UofM NERS/BIOE 580 - 09_Image

NERS/BIOE 580
Lab09 - Image Module A

Purpose:

In the previous module, we examined the performance of a detector system used for general radiography and another used for mammography. The detective quantum efficiency (DQE) was computed for polyenergetic radiation penetrating a typical thickness of tissue. To determine DQE, the noise equivalent quanta (NEQ) associated with a specific exposure (mA-s) was computed. The NEQ is simply the square of signal to noise ratio (SNR) in the recorded image.
In this module we examine the contrast to noise ratio (CNR) associated with a small target object embedded within the tissue structure being radiographed. Specifically, the kVp which optimize the CNR for a particular imaging task is sought.

Discussion:

When radiographing an object, projections through a small target object will have a transmission that is different compared with neighboring regions which often have relatively uniform transmission. We define the relative contrast as the signal difference between the target and background region divided by the signal in the background region;
C_r = (S_t - S_b)/S_b

The ability to observe the target image in the recorded radiograph is largely dependent on the absolute signal difference divided by the noise in the signal in the background regions, σ_b. Therefore the CNR is the product of C_r and the signal to noise ratio in the background region:
CNR = (S_t - S_b) / σ_b
= C_r (S_b / σ_b)
= C_r * sqrt(NEQ)
CNR can thus be determined by computing the relative contrast as long as the NEQ in the background region is known.
For monoenergetic radiation beams, C_r can be easily shown to be equal to;
C_r = exp[ -(µ_t - µ_b)δ_t ] - 1
where µ_t and µ_b are the attenuation coefficients in the target and neighboring background regions and δ_t is the thickness of the target. For small arguments of the exponent this is well approximated as
C_r = -(µ_t - µ_b)δ_t.

When considering polyenergetic beams, the energy dependent transmission and detector signal efficiency must be accounted for when determining C_r . When deriving this, there is a transmission term of the form exp(-µ(E)δ_t) that occurs within the integrations over pathlength and energy that are used to compute the signal in the target region, S_t, and the signal in the background region, S_b. For a small target, the attenuation difference comes from the difference in µ(E) over the region of the target, µ_t(E) - µ_b(E). When [µ_t(E) - µ_b(E)]δ_t is small, these equation can be simplified to yield;

where h_s is the detector signal absorption efficiency, and f(E) is the transmitted x-ray energy spectrum that is incident on the detector. The denominator is seen to be simply S_b and the numerator is the signal difference, S_t - S_b , caused by the difference in attenuation coefficients in the region of the target and in the background regions.
If we define the effective attenuation as a weighted average of µ(E),

then C_r can be expressed as
C_r = (µ_t^eff - µ_b^eff)*δ_t
In this module, we will use a computational routine to obtain µ^eff and use this to deduce C_r and CNR.

Task Img-A1: effective attenuation coefficients.

In the documentation directory, _doc, there is a description of the program `mu_eff' that computes the effective attenuation coefficient associated with a material. Read the documentation for mu_eff The value of µ_eff depends specifically on the spectrum in the spectra.tmp file which is taken to be the spectrum input to a detector. It is also dependent on the energy absorption efficiency of a particular detector.
Now work from a directory with a spectra.tmp file copied from the previous lab module for a tungsten target tube with a kVp of 150, typical tube filtration, and object tissue (17 cm muscle and 3 cm fat). Start the command window with a link.tcl file that sources the tcl procedures. Then run mu_eff from the command window using the muEff tcl procedure. Specify a tissue material and the Sel-tft detector from the files available in the _materials and _detectors directories. Run the muEff procedure with the print flag on and then off;

muEff muscleNBS Sel-tft.det 1
muEff muscleNBS Sel-tft.det 0

Then use atten_coeff (attenCoeff tcl procedure) to determine the energy for which the attenuation coefficient of muscleNBS is equal to the effective attenuation coefficient. Plot the spectra.tmp file this energy identified on the horizontal axis . This is the effective energy with respect to image contrast for this particular material and this radiographic technique.
Note: The indentification of this energy can be done using the 'SET ARROW ..' gnuplot command in the plot script. For example, if the effective energy is identified as 63 keV, the command would be similar to:
SET ARROW from 63.0,0 to 63.0,20000.0

Task Img-A2: Contrast to Noise ratio for tissue targets.

