, this method does not only yield the time-dependent concentration of contrast agent within the patient’s brain vasculature. It also yields additional flow parameters such as a description of the patient’s periodic cardiac activity, flow velocities, and volumetric flow rates within the vessel segments under consideration. Before elaborating more on model-based flow estimation and dye propagation using virtual angiography, we will first concentrate on another novel flow reconstruction approach we have developed recently, named 4D DSA. This method is purely imagebased by construction and does not rely on any simplifying physical and physiological flow model. As a consequence, the 4D DSA method can be considered inherently patient-specific. 2.3.1 4D DSA—Generation of Time-Resolved Vascular Volumes 4D DSA refers to a novel angiographic imaging method for approximately reconstructing time-resolved series of vascular volumes using C-arm scanners. The term “4D” thus refers to 3D plus time. The fundamental idea is that, based on prior knowledge, the time-resolved series of vascular 3D datasets is generated from undersampled input data. The prior knowledge consists of an initially reconstructed vascular 3D dataset, which is then used to constrain the generation of the set of temporal volumes. Therefore, this 3D dataset is also referred to as the constraining volume (or constraint volume). A comprehensive discussion of the 4D DSA method can be found in Refs. [52–54]. Similar approaches were presented for CT imaging as well as for MRI. We again refer to the survey article [52] and to the rich body of literature referenced therein. Fig. 13.5 shows an illustration of the 4D DSA method. A clear advantage of this novel 4D vascular imaging technology is that it can provide any view at a series of successive time instances. This is particularly true for viewing directions (i.e., angulations of the C-arm) that are mechanically unreachable.

Interventional Quantification of Blood Flow

Fig. 13.5 Principle of the 4D DSA method: first, a static 3D vascular dataset is reconstructed. Afterwards, the log-subtracted projection images are revisited, and the time series of vascular volumes is generated.

As a consequence, the 4D DSA method has the potential of reducing the number of 2D DSA acquisitions that are needed to determine the best possible working projection for diagnosis, surgical planning, and treatment. This would lead to reductions in X-ray dose and contrast agent load. However, further clinical studies are required in order to corroborate this hypothesis. Data Acquisition. In the current 4D DSA implementation, the data acquisition is based on a 3D DSA scan protocol that comprises two rotational runs of the angiographic C-arm device: the mask run and the fill run. The contrast injection is timed such that the inflow of contrast agent can be captured in the projection images of the fill run. Alternative scan protocols that consist solely of a contrast-enhanced rotational run of the C-arm and use suitable bone removal and vessel enhancement techniques in order to represent vascular data only may be used in the future as well. The angular scan interval is chosen such that a sufficiently large number of projection images can be acquired over an adequate time interval: typically about 260 degree due to mechanical limitations of today’s conventional C-arm scanners.6 As a by-product of our 6 From the standpoint of CT reconstruction theory, a scan range of 180 degree plus the fan angle of the

X-ray beam is sufficient to reconstructed a (2D) object [45]. For today’s angiographic C-arm devices, this leads to angular ranges of about 200 degree.

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current 4D DSA software prototype implementation, a high-quality 3D vascular dataset is generated during the reconstruction of the time-resolved volumes, which eventually leads to the previously mentioned constraining volume. Algorithmic Aspects. The basic algorithmic block of the 4D DSA method that generates the time-resolved series of vascular volumes based on an initially reconstructed static vascular volume can formally be written as follows. Let I : R3 → R be the initially reconstructed vascular 3D image and C : R3 → R the respective constraining volume. Commonly, C contains even fewer nonzero voxels than I and may be generated from I by appropriate thresholding and noise reduction, for instance, in order to isolate vascular voxels. In addition, we use p : R2 × N → R to refer to the time-dependent log-subtracted projection images, i.e., p(u, t) refers to the projection point that corresponds to the discrete time point t and detector coordinate u, which is assumed to be continuous for the purpose of this algorithmic description. Note that the time point t in our notation corresponds to the projection angle of the C-arm device. The mapping A : R3 × N → R2 is introduced to represent the perspective mapping of the 3D space to the projection image corresponding to time point t, i.e., A(x, t) = u. Finally, we define L(u, t) = {x ∈ R3 ; A(x, t) = u} as the X-ray path through the object point x at time t hitting the detector at position u. Using these definitions, the basic scheme of the 4D DSA method for generating a time series of vascular volumes V (x, t) is given by p(A(x, t), t) . L(A(x,t),t) I(y)dy

