INTERACTIVE RECONSTRUCTION AND VISUALIZATION

OF DYNAMIC 3D ULTRASOUND DATA SETS

Timo Ropinski

, Borislav Petkov

, Larissa Fabritz

and Klaus Hinrichs

Visualization and Computer Graphics (VisCG) Working Group, University of M

unster

Einsteinstraße 62, D-48149 M

unster, Germany

Department of Cardiology and Angiology, University Hospital of M

unster

Albert-Schweitzer-Straße 33, D-48149 M

unster, Germany

Keywords:

Ultrasound acquisition, volumetric reconstruction.

Abstract:

In this paper we describe techniques which have been developed in order to interactively visualize dynamic 3D

ultrasound (US) volume data sets acquired using a small animal 2D US scanner. The 2D frames are acquired at

different spatial positions and gated based on the ECG signal. For the reconstruction process a user interface is

speciﬁed, which allows the user to select 2D frames acquired during different ECG phases at different spatial

locations. Thus it is possible to reconstruct and visualize a volumetric model based on several 2D frames for

different phases of the heart cycle. To improve the interactive visualization, we facilitate ﬁltering techniques,

which have been implemented on the GPU.

1 INTRODUCTION

Medical imaging has the intent to harness the ever-

growing graphics computing power of modern archi-

tectures for the visualization of medical data. A ma-

jor goal is the visual analysis of images of biologi-

cal objects acquired with different medical scanning

technologies such as CT, MRI or PET. One impor-

tant application of medical imaging is cardiac and car-

diovascular research. According to the World Health

Organization, cardiovascular diseases (CVDs) are the

number one cause of death globally, representing 30%

of all global deaths (Organization, 2006). There-

fore researchers need to better understand the func-

tions and processes of the heart in vivo. Non-invasive

small-animal imaging techniques have a great po-

tential to allow a better understanding for both re-

searchers and physicians in the inquiry and prophy-

laxis of cardiovascular diseases. The potential of a

system allowing an easy reconstruction and visualiza-

tion of medical data is immense and lies primarily in

its ability to support the members of the physicians in

their decision-making process concerning proper pa-

tient treatment and disease prophylaxis by visualizing

internal structures. In addition, a 3D visualization has

beneﬁts in contrast to classic 2D visualization sys-

tems. For instance, when visualizing a dynamic 3D

heart, a physician is able to make accurate and reliable

3D observations of heart movement and ventricle de-

formation during a heart cycle as well as volumetric

measurements.

Although US technology is used in a large number

of biomedical imaging areas, the registration and vi-

sualization of moving internal structures such as heart

ventricles and blood ﬂow or prenatal fetal facial fea-

tures are among the more prominent examples. Con-

sequently, the automatic generation of 3D US volume

data from moving biological structures scanned at a

high resolution adds to the complexity of the task of

volumetric visualization primarily because of the in-

coherency of the single 2D scan slices with respect to

creating a static volume out of them, and secondly, be-

cause of the relatively high speed of movement of cer-

tain organs. Therefore, a certain additional alignment

measure has to be introduced in order to be able to

create coherent volume representation of organs from

slice scans of moving tissue.

In this paper we propose an interactive visualiza-

tion system, which allows to acquire dynamic volu-

metric ultrasound (US) data sets by using a 2D scan-

ner. In particular we describe the preprocessing as

well as the visualization of raw US data and explain

how a user can interactively create and manipulate

volumetric data sets originating from 2D US B-scan

slices. Therefore the 2D US B-Mode scan data and

metadata is analyzed and prepared for display. De-

308

Ropinski T., Petkov B., Fabritz L. and Hinrichs K. (2008).

INTERACTIVE RECONSTRUCTION AND VISUALIZATION OF DYNAMIC 3D ULTRASOUND DATA SETS.

In Proceedings of the Third International Conference on Computer Graphics Theory and Applications, pages 308-315

DOI: 10.5220/0001097003080315

 SciTePress

pending on the type of the scanned data, the user

may choose between automatic generation of a vol-

ume data set or an interactive generation. Due to the

relatively noisy nature of the US data, several ﬁltering

techniques are applied in order to improve the visual

quality of the data and remove artifacts introduced by

the acquisition procedure.

