Reconstruction of blood propagation in three-dimensional

rotational X-ray angiography (3D-RA)

Holger Schmitta,*, Michael Grassb, Rolf Suurmonda, Thomas Kohlerb, Volker Rascheb,

Stefan Hahnelc, Sabine Heilandc

aPhilips Medical Systems, X-Ray Predevelopment, NL-5680 DA Best, The NetherlandsbPhilips Research Laboratories, Sector Technical Systems, D-22335 Hamburg, Germany

cDivision of Neuroradiology, University of Heidelberg Medical Center, D-69120 Heidelberg, Germany

Received 11 January 2005; accepted 10 March 2005

Abstract

This paper presents a framework of non-interactive algorithms for the mapping of blood flow information to vessels in 3D-RA images.

With the presented method, mapping of flow information to 3D-RA images is done automatically without user interaction. So far, radiologists

had to perform this task by extensive image comparisons and did not obtain visualizations of the results.

In our approach, flow information is reconstructed by forward projection of vessel pieces in a 3D-RA image to a two-dimensional

projection series capturing the propagation of a short additional contrast agent bolus. For accurate 2D–3D image registration, an efficient

patient motion compensation technique is introduced. As an exemplary flow-related quantity, bolus arrival times are reconstructed for the

vessel pieces by matching of intensity–time curves. A plausibility check framework was developed which handles projection ambiguities and

corrects for noisy flow reconstruction results. It is based on a linear programming approach to model the feeding structure of the vessel.

The flow reconstruction method was applied to 12 cases of cerebral stenoses, AVMs and aneurysms, and it proved to be feasible in the

clinical environment. The propagation of the injected contrast agent was reconstructed and visualized in three-dimensional images. The flow

reconstruction method was able to visualize different types of useful information. In cases of stenosis of the middle cerebral artery (MCA),

flow reconstruction can reveal impeded blood flow depending on the severeness of the stenosis. With cases of AVMs, flow reconstruction can

clarify the feeding structure.

The presented methods handle the problems imposed by clinical demands such as non-interactive algorithms, patient motion

compensation, short reconstruction times, and technical requirements such as correction of noisy bolus arrival times and handling of

overlapping vessel pieces.

Problems occurred mainly in the reconstruction and segmentation of 3D-RA images in cases of complex AVMs. The concentration of

injected contrast agent was often not sufficient to provide highly contrasted vessels in 3D-RA images.

Another segmentation-related problem is known as ‘kissing vessels’ [19]. Kissing vessel artifacts introduce artificial vessel junctions and

thereby distort the feeding structure of the vessel. This may finally cause implausible flow reconstruction results and inverse flow directions

in vessel segments.

We are currently planning to validate our reconstruction results using particle imaging velocimetry (PIV). PIV experiments with phantoms, for

which the true flow parameters are known, will allow for the assessment of the accuracy of our contrast agent based method. In the context of

computational fluid dynamics techniques, the potential of the presented flow reconstruction method is high. Flow reconstruction results based on

the presented method could be used both as boundary conditions for simulations and as a reference for the validation of simulation results.

Computational fluid dynamics provide useful information such as arterial wall shear stress and complex flow patterns in aneurysms.

q 2005 Elsevier Ltd. All rights reserved.

Keywords: 3D rotational angiography; Flow reconstruction; Bolus arrival time; 2D–3D mapping

0895-6111/$ - see front matter q 2005 Elsevier Ltd. All rights reserved.

doi:10.1016/j.compmedimag.2005.03.006

* Corresponding author. Tel.: C31 40 2763227; fax: C31 40 2765657.

E-mail address: holger.schmitt@philips.com (H. Schmitt).

1. Introduction

In neuroradiology, three-dimensional rotational angio-

graphy (3D-RA) is commonly used to display the

Computerized Medical Imaging and Graphics 29 (2005) 507–520

www.elsevier.com/locate/compmedimag

H. Schmitt et al. / Computerized Medical Imaging and Graphics 29 (2005) 507–520508

morphology of vessel malformations such as stenoses,

arteriovenous malformations (AVMs) and aneurysms [1–3].

Highly accurate images [4] of the vessel geometry are

essential for making a diagnosis and the planning of

interventions. For example, the deployment of coils in an

aneurysm is controlled, or a stent with an appropriate size is

chosen for a given stenosis.

Additional insight to the vascular disease can be

gained if dynamic blood flow1 properties are measured,

e.g. the blood flow velocity. Usually, a contrast agent

bolus is tracked in a series of X-ray projections in order

to reconstruct dynamic properties [5–8]. The available

methods are applied to 2D images, in which a user

performs a vessel segmentation or selects individual

control points in order to calculate the desired

information.

In our approach, the control points are chosen automati-

cally in a segmented 3D-RA image. As an examplary flow-

related quantity, we chose the bolus arrival time (BAT) to be

mapped from a series of 2D images to the vessels in a 3D-

RA image. In a previous publication [9], we have shown that

the 3D reconstruction of BATs is basically feasible from a

technical point of view.

In this paper, we present improvements of our approach,

which mainly consists of three points: an efficient motion

compensation approach to handle patient motion between

the acquisition of 3D and flow data, a method for the

detection of vessel pieces that overlap in the superposition

of 2D and 3D data, and a linear programming based

framework for the correction of noisy BATs, which

incorporates the feeding structure of the complete vascular

system under examination.

The paper is organized as follows. In Section 2, the

acquisition of the input data on an X-ray angiography

system is described. Section 3 presents preparatory

methods applied to the input data in order to enable 3D

blood flow reconstruction. Section 4 illustrates the super-

position of 3D and 2D data using a forward projection

technique which incorporates patient motion compen-

sation. The implemented method for the reconstruction of

BATs on the basis of intensity–time curves is described in

Section 5. In Section 6, we present a method for the

detection of vessel pieces that overlap in the superposition

of 2D and 3D data. In Section 7, a framework of

plausibility checks is introduced which are based on a

priori knowledge about the feeding structure of the vessels

derived individually for every data set. Clinical results are

given in Section 8, whereas Section 9 concludes the work

and gives an outlook.

1 The term flow will be used in a broad sense throughout this manuscript,

meaning not only the flow rate but also the time-dependent propagation of

blood or a contrast agent bolus, respectively.