V (x, t) = C(x) 

(13.14)

Note that Eq. (13.14) corresponds to a multiplicative perspective backprojection of normalized projection values into the constraining image C. The normalization of the projection values p(A(x, t), t) is accomplished by introducing the denominator in Eq. (13.14). This normalization step accounts for the proper scaling of the values stored in the constraining image C(x) independent of the path length of the respective ray through the vasculature from the X-ray focal spot to the detector plane. Eq. (13.14) further implies that the spatial resolution of the constraining image C(x) will be preserved by the time series V (x, t) of vascular volumes; see again [54]. Obviously, the quality of the time-resolved series of vascular volumes will be compromised due to vascular overlap. The filling states of overlapping vessels can only be restored approximately when using limited angular ranges of projection images. Heuristic approaches based on the interpolation of voxel-specific time-attenuation curves (TACs) may be used in order to mitigate this effect (referred to as regularization in Fig. 13.5). Therefore, the quality of the generated 4D dataset—its temporal resolution, in particular—depends on the sparsity of the vessel tree under consideration [54]. From the standpoint of image reconstruction theory in CT [45, 55], it is important to point out that 4D DSA is an approximative algorithm for generating time-resolved vascular data in 3D. This is for several reasons.

Interventional Quantification of Blood Flow

First, due to the circular sampling trajectory, Tuy’s data sufficiency condition is violated and the object therefore cannot be reconstructed exactly [45, 55]. According to Tuy’s condition, every plane that intersects the irradiated object must contain an X-ray focal point such that the object can be reconstructed exactly.7 Apparently, this intersection criterion is not true for those planes that are parallel to the mid-plane (i.e., the plane in which the X-ray source rotates along its circular path), but not equal to it. Note that, as a particular consequence of Tuy’s condition, the widely used Feldkamp-Davis-Kress (FDK) method does not represent a theoretically exact conebeam reconstruction algorithm. Second, due to the propagation of dye during the rotational fill run, the acquired projection images are highly inconsistent. In the early projection images, only arteries are enhanced, while venous structures will typically be filled with contrast agent toward the end of the fill run. Consequently, the initially reconstructed 3D vascular dataset and therefore the constraining volume may be impaired by artifacts such as streaks, for example. This is essentially based on the fact that not all vascular structures are irradiated from all projection directions while they are filled with contrast agent. This is a general issue in X-ray CT of vascular structures based on the administration of iodinated contrast agent, which is not just the case for brain imaging. Third, the previously mentioned issues due to vascular overlap will compromise the accuracy of the time series of volumes. Sophisticated interpolation schemes in order to close gaps in a vascular voxel’s TAC that are characterized by incorrect X-ray attenuation data due to vessel overlap can enhance the accuracy of the results. However, the reconstruction of highly accurate temporal volumes cannot be accomplished for the case of severe vascular overlap using a limited number of projection images only [54]. Clinical Applications. First applications of the 4D DSA method focus on the assessment of cerebral vascular disorders. Ongoing clinical research projects concentrate on the application of 4D DSA for assessing the blood flow in brain AVMs and DAVFs, among others. For example, in order to guide catheter-based AVM embolization procedures, it is important to understand its angioarchitecture in full detail, which covers the temporal behavior of its arterial feeders and draining veins, as well as the structure of the nidus, e.g., the occurrence of intranidal aneurysms which are associated with enhanced bleeding risk. As an example, Fig. 13.6 illustrates a 4D DSA dataset of a brain AVM at five successive time instances. See Ref. [54] for further early clinical results. In addition, a recent comment published in a neurosurgery journal also highlights the potential of the 4D DSA method [56]. 7 Intuitively, Tuy’s condition ensures that all plane integrals that are needed for the computation of the

inverse Radon transform of the irradiated object can be computed from the acquired X-ray projection data. See again [45, 55] for details.

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Fig. 13.6 Example of five successive time instances of a 4D DSA dataset of a brain arteriovenous malformation (AVM): the images in the top row refer to a different projection direction (anteroposterior view) than the images in the bottom row (lateral view).