2 RELATED WORK

US has been used in many medical subdomains, as

for instance prostate and heart examinations (Gee

et al., 2003). Fenster and Downey give an exten-

sive overview over developments in 3D US technol-

ogy and visualization (Fenster and Downey, 2000).

Thus, several techniques for US data acquisition with

the purpose of creating volumetric data sets have been

developed up until now. Gee et al. (Gee et al., 2004)

divide these techniques into two major categories. On

the one hand, volume data sets can be generated by

utilizing a dedicated US 3D probe which can scan

a ﬁxed-size volume from a short distance. On the

other hand, conventional 2D US transducers can be

employed for the generation of arbitrarily-sized scalar

ﬁelds. But the latter case requires the process of vol-

ume reconstruction and temporal and lateral 2D frame

synchronization. In addition, the irregular spatial dis-

tribution of the 2D slices adds additional complexity

to the process which may result in different scan re-

sults of the same anatomical structure under differing

directions of soniﬁcation. Gergs et al. (Gergs et al.,

2004) have shown that besides 3D US data sets, 2D

data sets have also the potential to show clear silhou-

ettes for certain application cases.

The side-ﬁre probe which is used for acquiring cir-

cular B-scan slices forming cylindrical data sets (Gee

et al., 2003) is similar to the technique described in

this paper. However, an additional positional sensor is

attached to the transducer head whose constant input

is used for receiving the relative positions and angu-

lation of each 2D slice and then aligning them within

the volume cuboid during volume generation (Fenster

and Downey, 2000).

To improve the visual quality of the acquired data

sets, different ﬁltering techniques can been used. In

(Sakas et al., 1994), Sakas et al. have attempted to

evaluate the deployment of a combination of several

low-pass ﬁlters for improving the quality of visual-

ized US data sets through ﬁltering. In their work,

they have used a 3D Gaussian ﬁlter for noise/speckle

reduction and a 3D median ﬁlter for additional con-

tour smoothing and small gaps closing caused by mis-

alignment of consecutive B-scan slices. They claim

that the results of this undertaking has been encour-

aging, but still see room for improvement by mod-

ifying the ﬁltering technique and adjusting it to the

nature of the US signal. Besides the application of

Gaussian ﬁlters, the BLTP ﬁltering technique (Sakas

and Walter, 1995) has been developed speciﬁcally for

the purposes of ﬁltering US volume data. However,

discussing these ﬁlters in detail is beyond the scope

of this paper and we refer to (Gonzalez and Woods,

2001) for more information.

3 SYSTEM SETUP

In our system setup we use a VisualSonics Vevo 770

small-animal US scanner for scanning mice in vivo. It

provides most common US scan modes, and supports

ECG-gated acquisition of 2D slices. It allows multi-

ple types of physiological measurements on animals,

from which we have used the ECG signal. Addition-

ally, the Vevo 770 scanner performs respiration gating

by acquiring data only during the rest sub-period in

the respiration cycle. In doing so, excessive moving

artifacts caused by the heaving of the chest cavity of

the animal are obviated.

We use a special scanning mode which is a pro-

prietary variant of an ECG-gated scanning procedure.

The so-called EKV (ECG-based Kilohertz Visualiza-

tion) mode is a scanning technique, during which

multiple B-Mode images from consecutive heart peri-

ods are acquired and interpolated into a single, com-

plete heart period of the animal (VisualSonics, 2005).

Thus a complete heart period is represented by a set of

frames for each lateral position. Therefore, in using

the EKV-Mode in this paper, the creation of precise

volume ”stills” of the scanned organ simpliﬁes the

frame synchronization routine signiﬁcantly. Thus, by

choosing the corresponding frames out of each syn-

chronized frame set recorded at each lateral position,

a volume data set can be created for each phase of the

heart cycle. Subsequently, the volume data sets re-

constructed in this manner comprise a whole dynamic

data set collection.

In order to acquire an EKV cine loop of the heart

period, the scanner needs proper ECG-data from a

probe attached to the animal. This is accomplished

by sensing the animal’s heart rate from four small

ﬁelds on the warmer plate where the mouse is fas-

tened. Constant monitoring and supervision of the an-

imal’s vital signs and telemetry is required. Addition-

ally, the animal’s temperature is monitored through a

signal delivered by a small rectal probe connected to a

module responsible for monitoring the overall physio-

logical condition of the scanned animal. Additionally,

INTERACTIVE RECONSTRUCTION AND VISUALIZATION OF DYNAMIC 3D ULTRASOUND DATA SETS

309

the respiration rate of the animal is derived from its

ECG signal and also delivered to the monitoring unit.