2. Data acquisition workflow

For the acquisition of X-ray projections, a standard

Philips Integris BV3000 C-arm angiography device (Philips

Medical Systems, Best, The Netherlands) was used. In the

rotational scan protocol, 100 projections were acquired in a

range of 1808. In addition, the flow scan protocol was

implemented which acquires a variable number of projec-

tions using a fixed C-arm angulation over time. For the flow

scan, an acquisition speed of 50 frames per second (fps) was

chosen. Four projection angles have been made available for

the flow scan: frontal view, lateral view, and two oblique

views (left and right).

Calibration data was collected for any of the acquired

projections. Thus, distortions induced by the magnetic field of

the earth can be corrected, and the position of the X-ray source

and the detector can be determined accurately (cf. [10]).

During image acquisition, contrast agent is injected into

the vessel under examination using a motorized injection

pump (Mark V ProVis, Medrad, Indianola, PA, USA). An

injection time of 9 s was chosen for a rotational scan. The

injection is initiated manually, and the vessel is filled

completely before the rotational scan is started. For the flow

scan, an injection time of 2 s was chosen. The flow scan

acquisition is started while the vessel is not opacified, and

the contrast agent is injected during the flow scan. Thus, the

gradual filling of the vessels is captured. Injection rates

between 2 and 4 ml/s were chosen depending on the size of

the examined vessel.

In the course of our work, it turned out that it is favorable

to acquire the flow scan first in order to minimize patient

motion between the acquisition of the image series. Since

only a small amount of contrast agent is injected during a flow

scan, side effects caused by the contrast agent are rare after a

flow scan. This means that involuntary head movement

effects are reduced compared with the time after a rotational

scan, where a larger amount of contrast agent is applied. As a

consequence, the following workflow was applied:

(1) Preparethepatientforarotationalscan.Positionthepatient

at the iso-center of rotation of the C-arm system. Prepare a

sufficient amount of contrast agent for both scans.

(2) Choose a flow scan projection angle. Perform the flow

scan.

(3) Perform the rotational scan.

Twelve patients, who gave informed consent, were

examined with an additional flow scan during the last two

years in a study approved by the local ethics board and the

German Federal Office for Radiation Protection.

3. Preparation of raw data

The two image series from the flow scan and the

rotational scan are transferred to a workstation running the

Fig. 1. Volume rendered view of a segmented vessel tree in a 3D-RA image.

An aneurysm is found at the trifurcation of the middle cerebral artery (see

arrow).

Fig. 2. Forward projection of a vessel voxel. A ray from the X-ray source F,

crossing a vessel voxel, hits the detector at a certain pixel. The position of

the focal spot F, the voxel in a 3D-RA image and the detector plane are

known from calibration measurements.

H. Schmitt et al. / Computerized Medical Imaging and Graphics 29 (2005) 507–520 509

commercially available Philips Integris 3D-RA imaging

software. The rotational scan is used to reconstruct a 3D-RA

image for which the radiologist may make custom settings

for the field of view, resolution, etc. Vessel segmentation

functions of the existing imaging software are used to

separate vessels in the 3D-RA image from surrounding

tissue and bone. Fig. 1 shows an example of a binary

segmented 3D-RA image.

After segmentation, a vessel structuring algorithm [11,9]

is applied to the vessel. The structuring method creates

cross-sectional vessel pieces and traces the neighborhood

relations of the vessel pieces. The vessel structuring is

started at the most caudal vessel voxel that can be found in

the segmented 3D-RA image. Since vessels are curved

objects, this voxel is not necessarily the site where contrast

agent is injected into the vessel. The contrast agent inflow

site, i.e. the trunk of the vessel tree, will be verified by a

procedure described in Section 7.

The vessel pieces, which are obtained from the

structuring algorithm, are taken as the entities to which

bolus arrival times will be assigned in the following. As the

vessel pieces are composed of sets of vessel voxels, a vessel

piece will also be referred to as a cluster.

4. Motion compensated forward projection

4.1. Forward projection of vessel voxels

In order to incorporate the flow information into the

reconstruction process, it is the first step to apply a forward

projection algorithm to the clusters of the 3D vessel tree.

This algorithm is used to find the image area in a

two-dimensional flow scan projection corresponding to a

given vessel cluster in the 3D-RA image.

Fig. 2 illustrates the forward projection process based on

the geometry of the X-ray system. In Fig. 2, the vessel voxel

(vx, vy, vz) is linked with the flow scan projection pixel (px,

py). The forward projection technique is described in detail

in [9].

A binary projection of the vessel voxels is obtained by

assigning the value ‘1’ to all detector pixels where at least

one voxel of the 3D vessel tree is projected to, and ‘0’ to all

other detector pixels. Such a binary image can be thought of

as the shadow of the binary segmented vessel in a given

projection geometry.

4.2. Effects of patient motion

Patient motion is inevitable during angiographic exam-

inations. Even with sedated or cooperative patients, small

head movements are introduced by breathing and

swallowing.

Two different types of patient motion may be encoun-

tered. The first occurs during the acquisition of an image

series. Using our flow reconstruction workflow, this may be

the case during the rotational scan or during the flow scan.

For movements during a rotational scan, a correction

technique is currently not available. The 3D reconstruction

algorithm assumes that the vessels do not change position as

long as the rotational scan is performed. An artifact of head

movements is blurring of the 3D-RA images.

Movements during a flow scan can be compensated for

by an algorithm described in [12]. This algorithm is

designed to improve the image quality in digital subtraction

angiography and is also applicable to the images in a flow

scan series. However, the movements during the flow scans

acquired in this study were small due to the short duration of

Fig. 3. Displacements introduced by patient motion between the flow scan

and the rotational scan. The ‘shadow’ of the forward projected vessel voxels

is superimposed on an image of the flow scan. Straightforward application

of the projection algorithm makes it impossible to find the 2D reference

points for the 3D vessel voxels.

H. Schmitt et al. / Computerized Medical Imaging and Graphics 29 (2005) 507–520510

the scans. Consequently, the compensation algorithm was

not implemented in this work.

