Leroy C., Rancoita P.-G. Principles Of Radiation Interaction In Matter And Detection

Подождите немного. Документ загружается.

January 9, 2009 10:21 World Scientiﬁc Book - 9.75in x 6.5in ws-bo ok975x65˙n˙2nd˙Ed

780 Principles of Radiation Interaction in Matter and Detection

one after the other. Of course, for the immobile atoms, this gradient has no ef-

fect since each lobe will nullify the eﬀect of the other one. But, a moving nucleus

will be aﬀected. Therefore, to see the blood movement, one has to take the image

twice (once with and once without the bipolar gradient) and subtract one from

the other. The immobile matter will disappear, while the moving matter will have

diﬀerent intensities depending on its velocity.

The last technique is the most used: the contrast enhanced angiography. It is

based on the principle that the relaxation time, T

, changes when a paramagnetic

contrast agent is injected into the blood. In brief, T

changes with the blood’s

surroundings. And as it changes, contrasts can be seen. A rapid data acquiring

sequence is used.

11.3.2.5 Functional MRI

Using a sequence of impulsions and gradients called the echo-planar imaging, it

is possible to gather the information needed for a whole image in the short time

perio d TR. This allows one to take several images pictures per second just like a

video. This technique opens new avenues to study the human body. For example, it

is possible to track the blood ﬂows in the brain allowing an elaborate study of the

brain’s reaction to stimuli.

The idea behind echo-planar imaging is to sweep all sections of a k-space (the

Fourier transform of the image) [Hornak (2002)]. First, a saturation pulse and a slice

selective gradient are applied to the system. Then, simultaneously a phase and a

frequency encoding gradients are injected, bringing the initial data to a “corner” of

the k-space. A bit after, an inversion pulse is applied. Finally, the following sequence

is used to sweep the k-space: a phase gradient is applied, immediately followed by

a frequency gradient, during which data is gathered; then, another phase encoding

gradient is applied after which another echo is produced; and the previous steps are

repeated, until the entire k-space is swept.

11.4 X-Ray Medical Imaging with MediPix Devices

The MediPix device, discussed in Sects. 6.5.1-6.5.2.5, can be exploited for medi-

cal imaging. Medical imaging is typically in the 5–80 keV X-ray energy range. The

photoelectric eﬀect is the dominant interaction between X-ray photons and detect-

ing material in that energy range. In this section, we look at the application of

MediPix-type devices in X-ray medical imaging. The MediPix-type devices, when

exposed to X-ray beams, produce real-time digital images that can be stored and

analyzed. These devices can improve the quality of image as the X-ray detection

is improved while the noise is reduced. This improvement of the image quality al-

lows the reduction of the radiation exposure to the patient. The image quality is

expressed in terms of several parameters. Some of the most important parameters

January 9, 2009 10:21 World Scientiﬁc Book - 9.75in x 6.5in ws-bo ok975x65˙n˙2nd˙Ed

Medical Physics Applications 781

are brieﬂy reviewed below. However, this list is non-exhaustive and readers who

wants to complete their information are invited to consult [Mikulec (2000); Pfeiﬀer

(2004); Stoehr (2005); Norlin (2007)], for instance.

11.4.1 The Contrast

In the 5–80 keV energy range, tissue, bone and calciﬁcations have very distinct

absorption coeﬃcients and high-contrast images can be formed. The contrast, C,

is describing the diﬀerence in intensities I

and I

between two adjacent regions

(several pixels) which present diﬀerent absorptions of X-rays. If one uses a photon

counting system, the contrast can be expressed in terms of counts between the

two adjacent regions. If N

and N

are the photons counted in the two regions

(normalized to the same area), the contrast is deﬁned as [Mikulec (2000); Anton et

al. (2006)]:

C =

− I

+ I

− N

+ N

. (11.43)

Since the numbers of counted photons have a Poisson noise, one deﬁnes a signal-

diﬀerence-to-noise ratio (SDNR) which measures the visibility of a given con-

trast [Anton et al. (2006)]:

SDN R =

− N

−N

= C

+ N

, (11.44)

where σ

−N

is the variance of the counts distribution. For a contrast C, a parti-

cular value of SDNR can be achieved by either long exposure to photon counting

(large incident photon ﬂuence) or a large pixel-area [Anton et al. (2006)].