For proper ultrasonic acoustic transmission, the space

between the animal’s chest and the US transducer is

ﬁlled with a layer of water-based US gel in order to

diminish the attenuation of the reﬂected wave signal.

4 INTERACTIVE DATA

PROCESSING

In this section we describe our approach allowing in-

teractive 3D reconstruction of 3D US data sets based

on 2D slices acquired with the system setup described

in Section 3. After the reconstruction has been per-

formed (see Subsection 4.1), image processing tech-

niques are applied in order to enhance image quality

(see Subsection 4.2).

4.1 Volumetric Reconstruction

We support two approaches for reconstructing a 3D

US data set out of 2D slices. First, the standard ECG-

gated automated technique, and second, an interac-

tive technique. As mentioned in Section 1 the au-

tomatic reconstruction, which can be considered as

a well known standard technique, has several draw-

backs. With this technique, 2D scans of the heart

are captured only at designated locations within the

ECG heart cycle, thereby ensuring a relatively coher-

ent volume data set. However, the assumption that

heart form and deformation during each heart cycle

is identical during the whole duration of the acquisi-

tion process is misleading. Firstly, especially in cases

where the heart of the subject is contracting in an ir-

regular manner either due to immediate application

of a medication or to some kind of a heart disease,

each ECG heart cycle differs considerably from the

other, and this results in a large number of incoher-

ence artifacts in the resulting volume. Secondly, addi-

tional external factors such as respirational movement

or movement caused by instability of the biological

object can also cause irregularities in the single scans,

resulting again in incoherent data sets.

Our alternative interactive approach alleviates

these problems during the volume reconstruction by

integrating the user input into the process of selecting

the required number of slices and situating them at

their respective locations in order to construct a volu-

metric data set. In order to do so, the ECG curve of

the heart rate during which the 2D slices have been

recorded is shown. Based on this display, the user can

select an arbitrary slice depending on its position as

well as its location within the heart cycle.

Figure 1: Visualizing the entire sequences of ECG cycles

leads to visual clutter and makes it difﬁcult for the user to

identify a single frame within the whole cycle.

However, displaying the ECG cycle is a criti-

cal task. Therefore, in order to extenuate inco-

herency artifacts in the ECG cycle, the Vevo 770 US

scanner is conﬁgured to record high resolution ECG

data throughout the whole B-Mode scanning session.

However, this accumulated high bandwidth of ECG

frames alongside 2D US scans poses another prob-

lem. The length of the recorded ECG data exceeds

largely the length of the period of B-scan recording

because the US scanner keeps as many sequences of

ECG heart cycles as possible for purposes of inter-

polating them all into a spatially precise heart cycle

synchronized with the animal’s ECG. However, this

excessive amount of ECG heart cycles should not be

displayed entirely because the large number of single

ECG frames clutters the display (see Figure 1). In

order to create a usable display of the long ECG se-

quence of multiple heart periods, the interval of ECG

frames is cut off at the points which coincide with the

subinterval between the time stamps of the ﬁrst and

last recorded frame. Thus we obtain an ECG display

with considerably less cluttering, as it is seen in the

ECG overlay in Figure 2. The blue lines on top of

the ECG curve represent the slices which have been

recorded. The information about each slice is ex-

tracted from the meta data, which is generated by the

scanner. Besides other, this meta data also contains X-

and Y-resolution of each frame, start and end times-

tamps of the ECG data portion so that ECG samples

can be extracted, B-Mode ECG frequency enabling

the accurate positioning of frames in the ECG heart

cycle graph, heart period length and each frame’s di-

mensions in mm with respect to the scanned object.

After a slice has been selected by clicking on the

overlay display, its content can be displayed. In the

case of US slices, a greyscale image containing the in-

tensity values of the US 2D frame is generated and in-

serted into the display. This gives the user the control

over which slices to select for the data set and at which

positions to situate them. Moreover, the additional

display of the slice contents allows the user to addi-

tionally ”preﬁlter” those slices which, although situ-

ated at a suiting position, contain a large amount of

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310

Figure 2: The user interface supporting interactive US

volume reconstruction. The ECG curve is reduced to

avoid clutter and a B-scan frame display overlay is shown,

whereas the frame is enhanced by applying histogram

equalization.

noise and their insertion in the volume would merely

worsen the volume generation with respect to the geo-

metrical consistency of tissue surfaces. After the user

selects the required number of slices, the contents of

each slice are concatenated, combined into a data set

and can be stored and later on visualized.