A second type of motion occurs in the time between the

flow scan and the rotational scan. Usually, time is needed

between the two scans to change the system acquisition

protocol and to program the contrast agent injector. This

may take up to 30 s, depending on how experienced the

radiologist and the technicians are.

Patient motion between the two scans has an effect on the

forward projection procedure described above. In principle,

the position of a forward projected vessel voxel is shifted by

an unknown displacement. If the geometry is not corrected

for this displacement, the detector pixels, which should

correspond to vessel voxels, are misaligned as illustrated in

Fig. 3.

Obviously, this is unacceptable for the purpose of flow

reconstruction. The following paragraph will further address

this issue and introduce an adequate compensation

algorithm for patient motion between the flow scan and

the rotational scan.

Fig. 4. Entropy image calculated from flow scan projections. The image

shows a lateral view of the territory fed by the left internal carotid artery

with an aneurysm of the middle cerebral artery. The summation image is

obtained by a combination of 120 flow scan projections which show only

partly filled vessels.

4.3. Entropy images

Since patient motion introduces distortions, a realign-

ment of the projected vessel voxels is needed. The

realignment must be performed with regard to a reference

image of the vessels.

The selection of one projection out of the flow scan

would be an option to obtain such a reference image.

However, the choice should be made automatically as user

interaction is undesired. An algorithm for the automatic

selection of one projection, which shows the vessels in the

highest possible quality, would surely be non-trivial. It is

probable that none of the projections in the series shows a

completely opacified vascular system, because a short

contrast agent bolus is used, which travels with the blood

stream.

Instead, it is convenient to combine all the projections in

the flow scan and calculate one summation image that

contains information about the complete vessel tree.

Therefore, a novel stacking algorithm is used that calculates

such a summation image on the basis of the entropy of the

intensity values of the flow scan image pixels over time. It is

based on the assumption that vessel image areas experience

intensity changes during the flow scan. Thus, the calculation

and display of the entropy of the intensity values along the

time axis yields an image of the vascular system [13].

Fig. 4 shows a typical entropy image as it is used as a

reference image for motion compensation in the following.

In an entropy image, vessels appear as light objects whereas

the intensity of bone and surrounding tissue is suppressed.

4.4. Motion compensation algorithm

In order to find the corresponding flow scan image pixels

for every vessel voxel in the 3D-RA image, motion

compensation is essential. As the underlying head move-

ments are three-dimensional, a simple approach for a

correction algorithm would be to translate and rotate the 3D-

RA image in space until a good correspondence is achieved.

H. Schmitt et al. / Computerized Medical Imaging and Graphics 29 (2005) 507–520 511

The correspondence can be measured by correlation of a

binary image of the forward projected vessel voxels with an

entropy image calculated from the flow scan. For two Nx!Ny sized images, I1(x, y) and I2(x, y), the correlation C—

without any normalization concerning image size and

values—is generally calculated as

C ZXNxK1

xZ0

XNyK1

yZ0

I1ðx; yÞI2ðx; yÞ: (1)

As vessel areas are represented by high values in entropy

images, patient motion can be compensated by maximizing

the correlation between the binary shadow image of the

vessel tree and the entropy image.

Estimations have shown that a motion compensation,

which reconstructs the underlying three-dimensional

motion of the head, would be computationally rather

expensive, because several degrees of rotation and

translation would have to be considered. Consequently, a

2D correction algorithm was implemented which is similar

to the one presented in [12]. The correction algorithm is

based on the fundamental idea that it is sufficient to

calculate a 2D compensation shift for each forward

projected vessel voxel in the flow scan projection plane in

order to model the influence of the 3D patient motion with

respect to the given projection geometry.

It was shown that a motion in 3D, which is projected to a

2D plane, can be compensated for by 2D transformations

(see [12] and references therein). Therefore, a projection is

cut into pieces, and these pieces are shifted separately from

one another to compensate for the motion. In the presented

algorithm, the pieces are quadratic, have all the same size

and have a control point in the center. Such a piece is

referred to as a window in the following.

First, the entropy image E(x, y) is calculated from the

flow scan projections. The binary vessel shadow S(x, y) is

then created by a forward projection of the 3D vessel tree.

The center of gravity is calculated for every cluster of

voxels in the 3D vessel tree. For each cluster, the center is

projected to the binary shadow image, and the projected

center point is taken as a control point with a window

around it.

Let the clusters in the vessel tree be numbered from 1 to

nc. A set of forward projected cluster center points ðqdðiÞ in

the detector plane is then obtained:

ðqdðiÞ Zqdxi

qdyi

� �; 1% i%nc: (2)

The window, which contains a small part of the binary

vessel shadow, is shifted in the entropy image in order to

maximize the correlation between the binary image window

and the covered part of the entropy image.

Experiments have shown that a window size of 50!50

pixels is appropriate for the given resolution of 5122 pixels

of the flow scan projections. Generally, the window size is

referred to as sw, and the shift range of the window in the

entropy image as sr.

Furthermore, let p(i) be the neighborhood relation of the

clusters as provided by the region growing procedure, i.e.

p(i) is the cluster which has been found just one step before

the cluster with the index i(1!i%nc). Initially, the window

of the first cluster is shifted in order to maximize

C1ðrdx; rdyÞ ZXqdx1C1

2sw

xZqdx1K12sw

Xqdy1C12sw

yZqdy1K12sw

Sðx; yÞEðx Crdx; y CrdyÞ;

(3)

where

Ksr %rdx%sr and Ksr%rdy%sr

denote the shift of the window in both directions of the

detector plane. The combination of rdx1 and rdy1, which

maximizes C1, is the 2D motion compensation shift ðrd1 of

the first cluster. Note that only compensation shifts are

accepted which keep the shifted window completely within

the field of view of the entropy image.

The motion compensation procedure is repeated for

every remaining vessel cluster. Each of the successive

clusters i(iO1) takes the compensation shift ðrd pðiÞ of its

already processed neighbor cluster p(i) as an initial guess.