The Sel-tft detector is typical of detectors used for general radiography. For thoracic imaging, high kVp is often used to compress the range of transmitted signal in the region of the lung relative to the mediastinum. In this task we will set up a model representative of a thoracic imaging system and examine the contrast to noise of small tissue targets. For simplicity, we will assume that the background µ_b is 0 and is associated with air in the lung. The target background will be tissue (muscleNBS) which is taken to be representative of a small cancer nodule that could be located in the lung.
Create a model using the following:

Initialize xSpect: source link.tcl (with procedures)

... ...

source: spectGen

filtration: atten

distance to object: sr2cm

input exposure: mR

object attenuation: atten

object exit distance: cm2cm

exit exposure: mR

detector distance: cm2cm

target effective mu: mu_eff

detector NEQ: detect

... ...

output: ----

This is similar to the model used in the previous module. For the x-ray source, use a tungsten target with a constant potential and a target angle of 10 degrees. In this task, we will examine kVp values up to 300, thus a dkeV of 2 should be used in `spect_gen' to maintain the total number of data points in the spectrum below the limit of 300. For added filtration use 0.24cm glass-pyrex, 0.31cm oil, 0.27cm lexan (GE Maxiray 125), and an added 0.15cm al_1100 as was used in the prior module.
Set the distance to the object at 150 cm using the sr2cm routine . For the object use a total thickness of 14 cm comprised of 12 cm of muscle and 2 cm of fat. The distance to the object exit should then be adjusted using the cm2cm routine to account for the object thickness. After getting the exit exposure using the mR routine, the distance to the detector should be set at 180 cm using the cm2cm procedure.
For the arguments to the various XSPECT procedure calls used in the model, use variables in the procedure calls and define the variable values at the beginning so that the model can be easily changed. Then initiate a loop over the kVp that will compute the effective attenuation coefficient and NEQ as a function of kVp;

set muscle 12.0
set fat 2.0
set targetT .1 ;#thickness of tissue target, cm
set Ap .0004 ;#pixel area cm2, size = .2 mm.
set At [expr $targetT*$targetT*3.14/4.0] ;# area
set mas 3.0 ;#mA time seconds
set Al .15 ;#added filtration thickness
set minKV 40
set maxKV 250
set Incr 5
...
set kVp $minKV
while {$kVp <= $maxKV} {
...
... [model procedure routines]
...
incr kVp $Incr
}

A detector pixel area of .0004 cm^2 is typical (i.e. .2 mm x .2 mm) as is an mA-s of 3.0. The target area should be set equal to the area of a circle with diameter equal to the target thickness as shown above.
Within the body of the script loop where the procedure calls for the model are located, the results for the input and output exposure should be set to output variable values along with the effective attenuation coefficient and the detected NEQ. Remember to explicitly account for the mA-s when getting the exposure results. Finally deduce the CNR as the product of the C_r = µ_eff*δ_t and the SNR.
The SNR is computed on the basis of the detector pixel area. For the larger area of the target, a better CNR is expected. Therefore, the CNR should be increased by multiplying by the square root of the ratio of the areas, sqrt(At/Ap).
For human subject radiography, a figure of merit that is useful is the CNR in relation to the radiation exposure to the patient. Since the CNR is proportional to the square root of mA-s and the exposure is proportional to mA-s, the CNR can be normalized by dividing by the square root of the exposure. This figure of merit, FOM, is then independent of the mA-s. For this model, use the square root of the average of the input and exit exposures;
FOM = CNR / mR_avg^1/2

Now produce a plot of this FOM, i.e. the exposure normalized CNR, for a 1 mm thick tissue target with a projected area equivalent to a 1 mm diameter object as a function of kVp for energies from 40 to 250 kVp (increments of 5 kVp are sufficient). An optimum of about 1.3 should be observed at a kVp of about 115. Thus for an average exposure of 16 mR, the CNR would be about 5 which would make this target just visible. The total tissue thickness used of 14 cm is typical of Posterior to Anterior (PA) projections through the lung. Within the lung, tissue targets of about 1 mm size are the limit of that which can be observed.
By redefining the detector as an ideal detector, ideal.det, produce a similar plot. It will be apparent that the detector causes a significant shift in the optimal kVp. Save this model as it will be needed in the next laboratory module (10_Image_B).
Now change the tissue thickness to 28 cm (24 cm muscle, 4 cm fat) and produce the same plot as above using the Se detector. You will see that the optimal kVp increases to about 155 and the normalized CNR is reduced to about .27. For an average exposure of 16 mR, this would produce a CNR of about 1 which would not be visible in relation to the surrounding noise in the signal. This tissue thickness is typical of mediastinal regions in the thorax and regions below the lung where reduced contrast to noise is observed in chest radiography.

Task Img-A3: Contrast to noise for small calcified targets.