Figure 2 shows the user interface which is used

for the interactive 3D volume reconstruction. The

text box at the top contains information pertaining to

the current object, be it a volume data set or a sin-

gle frame. The checkboxes below are used for ac-

tivating different auxiliary tools such as ECG heart

period overlay, B-scan frame overlay, application of

the transfer function and the thresholding of the voxel

values. All these features can be applied interactively

by providing immediate visual feedback.

Besides these standard volume visualization con-

trols, the system provides the interaction capabilities

necessary for the volume reconstruction. The shown

synchronization box is relevant for data sets acquired

through Vevo’s EKV-mode and can be used for play-

ing a data set collection dynamically. The custom

widget underneath has been developed to aid the po-

sitioning of single slices within a volume data set. By

selecting one of the rectangular boxes, the user se-

lects to display all frames which the US scanner has

recorded at the corresponding lateral position of the

scanhead. The currently selected position is high-

lighted by the green box contours and only those

frames are visualized on top of the ECG signal, which

have been acquired at the corresponding lateral posi-

tion. After a frame has been selected and its contents

inspected, if necessary, the user can add its raw con-

tents to the data set to-be-created by pressing the ”add

frame to data set”-button above. The current lateral

position is then disabled and the reconstruction can

be continued.

4.2 Image Processing

The US signal has a lower signal-to-noise ratio than

other medical scanning paradigms such as CT or

MRI, and, as a result, visualizing the raw, unmodi-

ﬁed US data delivers data, which can be optimized by

preprocessing. In order to deal with this effect, our

system allows to apply different image processing ﬁl-

ters to the selected slices. The ﬁlters can be applied

interactively, and the type of ﬁlter as well as the ﬁlter

parameters can be chosen using the user interface (see

Figure 2).

We have integrated two kinds of ﬁlters: linear as

well as non-linear spatial ﬁlters. Although (Sakas and

Walter, 1995) suggests their usage only in a prepro-

cessing step due to their resource-intensive computa-

tion, we were able to perform them interactively, since

the dimensions of the generated US data sets are rela-

tively small.

The linear ﬁlters operate in the spatial domain of

the input signal and, as such, are used for blurring and

noise reduction of the image data. Considering the na-

ture of noise artifacts in the US signal, this family of

ﬁlters is the most natural approach towards improv-

ing the visualization of US data. What is more, they

remove small artifacts and noise from images which

are very similar in structure and origin to common US

noise and speckle.

Characteristic for all linear spatial ﬁlters is that

they compute an intensity value of each pixel based

on the intensities of a number of neighboring pixels

selected by a square ﬁlter mask and a linear ﬁltering

function. Based on the latter, these ﬁlters are some-

times called averaging ﬁlters (Gonzalez and Woods,

2001). Since noise and image artifacts are substanti-

ated in the greyscale intensity distribution of an image

pixel grid as abrupt changes in grey levels, the averag-

ing function applied during ﬁltering brings all values

to an approximate image-wide average whose value

is determined by the surrounding pixel intensities and

the width of the ﬁlter mask. Hence, the main effect

of this type of ﬁltering is blurring of image regions

which differ radically from the rest of the image. The

disadvantage of using such ﬁlters is that along with

the noise removal, particular image segments such as

edges or contours similar to noise but corresponding

to the edge of a structure are also blurred, although

they are parts of the image that should not be mod-

INTERACTIVE RECONSTRUCTION AND VISUALIZATION OF DYNAMIC 3D ULTRASOUND DATA SETS

311

(a) no ﬁltering (b) arithmetic mean ﬁltering (3 × 3

kernel)

Figure 3: Application of different ﬁltering techniques to a single lateral slice. From left to right: no ﬁltering, arithmetic mean

ﬁltering and median ﬁltering.

iﬁed. A simple linear spatial ﬁlter is the arithmetic

mean ﬁlter, which computes the average sum of the

pixels under the ﬁlter mask and assigns the resulting

value to the center pixel, in the case of an equilateral

ﬁlter mask and in the two-dimensional case:

I(p

) =

∑

i=1

, p

∈ P. (1)

In the above formula, p

, p

denote pixels in the

set of pixels P belonging to an image and k de-

notes the side length of the equilateral ﬁlter mask. A

slight modiﬁcation of the arithmetic mean ﬁlter is us-

ing a mask which assigns to each pixel a different

weight and thus different importance of each pixel

with which it participates in the sum. However, both

ﬁlter versions deliver similar results due to the fact

that the ﬁlter mask is small relative to the size of the

noise grains in the image. Its application is shown in

Figure 3(b).