An optimization is performed only in the range of Gsr

around the compensation shift predetermined by the

processed neighbor. This procedure is applied recursively

for all clusters in the vessel tree, such that

Ciðrdx; rdyÞ ZXqdxiC

12sw

xZqdxiK12sw

XqdyiC12sw

yZqdyiK12sw

Sðx; yÞEðx Crdx; y CrdyÞ

(4)

is maximized, while the shift range is set to

ðKsr CrdxpðiÞÞ%rdx % ðsr CrdxpðiÞÞ

and

ðKsr CrdypðiÞÞ%rdy % ðsr CrdypðiÞÞ

For each vessel cluster, a 2D shift is obtained which

maximizes the correlation measure and compensates for the

underlying patient motion. For the shift range sr, a

distinction is made between the first cluster of the vessel

tree and the remaining clusters. The first cluster is given

more freedom to locate the vessel in the entropy image,

whereas the following clusters are assumed to need more or

less the same shift as their relative neighbor cluster p(i). It

was found that srZ15 is an appropriate value for the first

cluster, and srZ2 is sufficient for the remaining clusters.

Note that the compensation shift for all clusters with iO1

is not limited to a G2 pixel area around the compensation

shift calculated for the first cluster. As the G2 pixel shift

range is used recursively for a sequence of clusters, the

compensation shifts in different branches of the vessel tree

Fig. 5. Motion compensation result. The images show the situation before (a) and after motion compensation (b). The first cluster (iZ1) is located at the lowest

displayed vessel position. After motion compensation, the binary shadow covers the corresponding vessel segments. Note that only a sub-volume of the head is

reconstructed in the 3D-RA image and the segmentation did not provide all vessel details.

H. Schmitt et al. / Computerized Medical Imaging and Graphics 29 (2005) 507–520512

may differ substantially. This is why the presented

algorithm is suited for the compensation of combined

translations and rotations in three-dimensional space.

Fig. 5 shows an example of clinical data, which has been

corrected using the developed motion compensation

algorithm. In order to improve the results and suppress

noise in the entropy image, only the upper 40% of the

entropy image value range is used. Furthermore, the binary

shadow of the vessel voxels are highlighted by a 3!3 pixel

neighborhood instead of only a single pixel. The compu-

tation time for motion compensation is less than 10 s for any

of our clinical 3D-RA images with a resolution of 2563

voxels and flow scan projections with 5122 pixels.

5. Bolus arrival time reconstruction

5.1. Intensity–time curve lookup

The preceding paragraphs have shown how the corre-

sponding flow scan projection area is found for a given vessel

voxel by forward projection and motion compensation. This

paragraph describes the intensity–time curve (ITC) lookup

procedure for a cluster of vessel voxels. An ITC contains the

time course of the intensity in the projection area which is

geometrically related to a vessel cluster via motion

compensated forward projection. The intensity changes

from high (light) values to low (dark) values when the

contrast agent bolus arrives, and vice versa when the contrast

agent is washed out (cf. [6,7], for example).

For the ITC lookup, all the voxels in a vessel cluster are

forward projected, and the determined motion compensation

shift of the cluster is used in order to make sure that the voxel

correspondences are aligned with the vessel information in the

flow scan images. The forward projection algorithm provides

an intersection pixel on the detector plane for each projected

voxel. For better coverage in the area of interest, the four pixels

that are immediate neighbors are added. Thus, one vessel

voxel corresponds to five detector pixels.

More sophisticated methods for the forward projection of

voxels were discussed in [9], e.g. on the basis of the real voxel

size and the projection geometry. However, experiments

have shown that such complex methods do not provide

substantially improved results. They do, on the other hand,

lengthen the runtime of the flow reconstruction process.

If the five pixels, which are found for a vessel voxel, are

followed over time in a flow scan series, a collection of

intensities is obtained. The mean intensity of the pixels is

taken as the voxel-related intensity in one flow scan image.

In the same way, the mean ITC is calculated for a vessel

cluster on the basis of the curves of the contained voxels.

ITCs are calculated for every cluster in the vessel tree.

Thus, the intensity changes that are caused by the contrast

agent in the flow scan series are reconstructed for every

cluster.

The ITCs of the clusters are smoothed and normalized to

suppress noise and assimilate the curves. Smoothing is

performed using a 5-point mean filter, i.e. five adjacent values

are averaged to one filtered value in the center. Afterwards, the

curve values are scaled so that the value range [0, 255] is used

entirely in each ITC. Fig. 6 shows two typical ITCs.

5.2. Relative bolus arrival time determination

by template matching

The bolus arrival time (BAT) is the point in time at which

the contrast agent bolus reaches a certain location in the

vascular system. This section introduces a method for the

BAT determination on the basis of vessel clusters. For every

vessel cluster, the BAT is derived from the respective ITC.

Similar approaches have been published in [7,14,15]. A

literature review is given in [5].

Fig. 6. Typical intensity–time curves of two clusters from different data

sets. In the first case (solid line), contrast agent wash-in and wash-out are

included. In the second case (dotted line), only the wash-in phase is

included as the radiologist interrupted the image acquisition after the region

of interest was filled with contrast agent.

Fig. 7. Intensity–time curves of three clusters from the same vessel tree. The

clusters are located at different distances from the contrast agent inflow site.

The template cluster (solid line) is reached by the contrast agent earlier than

the two other clusters. Using Eq. (5), a relative bolus arrival time of C0.2 s

is calculated for the second cluster (dashed line) and C0.52 s for the third

cluster (dotted line).

H. Schmitt et al. / Computerized Medical Imaging and Graphics 29 (2005) 507–520 513

Several methods based on ITC criteria have been

published, e.g. locating the overall minimum intensity or

the inflection point in the descending part of the curve.

However, these criteria depend on assumptions on the curve

shape, which may not be met in many cases due to pulsatile

blood flow, variations in the contrast agent concentration, or

imperfections of the acquisition system.

Consequently, a more general approach is used in this

work. It is assumed that every vessel cluster experiences the

same ITC shape, shifted along the time axis for different

cluster locations. No assumptions on the shape itself are

made. The largest cluster of the vessel tree acts as template

cluster. This means that the cluster with the largest number

of vessel voxels provides a template ITC. The largest cluster

is chosen, because it provides a smooth ITC due to the large

number of voxels. The template cluster is commonly located

in the feeding cranial artery, where the catheter is

positioned.