Parametric Color Coding. 3D parametric datasets can be derived from timeresolved series of vascular volumes. The resulting quantities can be color-coded correspondingly. As an example, Fig. 13.7 shows two views of a color-coded (gray scale) representation of the bolus arrival times of the 4D dataset presented in Fig. 13.6. For each voxel, its bolus arrival time was defined as the first point in time at which its timeattenuation curve (TAC) reaches one-third of its peak. The resulting parametric volume was then rendered appropriately. Fig. 13.7 is based on a ray casting algorithm using a Phong lighting model to improve 3D perception [57]. Empirical vessel segmentation along the rays was implemented in order to ensure that the first vessel hit by a ray determined the color of the respective image pixel, thus reducing artifacts due to vascular overlap. Note that the color allows for easy delineation of the draining veins shown, which may help the physician to identify these important structures and consider them during the planning of the AVM treatment. Future research on 4D DSA may concentrate on the determination of time-resolved 3D velocity fields. These flow fields can—together with estimates of cross-sectional areas of the respective vessel segments—be used to determine time-resolved volumetric flow rates. Clinically, this may lead to improved efficacy assessment of a variety of

Interventional Quantification of Blood Flow

Fig. 13.7 Color-coded (gray scale) representation of bolus arrival times based on the 4D AVM dataset shown in Fig. 13.6: (left) anteroposterior view; (right) lateral view.

endovascular interventions, e.g., stenting procedures. See Ref. [58] for more details on an approach based on the estimation of dense 3D velocity fields using an optical flow algorithm as well as first results. 2.3.2 Computational Fluid Dynamics (CFD) Blood flow assessment techniques using numerical CFD simulation represent a family of approaches that are characterized by models of the patient’s physiology, blood flow, and contrast agent transport. These models are commonly given by a set of mathematical equations that need to be solved numerically in order to determine the required physical quantities. Depending on the complexity of the flow model, CFD-based approaches yield a variety of parameters such as velocity fields, pressure, wall shear stress, etc. The simulation of hemodynamics is commonly based on the numerical treatment of the unsteady incompressible Navier-Stokes equations in 3D, given by   ∂u + (u · ∇)u = −∇p + μu + F, (13.15) ρ ∂t which is referred to as the momentum equation and essentially relates pressure gradients to velocity fields, and ∇ · u = 0,

(13.16)

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which is referred to as the continuity equation for incompressible fluids (i.e., density changes are negligible). As usual, the operator · denotes the scalar product (inner product). Additionally, u = u(x, t) represents the time-varying velocity field, p = p(x, t) is the pressure, ρ and μ stand for the density and the viscosity of the blood, respectively, and the term F = F(x, t) summarizes all external forces, e.g., gravity as well as other potentially time-dependent effects. Note that the operators ∇ and  in Eqs. (13.15), (13.16) refer to spatial dimensions only, i.e.,   ∂ ∂ ∂ T , , (13.17) ∇= ∂x ∂y ∂z and =

∂2 ∂2 ∂2 + + . ∂x2 ∂y2 ∂z2

(13.18)

For further details, we refer to the textbook [59] as well as the brief introduction to CFD in article [27]. Note that, for the sake of simplicity, blood is commonly modeled as a continuous Newtonian fluid, cf. [60] for comments on extensions of these simplifying assumptions. Appropriate boundary conditions are further needed in order to solve Eqs. (13.15), (13.16), e.g., time-varying velocity profiles at the inlets as well as time-varying pressure values at the outlets of the vascular territory under consideration. See again [59] for a general introduction to fluid mechanics and [61] for an introduction to numerical methods for fluid simulation. The computational domain of the flow simulation is defined by the patient’s vascular segment under consideration. Due to the resulting high spatial resolution, CBCT is today’s method of choice for imaging a patient’s brain vasculature. The boundary conditions for the CFD simulation as well as the density and the viscosity of the blood— cf. Eq. (13.15)—are either taken from the literature or directly measured in the patient. It is obvious that patient-specific simulation parameters will generally lead to more accurate and realistic computational results than average quantities taken from the literature. CFD Simulations in Brain Aneurysms and Virtual Stenting. The analysis of hemodynamics in cerebral aneurysms and the assessment of their rupture risks represent a major clinical CFD research topic. We refer to the overview provided in Ref. [60] and the references listed therein. An analysis of the statistical correlation between computational results based on CFD and aneurysmal rupture events was recently presented in Ref. [62]. The authors came to the conclusion that ruptured aneurysms tended to be characterized by complex unstable flow patterns, whereas unruptured aneurysms exhibited simple stable flow patterns. However, biological effects, which also