11.4.2 The Modulation Transfer Function

One deﬁnes the modulation transfer function (MTF) as the spatial frequency re-

sponse of an imaging system or a component. The spatial frequency is measured

in units of cycles per mm (c/mm) or also in units of line pairs per millimeter

(lp/mm). The MTF is the contrast at a given spatial frequency relative to low

frequencies and therefore measures the quality of transmission (in to out) of the

contrast of an object through an imaging chain for a given spatial frequency. High

spatial frequencies correspond to ﬁne image detail. Signals which change often over

a given distance have a high spatial frequency. Signals with low spatial frequency,

i.e., which change slowly over the same distance are easier to detect than those of

high spatial frequency. The MTF at a spatial frequency ν is deﬁned as the ratio

between the modulation of a sinusoidal pattern M

and the modulation of image

out

obtained after transmission [Pfeiﬀer (2004)]:

MT F (ν) =

out

(ν)

. (11.45)

January 9, 2009 10:21 World Scientiﬁc Book - 9.75in x 6.5in ws-bo ok975x65˙n˙2nd˙Ed

782 Principles of Radiation Interaction in Matter and Detection

The M T F (ν) ranges between 0 and 1 for all frequencies. The MTF can be described

by analytical functions. In the case of square pixel (such is the case of MediPix1

and MediPix2) of size l

with uniform sensitivity over the whole pixel area, the

theoretical limit for MTF is [Pfeiﬀer (2004)]:

MT F (ν) =

sin(πνl)

π νl

. (11.46)

This parametrization comes from the possibility to decompose the information for a

given image into a set of sinusoidal functions of diﬀerent amplitude. Therefore, one

can say that the MTF gives the spatial response of a detector to a sinusoidal input

stimulus. There are several factors aﬀecting the MTF: a) focal spot blur: because

the X-ray source is not point-like and causes blur in the X-ray image. Standard

procedures to minimize this eﬀect is to reduce the focal spot size, optimizing (in-

creasing) the distance between the source and the subject of imaging and decreasing

the distance between the subject of imaging and the X-ray detector (basically what

one would do with a camera); b) the pixel size: the pixel size has to be as small

as possible (55 µm × 55 µm for MediPix2) possibly smaller than the details of the

image; c) scattering of photons produced from the conversion of absorbed X-rays:

this eﬀect can be minimized by the choice of an adequate conversion material.

11.4.3 The Detective Quantum Eﬃciency

The detective quantum eﬃciency (DQE) is the signal-to-noise ratio (SNR) transfer

function. It measures how the SNR at the input (SNR

, SNR of the incoming

X-ray ﬂux) of an imaging system is transferred to the output (SN R

out

, SNR of

the image) and measures its possible degradation by the imaging system. Then, the

DQE is expressed as:

DQE(ν) =

SNR

out

(ν)

SNR

(ν)

. (11.47)

The noise is from various origins: the electronic, ﬁxed pattern and quantum

noises. The electronic noise is produced by the read-out components of the imaging

system. The ﬁxed pattern noise originates from gain and oﬀ-set value variations

among pixels. The so-called quantum noise is the result of the random nature of the

X-ray photons: the number n

of X-ray photons produced by the source incident

per unit area and unit time on the detector has ﬂuctuations that follow a Poisson

distribution with a variance

√

. Then, with SNR

√

, Eq. (11.47) can be

written as

DQE(ν) =

SNR

out

(ν)

. (11.48)