The ITC C(t) of a cluster is compared with the curve of

the template cluster CT(t) by means of a least square fit. The

number of points in each intensity–time curve is np, and the

sum of squared differences

SðDtÞ ZXnpK1

0

ðCðtÞKCTðt CDtÞÞ2 (5)

is minimized with regard to the shift Dt. The shift Dt is an

integer value in the range 0.8np!Dt!0.8np. Missing values

in the shifted curve CT(tCDt) are filled with the margin

values CT(0) and CT(np–1) for Dt!0 or DtO0, respectively.

The shift Dt, which minimizes S, corresponds to the

number of images between bolus arrival at the template

cluster and bolus arrival at the cluster under investigation.

Thus, a multiplication with the image acquisition frequency

yields relative BATs with reference to the template cluster.

Fig. 7 shows three ITCs and indicates the relative BATs that

are calculated.

Since the template cluster is not necessarily the cluster

with the earliest BAT, negative relative BATs may occur. In

order to remove this offset, the smallest BAT, tmin, is

determined. For the nc clusters in the vessel tree, the

corrected BAT ti,pos(1%i%nc) is calculated from the

original BAT ti,orig as

ti;pos Z ti;orig K tmin C3; (6)

where 3 is set to an arbitrary value 3O0. The absence of

absolute BAT values is not problematic as the information is

contained in the relative BATs of the clusters in the territory

under examination.

Generally, the reconstructed BATs are noisy due to

imperfections of the X-ray system and the reconstruction

method, e.g. noisy projection data, pulsatile blood flow,

inhomogeneous mixing of blood and contrast agent or

overlapping vessels. Methods for the correction of disturbed

BATs are introduced in the following sections.

6. Detection of overlapped vessel pieces

Due to the fact that flow information for vessel pieces in

three-dimensional space is gained from two-dimensional

flow scans, different vessel pieces may correspond to the

same flow scan projection area. In this case, the vessel

pieces overlap. The ITCs, which are reconstructed for the

concerned vessel clusters, are disturbed due to the

interference of information from two or more independent

vessel sites. Therefore, it is necessary to identify overlap-

ping clusters and exclude them from further processing.

The developed algorithm for the detection of such

clusters is based on the detector pixels that are used for the

ITC lookup. A list is constructed for each detector pixel that

contributes to the ITC of some cluster. This list stores the

IDs of the clusters that make use of the pixel during ITC

Fig. 8. Schematic of the overlapping vessel detection algorithm. Vessel clusters in 3D are projected using the system geometry. For each detector pixel, a list is

created to store the IDs of clusters that are projected to the detector pixel. Note that motion compensation shifts must be incorporated in order to find the

correspondences of vessel pieces in 3D and detector pixels (cf. Section 4).

H. Schmitt et al. / Computerized Medical Imaging and Graphics 29 (2005) 507–520514

lookup. When all ITCs have been found, the list of a

contributing detector pixel contains one cluster ID, if the

pixel is used exclusively by one cluster, or more than one

cluster ID, if clusters overlap (see Fig. 8).

If more than half of the detector pixels, which are related

with a vessel cluster, cannot be utilized exclusively for this

cluster, the cluster is considered to be overlapped, and its

ITC is not used for flow reconstruction.

An exception must be made for adjacent vessel clusters.

As the boundaries of the clusters are not always aligned with

projection rays, adjacent clusters interfere with each other to

some extent in most cases. This is why a detector pixel is

still considered to be utilized ‘exclusively’ for one cluster,

even if an adjacent cluster makes use of it, too.

This introduces a negligible problem if two clusters

really overlap and are neighbors at the same time, i.e. when

they are neighbors in direction of the projection ray. In this

case, overlapping is not detected by the presented algorithm.

However, this is acceptable for two reasons. First, it is

acceptable if the same intensity–time curve is used for a

short vessel section. Second, only sections which are no

longer than two clusters are affected; a third cluster in the

same row will reveal the overlap.

Fig. 9. Vessel fragment with eight clusters. Neighborhood relations are

analyzed and segments and nodes are extracted. Clusters 1, 4, 7 and 8 are

nodes and cluster sequences in between are segments.

7. Plausibility checks based on linear programming

7.1. Segments and nodes

At this point of the flow reconstruction process, the

vessel tree consists of voxels which are grouped in clusters.

On a higher level of abstraction, the vessel tree is composed

of nodes and segments. Nodes are either branching points or

end points of the reconstructed vascular system, and

segments are sequences of clusters from node to node.

Fig. 9 illustrates this on the basis of a simple vessel

fragment. The neighborhood relations were registered by

the vessel structuring procedure (see Section 3).

7.2. Locating the inflow site

One of the outer nodes in the vessel structure corresponds

to the location where the catheter tip was positioned to inject

contrast agent. In order to understand the feeding relations

in the vessel structure, it is necessary to identify the inflow

node.

No single criterion proved to be sufficient to identify the

inflow node reliably. A fuzzy logic approach was

implemented to find the inflow node on the basis of a non-

binary combination of five criteria. All nodes in the vessel

tree are tested for each of the five criteria, and the node that

fits the criteria best is assumed to be the inflow node. The fit

is calculated by means of weights for each node. If a

H. Schmitt et al. / Computerized Medical Imaging and Graphics 29 (2005) 507–520 515

criterion is not fulfilled by a node, its weight is reduced. The

applied criteria and weights are the following:

(1) Only nodes that are in contact with exactly one vessel

segment are candidates for the inflow node. Thus, the

weight of nodes with one departing segment (outer

nodes) is set to 1.0, for all other nodes (inner nodes) the

weight is set to 0.0.

(2) Distal vessel clusters have a smaller diameter than

proximal ones. As the catheter is positioned at the most

proximal site in the reconstructed vessel system, the

weight of the largest outer node remains untouched and

the weights of all other outer nodes are multiplied with

0.7. The largest node is identified as the node containing

the largest number of voxels.

(3) The inflow node is expected to have the lowest BAT

compared with the other outer nodes. Therefore, the

weight of the outer node with the lowest raw BAT is

kept, and the weights of the other outer nodes are

multiplied with 0.5.