The median ﬁlter (see Figure 3(c)) is a non-linear

spatial ﬁlter, which operates by ordering the pixels se-

lected by the ﬁlter mask according to their grey level

intensities, then choosing the median out of them and

replacing with it the pixel intensity at the center of the

ﬁlter mask. In comparison to a linear ﬁlter a median

ﬁlter with the same sized ﬁlter mask delivers better

results in noise reduction and results in less blurring.

Thus sharp edges can be better retained in compari-

son to the mean ﬁlter (see Figure 3). Thus, we have

reduced the functionality of the user interface to be

able to apply the median ﬁlter instead of the mean ﬁl-

ter.

Additionally, we have integrated the BLTP ﬁl-

tering technique originally proposed by Sakas et

al. (Sakas and Walter, 1995). However, unlike their

implementation developed for surface extraction, we

have modiﬁed the opacity values to be binarized such

that they are not all positive voxel values but, instead,

they are selected through intensity thresholds which

are dynamically controlled by the user. As a result,

the criterion for removing a voxel value is determined

interactively by a lower and upper threshold within

the interval of the data set intensities. Thus a certain

amount of noise can be removed manually, thereby

improving the interactive rate of the ﬁlter’s response.

To adjust and improve the contrast of the separate

US B-scan images whose grey values are positioned

within a low dynamic range, we additionally apply a

histogram equalization.

5 APPLICATION EXAMPLES

The application examples for this paper have been

prepared from US data acquired from scanning sev-

eral laboratory mice specimen with genetically in-

duced LQTS (long qt) syndrome for the purposes of

medicament-based disease prophylaxis. Every ani-

mal’s cardiac section has been extensively scanned

while under light sedation, and the procedure has been

executed in strict compliance with cardiac research

norms dictated by the speciﬁcs supplied with each

medicament prototype.

When generating the volume data sets for this pa-

per, the scanhead was mounted onto a rail in order

to improve mobility and produce a B-Mode image at

several lateral positions within the animal (see Fig-

ure 4). The spacing between the B-scan mode slices

along the travel axis was 0.25mm. Since the scanned

cardiac region of the mouse is relatively small, at

least twenty slices in traveling direction were required

for sensible dimensions of the generated volume data

sets. A major problem when creating the data set was

aligning the acquired lateral frames from the mouse

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312

Figure 4: A single lateral slice showing a cross-section view

of the heart.

heart precisely so that a volume image of a still heart

could be created while the mouse was showing a

heart pulse of 300-450 bpm in an anesthetized con-

dition. After positioning the US scanhead over each

lateral location, the image acquisition was initiated

by switching the scanner to EKV mode. Consider-

ing the quality of the scans required, the EKV mode

took several minutes per lateral position, extending

the duration of anesthesia. In order to alleviate that,

additional measures of maintaining the animal’s tem-

perature within the normal range were undertaken and

the animal was placed under an infrared heating lamp.

5.1 Application Case 1

One of the possible utilizations of medical US in car-

diac research is the inquiry and measurement of the

heart septum, i.e. the wall separating the left and right

heart ventricle. One complication when this separat-

ing wall is damaged is known in the medical profes-

sion as Ventricular Septal Defect (VSD) (Lung and

Institute, 2006), which results mostly from a small

perforation located between the lower chambers of

the heart. When untreated, this heart defect degen-

erates into, among others, congestive heart failure, ar-

rhythmia and pulmonary artery hypertension. Cross-

sectional slices can show the septums’ condition only

at the particular lateral position of the scan (see Fig-

ure 4). A 3D view of the complete septum allows

much easier diagnostics of VSD and precise hole

measurements in contrast with 2D US. Therefore we

have conducted a scanning procedure in order to di-

agnose VSD in different mice.