SNR

out

is determined by using the noise power spectrum (NPS). The NPS describes

the noise transfer properties of the imaging system. The NPS is a quantity which

accounts for the distribution of noise variations with spatial frequency. Technically,

January 9, 2009 10:21 World Scientiﬁc Book - 9.75in x 6.5in ws-bo ok975x65˙n˙2nd˙Ed

Medical Physics Applications 783

the calculation of the NPS uses the Fourier transform of noise image to determine

the variance of noise power present at each spatial frequency. The shape of the NPS

shows where the noise power is concentrated in frequency space [Riederer, Pelc and

Chesler (1978); Boedeker, Cooper and McNitt-Gray (2007)]. In simpler terms, the

NPS gives the variance of a noise process, but distributes it as a function of the

spatial frequency. Hence, using the normalized NPS (NNPS) and the MTF, one

has [Pfeiﬀer (2004)]:

SNR

out

MT F

(ν)

NNP S(ν)

. (11.49)

Combining Eqs. (11.48), (11.49), one ﬁnds:

DQE(ν) =

MT F

(ν)

NNP S(ν) × n

. (11.50)

One can consult, for instance, [Mikulec (2000); Pfeiﬀer (2004); Stoehr (2005); Norlin

(2007)] for a review of results of the measurements of MTF, NPS and DQE done

with MediPix1 and MediPix2. A ﬁnal remark for this section is the phenomenon of

charge sharing and its implication for X-ray imaging. As discussed in Sect. 6.5.2.5,

charge sharing results from several mechanisms with the consequence that deposited

charges are shared among adjacent pixels. Particle physics may use the charge shar-

ing eﬀect for improved tracking. For medical physics charge tracking is viewed as an

adverse phenomenon as it decreases the photon detection eﬃciency. Depending on

the threshold set for the MediPix2-type device, incoming photons can be counted a

single time or several times. There are several ways envisaged to reduce the charge

sharing eﬀect and even to suppress it. It has been proposed to develop a readout

electronics which can sum the charge of several pixels [Llopart et al. (2002)]. This

solution has however a drawback as summing charges collected in several pixels

yields additional noise. The problem of charge summing and adequate noise control

will be hopefully solved with MediPix3, the successor of MediPix2 [Medipix Collab.

(2008)]. Another solution advanced for suppression of the charge sharing eﬀect is to

develop 3-D structure detectors in place of the standard planar pixel detectors. It

is advocated that the transverse electric ﬁeld in a 3-D structure (perpendicular to

the incoming photon) will force the electron to drift to the correct pixel [Norlin

(2007)]. This development has to be accompanied with an increase of the silicon

thickness for maintaining a practical quantum eﬃciency.

January 9, 2009 10:21 World Scientiﬁc Book - 9.75in x 6.5in ws-book975x65˙n˙2nd˙Ed

This page intentionally left blankThis page intentionally left blank

January 9, 2009 10:21 World Scientiﬁc Book - 9.75in x 6.5in ws-bo ok975x65˙n˙2nd˙Ed

Appendix A

General Properties and Constants

785

January 9, 2009 10:21 World Scientiﬁc Book - 9.75in x 6.5in ws-bo ok975x65˙n˙2nd˙Ed

786 Principles of Radiation Interaction in Matter and Detection

A.1 Conversion Factors

The conversion factors are from Appendix B.9 of [Taylor (1995)].

January 9, 2009 10:21 World Scientiﬁc Book - 9.75in x 6.5in ws-bo ok975x65˙n˙2nd˙Ed

Conversion Factors 787

January 9, 2009 10:21 World Scientiﬁc Book - 9.75in x 6.5in ws-bo ok975x65˙n˙2nd˙Ed

788 Principles of Radiation Interaction in Matter and Detection

January 9, 2009 10:21 World Scientiﬁc Book - 9.75in x 6.5in ws-bo ok975x65˙n˙2nd˙Ed

Conversion Factors 789