(4) For each segment, the line of best fit is calculated for the

raw BAT distribution in the segment. The gradient of this

line gives an idea of the flow direction in a segment. The

inflow node is the only outer node which experiences

outgoing blood flow. If the BAT gradient in the adjacent

segment is positive (outgoing flow), the weight of the

outer node is kept; if the gradient is negative (incoming

flow), the weight of the node is multiplied with 0.4. In case

of an even BAT line, it is assumed that a clear decision

cannot be made on the basis of the BATs, and the weight

of the node is multiplied with 0.9.

(5) The weight of the outer node, which is located most

caudally with respect to the patient’s anatomy, is kept.

The other weights are multiplied with 0.4. This criterion

takes into account that the catheter tip is positioned at the

most caudal site of the examined vessel part in most cases.

The outer node which carries the highest weight after this

procedure is assumed to be the real inflow site. The weights

and multiplication factors were determined experimentally

and were adjusted in a way such that the choice with the five

criteria is made for every available case in accordance with

the choice of a human observer. The factors are adapted to

the selectivity of the criterion. The more reliable a criterion

is, the larger the gap is chosen between the factors for

compliant and non-compliant nodes.

7.3. Assumptions on blood flow

In reality, blood flow is an extremely complex matter. A

comprehensive overview is given in [16]. In order to have a

sufficiently simple basis for the design of flow reconstruc-

tion methods, the following assumptions are made:

(1) The pulsatile nature of blood flow in arteries is

neglected. In reality, pulsations occur in the arteries

supplying the brain with blood. As a result, an injected

contrast agent bolus moves not only forward, but also

backward for short periods of the heart cycle. The

presented algorithms are not designed to handle

pulsations.

(2) The parabolic distribution of the flow velocity over the

vessel cross-section in tubular vessels is ignored. Blood

and contrast agent are actually flowing more quickly at

the center of the vessel than at the borders. It is assumed

that the flow velocity is the same for all radial locations.

(3) The flow velocity is assumed to be aligned with the

local vessel direction at every point in the vessel tree.

This rules out non-laminar flow.

(4) Dispersion and diffusion effects concerning blood and

contrast agent are not respected. The contrast agent

bolus is assumed to have the same shape, both at the

injection site and at more distal sites.

These assumptions can be applied to cylindrically shaped

vessels without severe consequences. However, blood flow

in aneurysms differs substantially from the assumptions, and

also stenoses and vessel bifurcations introduce disturbed

flow and complex flow patterns with vortices.

Furthermore, the reconstruction of vortices and disturbed

flow patterns in aneurysms from flow scan image series is

defeated by other shortcomings, namely the fact that the

spherical, three-dimensional aneurysm is projected to the

image plane, which introduces ambiguities. Thus, only

patterns parallel to the flow scan imaging plane could be

reconstructed. The listed assumptions can still be accepted

and applied to the majority of cerebral vessels if aneurysms

are excluded.

7.4. Feeding relations

When the contrast agent inflow site of the vascular

system is known, the feeding relations can be determined on

the basis of the vessel segments. Therefore, vessel segments

are followed successively starting at the inflow site.

Generally, it is assumed that blood flow is unidirectional

within one vessel segment. This means that one of the

boundary nodes of a segment is an inflow node while the

other is an outflow node.

As long as the vessel system has a proper tree structure,

exactly one feeding cluster f(i) can be found for a given

cluster i, i.e. for each cluster a neighbor is known which is

reached earlier by the injected contrast agent.

In case of circular connections, nodes can be reached via

different segment paths. In order to preserve a non-

ambiguous feeding relation, it is assumed that such a node

is fed by the segment with the lowest mean raw BAT. The

mean raw BAT is calculated for all possible feeding

segments, and the segment with the lowest (earliest) mean

BAT is chosen to be the real feeding segment of such a

node.

Fig. 10. Result of the plausibility check algorithm for a vessel segment with

52 clusters. The lines are the fitting functions to the raw BATs (diamonds).

Cluster 1 is the inflow site. The dotted line shows the results for lZ1,

whereas the solid gray line shows the results for lZ10.

H. Schmitt et al. / Computerized Medical Imaging and Graphics 29 (2005) 507–520516

7.5. Linear programming framework

In general, linear programming is used to optimize a

linear objective function subject to a number of linear

constraints [17]. For the correction of noisy raw BATs, the

objective function is set up to minimize the difference

between the raw BATs mi and a set of corrected BATs ti,

which are in accordance with the feeding relation f(i) of the

vascular system.

In addition, smooth local BAT changes for adjacent

vessel pieces are enforced by minimizing the second

derivative t 00i of the corrected BAT distribution. Altogether,

the objective function

E ZXN

iZ1

jmi K tijClXI

iZ1

jt 00i j (7)

is obtained, where N is the number of non-overlapped vessel

pieces, I is the number of inner vessel pieces with at least

two adjacent vessel pieces, and l is a factor for the

weighting of the fitting and the smoothing part of the

objective function. The fitting part of the objective function

is only applied to vessel pieces that are known to be non-

overlapped, because overlapped pieces are assumed to be

disturbed systematically.

The second derivative t 00i is calculated as

t 00i Z tf ðiÞ K2ti C1

jfjjf ðjÞ Z igj

Xfjjf ðjÞZig

tj; (8)

where j{jjf(j)Zi}j is the number of vessel pieces that

have the vessel piece i as their feeder. Thus, t 00i is calculated

as the usual discrete approximation of the second derivative

in cases where i is no bifurcation node.

A distribution of ti in accordance with the feeding

relation f(i) is enforced by the constraint

ti K tf ðiÞR0: (9)

This ensures that the reconstructed BAT of vessel piece i

cannot be earlier than the BAT of its feeder f(i).

In order to obtain a linear objective function, we

introduce auxiliary variables 3Ci and 3K

i to cover the cases

(tiOmi) and (ti!mi). In the same way, we use dCi and dK

i for

the cases ðt 00i O0Þ and ðt 00i O0Þ. Thus, the linear objective

function

El ZXN

iZ1

ð3Ci C3K

i ÞClXI

iZ1

ðdCi CdK

i Þ (10)

is minimized subject to the explicit constraints

ti C3Ci K3K

i Z mi (11)

t 00i CdCi KdK

i Z 0 (12)

ti K tf ðiÞR0 (13)

and the implicit constraints (tiR0), ð3Ci R0Þ, ð3K

i R0Þ, ðdCi R

0Þ and ðdKi R0Þ.