Interventional Quantification of Blood Flow

play a crucial role in the assessment of aneurysmal rupture, are not yet covered explicitly by today’s simulation techniques. For algorithmic approaches toward the visualization of simulated flow data and the respective enhancement of their perception, we refer to the textbook [57] and also the recent publication [63]. Enhancements of CFD methods for cerebral aneurysms cover the simulation of the effect of flow-diverting stents. This approach is often referred to as virtual stenting. It enables the simulation of the treatment of vascular pathologies and, to some extent, the prediction of the treatment success. Using virtual stenting, the physician has the possibility to simulate upfront the treatment of a cerebral aneurysm using a flowdiverting stent in order to figure out what type and size of stent to deploy, and how to implant it properly across the neck of the aneurysm in order to achieve the best possible flow diversion result. We refer to Refs. [64, 65] for descriptions of how to model the individual struts of a flow diverter that is placed within the parent vessel. In contrast, the approach described in Ref. [66] is based on a more macroscopic flow diverter modeling technique, which uses a representation of the stent as a porous medium and thus reduces the complexity of the geometric model and the subsequent numerical simulation. Note that such modeling and simulation techniques are still far from being applicable in clinical practice. Further validation studies are required in order to establish such an approach in clinical decision making. Dye Transport Simulation and Virtual Angiography. Available CFD software packages can be used to simulate blood flow, particularly in cerebral aneurysms. The computed velocity fields are then used in order to simulate the propagation of the contrast agent. Afterwards, the resulting time-dependent distributions of the contrast agent are forward projected in order to generate DSA-like image sequences. This approach is commonly referred to as virtual angiography [27]. For the sake of simplicity, the contrast agent is modeled as an ensemble of massless and dimensionless particles that are injected into and advected with the pulsatile bloodstream. In addition to this advective transport of dye, we also model contrast agent diffusion in the blood by estimating continuous concentration gradients from the discrete particle distributions. Based on these concentration gradients and the resulting diffusive forces, the particles are relocated correspondingly. This leads to a numerical time stepping scheme that consists of alternating particle motion steps due to advection and diffusion. In addition to this basic simulation approach, the additional modeling of gravity can further improve the similarity of real (i.e., acquired) and virtual (i.e., simulated) angiographic images. This further allows us to extract patient- and injection-specific parameters (e.g., heart rate, mean inflow velocity, bolus injection profile) from 2D DSA image series that are acquired in addition to the 3D vascular datasets needed to define the computational domains. The use of these parameters generally leads to more accurate simulations of blood flow and dye propagation.

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Virtual angiography has various applications. First, it can be used to visualize CFD results in a way that the physician is familiar with, i.e., as DSA-like image series. The comparison of such simulated DSA series with real DSA series represents an important step toward the validation of CFD simulation methods. Fig. 13.8 is taken from Ref. [27] and illustrates the virtual angiography workflow for validating CFD results. In particular, Fig. 13.8 demonstrates what parameters for the CFD simulation and the subsequent virtual angiography stage are retrieved from the input datasets (vascular geometry, heart rate, etc.). Additionally, once the user has gained confidence in the accuracy of virtual angiography images, an arbitrary number of simulated DSA series can be computed and viewed. In particular, these simulated DSA series may correspond to viewing directions that are mechanically unreachable and, therefore, cannot be acquired as real 2D DSA series. Second, virtual angiography can be used to generate test datasets for quantitative flow assessment methods such as 4D DSA, for example. The advantage is that, for the case of simulated input data, the ground truth flow is known and can thus be compared against the result that is delivered by the algorithmic flow assessment technique under investigation. Finally, virtually angiography can play an role in the context of virtual stenting. It may be employed in order to generate DSA-like image sequences that visualize the aneurysmal flow patterns pre- and poststenting such that the interventionalist can get an impression of the flow diversion effect to be expected from the respective treatment

Fig. 13.8 Virtual angiography workflow for the validation of CFD results by comparing virtual angiograms with real 2D DSA series.

Interventional Quantification of Blood Flow

option. In particular, methods for assessing the efficacy of flow-diverting stents discussed in previous sections may eventually be applied in order to assess virtual angiograms quantitatively and thus to predict the clinical outcome of the simulated flow diverter treatment.

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