In Figure 5(a) a rendered volume data set is shown

which is clipped up to the same cross-section as in

(a) Raw clipped data set (no ﬁltering).

(b) Application of a BLTP ﬁlter.

Figure 5: 3D data sets acquired during application case 1,

showing the same cross-section as shown in Figure 4. No

image-processing is applied (top), a BLTP ﬁlter as well as a

modiﬁed transfer function is applied (bottom).

Figure 4, such that this 2D slice is situated in the data

set. It shows that the septum wall in the upper right

corner of the volume cube is barely visible. In order

to be able to show more details of the septum wall,

several techniques are applied to the volume image.

The resulting data set is displayed in Figure 5(b),

after applying a BLTP ﬁlter with underlying Gaus-

sian with σ value of 0.621, resulting in a 1D kernel

mask of [1 3 1] and a BLTP threshold value of 0.15,

thus removing small speckle regions from the data set.

Although the ﬁlters and the thresholds have removed

parts of the original image, the septum can still be

distinguished in the bottom image. What is more, the

applied transfer function allows for easier demarca-

tion of each wall side of the septum, thereby reveal-

ing some of its anatomical properties such as width in

both clipping directions and location within the heart

structure. Additionally, by repeatedly changing the

clipping parameters of the volume, the user can in-

INTERACTIVE RECONSTRUCTION AND VISUALIZATION OF DYNAMIC 3D ULTRASOUND DATA SETS

313

spect the dimensions and spread of the septum wall in

the whole heart volume interactively.

The abrupt discontinuities visible especially in the

right upper side of the volume where the septum wall

is located are caused by the insufﬁcient amount of lat-

eral frames that constitute this volume data set (in this

case ∼ 20). This is due to the fact that with spacing of

0.5mm between each lateral position, the granularity

of the scanning installation is rather coarse in contrast

to the longitudinal size of a mouse heart of approxi-

mately 1cm.

5.2 Application Case 2

In order to somewhat alleviate the shortcoming of too

few lateral slices, the granularity of the scanning in-

stallation has been increased with an additional scale

in sub-millimeter precision. In Figure 6 two render-

ings of thus generated data sets are shown, the lateral

slices have been acquired with a spacing of 0.25mm.

This improves the overall visualization quality and

in particular the coherency of the single structures.

The effect is especially visible in Figure 6(b), where

the enclosing wall of the left heart ventricle can be

viewed as an almost coherent and contiguous struc-

ture. What is more, the ridge labeled as septum can

be followed from the frontal beginning of the cross-

section to the very end of the heart - the apex. Addi-

tionally, the same ﬁltering is applied to the data set:

BLTP with underlying Gaussian of σ value of 0.621

and BLTP threshold of 0.42. In this case, the ﬁlter

does not remove signiﬁcant parts of the heart structure

but merely blobs and artifacts hindering the proper

display of the inner anatomy.

6 CONCLUSIONS

In this paper we have presented techniques compris-

ing a possible 3D US preprocessing and visualization

scheme. With the proposed system we are able to

reconstruct 3D US data sets from 2D slices by ap-

plying a new interactive reconstruction approach. To

facilitate reconstruction, the 2D lateral scans are vi-

sually organized based on their position as well as

their phase within the heart period, which is recorded

during the scans by using ECG. In Contrast to exist-

ing techniques, which reconstruct a volume automat-

ically, the user has additional inﬂuence when using

our approach and is thus able to reconstruct volumet-

ric data sets having a higher quality. In addition to the

proposed reconstruction methods, we have applied ﬁl-

tering techniques in order to reduce artifacts.

(a) Raw clipped data set (no ﬁltering).

(b) Application of a BLTP ﬁlter.

Figure 6: 3D data sets acquired during application case 2.

No image-processing is applied (top), a BLTP ﬁlter as well

as a modiﬁed transfer function is applied (bottom).

Thus, the proposed interactive approach towards

volume reconstruction encompasses a ﬂexible way for

exercising maximum control when constructing vol-

ume data sets out of 2D slices by allowing the user to

select each single slice manually. By displaying the

contents of each slice and its temporal position in the

heart ECG, it provides for a user-based ”pre-ﬁltering”

of the ﬁnal volume contents.

ACKNOWLEDGEMENTS

This work was partly supported by grants from the

Deutsche Forschungsgemeinschaft (DFG), SFB 656

MoBil M

unster, Germany (projects Z1, C3).

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