After the objective function El has been minimized, the tivalues are the corrected BATs, which are as close as

possible to the raw BATs and, at the same time, in

accordance with the feeding structure of the vessel.

It is important to notice that the fitting part jmiKtij of

Eq. (7) is applied only to non-overlapped vessel pieces,

whereas the smoothing part jt 00i j is applied to all inner vessel

pieces. Hence, a smooth interpolation of corrected BATs is

obtained for overlapped vessel sections.

A frequently used method for solving a linear program,

i.e. minimizing the objective function, is the Simplex

algorithm (cf. [17]). In our work, a software implementation

of the Simplex algorithm by the Konrad-Zuse-Zentrum fur

Informationstechnik (ZIB, Berlin, Germany) is used [18].

The ‘SoPlex’ (sequential object-oriented Simplex) frame-

work offers an easy-to-use object-oriented software inter-

face for the composition of a linear program. Furthermore,

the solving strategy is optimized for sparse matrices and

allows for very short solving times.

Typical clinical cases, in which 3D-RA images with 2563

voxels are processed, have linear programs with 2000–3000

constraints and 4000–5000 variables. For all available

clinical cases, the solving time for the linear program in the

SoPlex environment is less than 1 s on a 1.8 GHz PC

system.

For the visualization of results of the linear programming

based plausibility checks, a single vessel segment was

selected from a clinical data set, and the BAT distribution

along the segment is plotted before and after correction.

Fig. 10 shows the results together with the influence of the

weighting factor l. Generally, lZ5 is used in this work,

because visual inspection showed a good compromise

between close fitting to raw BATs and the curve smoothness

for this setting. The higher l is chosen, the more the

corrected distribution approximates a linear fit to the raw

Fig. 11. Plausibility check results of a phantom data set. The topology of the phantom is given in (a). The locations of the vessel pieces are indicated by dots.

Raw and corrected BATs of the trunk and two branches are plotted in (b). Raw BATs are displayed with hollow symbols while the corrected BATs are

displayed with solid symbols.

H. Schmitt et al. / Computerized Medical Imaging and Graphics 29 (2005) 507–520 517

data. Fig. 11 shows results of the plausibility check for a

phantom used for flow measurements.

8. Clinical flow reconstruction results

The reconstructed propagation of contrast agent in vessel

trees is visualized in a volume rendering environment

(VGStudio, VolumeGraphics, Heidelberg, Germany). The

user can choose a point in time of the filling process. Vessel

pieces that have been reached by contrast agent before this

point in time are displayed in red color. Other vessel pieces

are displayed in gray.

The flow reconstruction method was applied to 12 cases

of cerebral stenoses, AVMs and aneurysms. The flow

reconstruction method was able to visualize different types

of useful information.

In cases of stenosis of the middle cerebral artery (MCA),

flow reconstruction can reveal impeded blood flow

Fig. 12. Flow reconstruction results for a patient with a stenosis of the middle cer

internal carotid artery (lower part of the images) the territories of the anterior cere

steps of the reconstructed propagation of contrast agent are given below the imag

depending on the severeness of the stenosis. Fig. 12 shows

an example for a patient with an MCA stenosis. Visual

inspection shows that the injected contrast agent bolus

propagates more slowly in the territory of the MCA than in

the territory of the anterior cerebral artery.

With cases of AVMs, flow reconstruction can clarify the

feeding structure. An example is given in Fig. 13. The main

feeder, i.e. the feeder which predominantly supplies the

AVM with blood, is the first target of neuroradiological

interventions that strive for an occlusion of the feeders.

Flow patterns in aneurysms cannot be reconstructed with

the presented method, because the vessel structuring method

does not allow for the reconstruction of arbitrary flow paths.

However, the propagation of contrast agent in the feeding

and draining vessels can be reconstructed and may show

abnormalities in the supply of brain tissue distal to the

aneurysm.

The processing time for flow reconstruction was about

2 min for all of the processed cases on an up-to-date

ebral artery (see arrow in (a)). After injection of contrast agent into the left

bral artery (left) and the middle cerebral artery (right) are displayed. Time

es.

Fig. 13. Flow reconstruction results for a patient with an AVM fed by the middle cerebral artery. In (b), two feeding arteries are displayed. Time steps of the

reconstructed propagation of contrast agent are given below the images.

H. Schmitt et al. / Computerized Medical Imaging and Graphics 29 (2005) 507–520518

standard PC system. For a complete examination, including

data acquisition, transfer of raw data to the workstation, 3D-

RA image reconstruction and flow reconstruction, an

average time of 10 min is needed.

The additional fraction of X-ray dose applied to the

patients ranged from 4.9 to 52.0%, with an average of 14.5%

and a median of 8.5%. The additional fraction of injected

contrast agent ranged from 2.2 to 15.3%, with an average of

6.2% and a median of 4.6%. The additional dose fraction,

which is needed for flow data acquisition, highly depends on

the complexity of the angiographic examination, i.e. the

number of images acquired besides the flow scan.

9. Discussion and outlook

This paper presents a framework of non-interactive

algorithms for the mapping of blood flow information to

vessels in 3D-RA images. With the presented method,

mapping of flow information to 3D-RA images is done

automatically without user interaction. So far, radiologists

had to perform this task by extensive image comparisons

and did not obtain visualizations of the results.

In the presented approach, flow information is recon-

structed by forward projection of vessel pieces in a 3D-RA

image to a two-dimensional projection series capturing the

propagation of a short additional contrast agent bolus. For

accurate 2D–3D image registration, an efficient patient

motion compensation technique was introduced. As an

exemplary flow-related quantity, bolus arrival times were

reconstructed for the vessel pieces by matching of intensity–

time curves. A plausibility check framework was developed

which handles projection ambiguities and corrects for noisy

flow reconstruction results. It is based on a linear program-

ming approach to model the feeding structure of the vessel.

The presented flow reconstruction method was applied to

12 clinical cases and proved to be feasible in the clinical

environment. The propagation of the injected contrast agent

was reconstructed and visualized in three-dimensional

images. In cases of MCA stenoses, the reconstructed images

allow for an estimate of the degree to which blood flow is

impeded by the stenosis. The main feeding arteries of

AVMs can be depicted.