Make a copy of the model just built and modify it to compute the exposure normalized CNR for a small mineralized target object in 5 cm of tissue recorded using mammographic imaging methods. As was done in the previous laboratory module, use a molybdenum target tube with a 16 degree target angle and a .08 cm berylium window with added filtration of .010 cm molybdenum. Use the CsI-ccd.det file for the detector. For the target material which produces the contrast, use bone2.2 which is similar to the calcifications found in breast cancer. In this case, compute the relative contrast by determining the effective attenuation coefficient for bone2.2 and for muscleNBS and subtract the two values. In the spectral generation routine, request an increment of .5 keV to provide detail in the spectrum. For the remaining parameters use;

set muscle 4.0
set fat 1.0
set targetT .015 ;#thickness of tissue target, cm
set Ap .0001 ;#pixel area
set At [expr $targetT*$targetT*3.14/4.0] ;#target area
set mas 200.0 ;#mA time seconds
set minKV 20
set maxKV 50
set Incr 2
Finally adjust the distance to establish a distance to the object of 60 cm and to the detector as 70 cm.
Similarly plot the exposure normalized CNR. You will observe an optimal kVp of about 28 which is typical of that used in clinics and hospitals performing mammography. The normalized CNR should be about 0.3. For an average exposure of 200 mR, this will result in a CNR of about 4 which would make this 150 micron thick mineralized target barely visible. This is typical of the limitations in clinical mammography.
By redefining the detector as an ideal detector, ideal.det, produce a similar plot. In this case, the optimal kVp is only slightly different. This is because the x-ray spectrum is dominated by the characteristic radiation which does not change in energy as the kVp is changed.
Finally, change the muscle component of the tissue to 6 cm for a total thickness of 7 cm. Again the optimal kVp is not significantly changed. The CNR is seen to be reduced by a factor of 3 which would make the 150 micron calcification not visible. This illustrates why physical pressure is used to compress breast tissue to a thin slab when performing mammography. At high kVp, the CNR is seen to slowly rise. This is due to penetration of the higher energy bremsstrahlung radiation through the molybdenum filter.

Comment:

Historically, determination of optimal radiographic technique factors evolved over time by trial and error. Since most radiography was performed with screen film systems having similar detection characteristics, these techniques became established at many centers.
Many new detection systems have been recently introduced for which x-ray detection occurs in materials with significantly different absorption characteristics than traditional film screens. Additionally, the wide range of response associated with modern digital radiography systems offers opportunities for imaging using techniques that are not practical with screen film systems. It has thus become important to examine optimal techniques with respect to kVp and added filtration for these new systems. The computational modeling techniques used in this module provide a way to simulate performance and deduce optimal techniques without performing tedious experiments.
There are two limitations of the method used here that can effect the results. First, we have not considered the effect of scattered radiation on contrast reduction and the manner in which it varies with the incident x-ray spectrum. Secondly, we have used a very approximate expression for the biologic risk of the radiation used (i.e. the average of the input and the exit exposure). A more accurate results would be obtained by normalizing CNR using the integral absorbed radiation dose.

Lab09 Results:

For this module, please turn in the plots for the spectrum showing the effective energy, and plots for both the thoracic imaging and the mammography systems which identify the optimal kVp when using actual detectors and when considering an ideal detector. As before, turn in the scripts used to generate the data for the CNR plots.

L09-Img-A1.png : spectral plot showing the energy where μ(E) = μ_eff.
L09-Img-A2_1.png : Tungsten FOM vs kVp, 14 cm tissue, Se detector.
L09-Img-A2_2.png : Tungsten FOM vs kVp, 14 cm tissue, ideal detector.
L09-Img-A2_3.png : Tungsten FOM vs kVp, 28 cm tissue, Se detector.
L09-Img-A2_2.tcl : Tungsten tcl script, 14 cm tissue, ideal detector (for lab 10).
L09-Img-A3_1.png : Moly FOM vs kVp, 5 cm tissue, CsI detector.
L09-Img-A3_2.png : Moly FOM vs kVp, 5 cm tissue, ideal detector.
L09-Img-A3_3.png : Moly FOM vs kVp, 7 cm tissue, CsI detector.
L09-Img-A3_2.tcl : Moly tcl script, 7 cm tissue, CsI detector.

L09-Img-A[2,3] Reference script: Lab09_ImgA2-3.tcl

Note: this reference script includes a tk window in which the model type is first selected;

General Radiography
Mammography
Angiography

and then a second window presents the default variable values in entry widgets which can be used to make parameter changes. As suggested in this lab the parameter values are set at the beginning of the script as group for each of the model types. An if {...} elseif {...} elseif {...} structure is used to set the selected variables.

The next module is 10-Image-B.

NERS/BIOE 580 Lab09 - Image Module A

NERS/BIOE 580
Lab09 - Image Module A