The presented methods handle the problems imposed by

clinical demands such as non-interactive algorithms, patient

motion compensation, short reconstruction times, and

technical requirements such as correction of noisy bolus

arrival times and handling of overlapping vessel pieces.

Problems occurred mainly in the reconstruction and

segmentation of 3D-RA images in cases of complex AVMs.

The concentration of injected contrast agent was often not

sufficient to provide highly contrasted vessels in 3D-RA

images. An injection rate of 2 ml/s in the vertebral artery, for

example, seems to be sufficient for normal vessels, but

insufficient for vessels with malformations. On the one hand,

contrast agent was highly diluted in high-flow compartments

of AVMs. On the other hand, radiologists did not want to

increase the injection rate in order to avoid vessel damage. As

a consequence, vessel and bone were often reconstructed

with the same intensity in 3D-RA images, and the

segmentation algorithm failed to separate them.

Another segmentation-related problem is known as

‘kissing vessels’ [19]. Kissing vessel artifacts introduce

artificial vessel junctions and thereby distort the feeding

structure of the vessel. This may finally cause implausible

flow reconstruction results and inverse flow directions in

vessel segments.

The currently used flow scan acquisition mode of 50 fps is

not sufficient to resolve local flow velocities in the vascular

system with high accuracy, for example in stenoses. Since

flow velocities of more than 100 cm/s may be found in

cerebral vessels, higher frame rates are desirable.

Future work will have to tackle 3D-RA image

reconstruction and segmentation problems in cases of

complex AVMs. Furthermore, the presented approach

should be extended to the reconstruction of pulsatile flow

and flow-related quantities other than bolus arrival times,

for example transit time or bolus mass reconstruction.

We are currently planning to validate our reconstruction

results using particle imaging velocimetry (PIV). PIV

experiments with phantoms, for which the true flow

parameters are known, will allow for the assessment of

the accuracy of our contrast agent based method.

H. Schmitt et al. / Computerized Medical Imaging and Graphics 29 (2005) 507–520 519

In the context of computational fluid dynamics tech-

niques (see, for example, [20,21]), the potential of the

presented flow reconstruction method is high. Flow

reconstruction results could be used both as boundary

conditions for simulations and as a reference for the

validation of simulation results. Computational fluid

dynamics provide useful information such as arterial wall

shear stress and complex flow patterns in aneurysms.

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Holger Schmitt received his Diploma in medical informatics from the

University of Heidelberg/University of Applied Sciences Heilbronn in

2000. In 2004, he received his PhD degree for his work on

videodensitometric flow reconstruction methods carried out in the Division

of Neuroradiology at the University of Heidelberg Medical Center. He is

now working on computational fluid dynamics applications in a joint

research project of Philips Medical Systems and the UCLA Medical

Center, Division of Interventional Neuro Radiology, in Los Angeles, CA.

Michael Grass received his Diploma degree in physics and the PhD

degree from the University of Osnabruck for his work in the area of

theoretical solid state physics in 1992 and 1995, respectively. In 1995,

he joined the Philips Research Laboratories, where he works as a senior

scientist in the research group Tomographic Imaging Systems,

Hamburg. His current research area includes computed tomography

and three-dimensional X-ray imaging, focusing on 3D image

reconstruction and dynamic volume imaging.

Rolf Suurmond received his Master’s degree in technical mathematics

from the Eindhoven University of Technology in 1996. After that, he

successfully completed the two-years post-Master’s program Mathemat-

ics for Industry, at the same university, with a final project on the topic of

acoustic time-of-flight tomography. Since 1999, he has been working as an

imaging scientist for Philips Medical Systems in Best, The Netherlands.

He works in the field of three-dimensional X-ray imaging for cardiac

applications, in particular coronary modeling, and blood flow imaging.

Thomas Kohler is senior scientist at the Philips Research Laboratories

in Hamburg. After graduating from Christian-Albrechts University in

Kiel, Germany, on microwave Fourier transform spectroscopy in 1994,

he started his PhD thesis project on the inverse problem of electro- and

magnetocardiography. He received his PhD degree in 1998 from the

University of Hamburg. Since then, he worked on iterative and

analytical reconstruction from cone-beam CT data.

H. Schmitt et al. / Computerized Medical Imaging and Graphics 29 (2005) 507–520520

Volker Rasche received his Diploma degree in physics from the

University of Bielefeld for his work in the field of computer science in

1990. He received his PhD degree in 1995 from the University of Bielefeld

for his work in real-time MRI imaging for intervention guidance. Since

1991, he is with the Philips Research Laboratories in Hamburg working

mainly in the field of cardiac imaging on various modalities including

MRI, CT and three-dimensional X-Ray imaging. His current research

areas are the cross modal integration of imaging and non-imaging

functional and anatomic data for improved intervention guidance.

Stefan Hahnel studied medicine at the universities of Halle/Saale and

Heidelberg, Germany. He received his MD degree from the University

of Heidelberg in 1993. After residencies in neuroradiology at the

University of Heidelberg Medical School and neurology at the Hospital

for Neurological Diseases in Bayreuth, he was appointed fellow in

neuroradiology at the Department of Neuroradiology, University of

Heidelberg Medical School in 1996. In 1998, he was appointed fellow

in diagnostic radiology at the Department of Clinical Radiology

(Oncology), University of Heidelberg Medical School. He passed board

examination in diagnostic radiology in 2000, and board examination in

neuroradiology in 2002. He is now senior radiologist at the Department

of Neuroradiology, University of Heidelberg Medical School. His

research interests include advanced techniques of minimally invasive

interventional neuroradiology.

Sabine Heiland received her Diploma degree in physics from the

University of Heidelberg in 1990. From 1990 to 1993 she was a PhD

student at the German Cancer Research Center (DKFZ) and she

received the PhD degree in 1993. Since 1993, she is with the Division

of Neuroradiology at the University of Heidelberg Medical Center. She

received professorship in experimental radiology from the University

of Heidelberg in 2001. She is now Professor and Chief of the

Experimental Neuroradiology Section at the University of Heidelberg

Medical School. Her research areas include the development and

application of dynamic and functional radiological techniques.