Evaluation of the Effects of Dose on Lung Ventilation Calculated

from 4D-CT using Deformable Image Registration

An Application of a Ventilation Calculation Algorithm based on 4D-CT

Kujtim Latifi, Thomas J. Dilling, Craig W. Stevens, Vladimir Feygelman,

Eduardo G. Moros and Geoffrey G. Zhang

Department of Radiation Oncology, Moffitt Cancer Center, Tampa, Florida, U.S.A.

Keywords: Deformable Image Registration, Ventilation Calculation, 4D-CT, Lung Ventilation, Radiotherapy,

Radiation Dose.

Abstract: Ventilation derived from 4D-CT using deformable image registration (DIR) has been found correlate to the

result from a conventional modality very well. How radiation affects ventilation in lungs is still not clearly

studied. In this paper, ventilation versus radiation dose is investigated using ΔV method, a ventilation

calculation algorithm based on 4D-CT and DIR. Diffeomorphic morphons was used as the DIR tool. Tidal

volume normalized ventilation was used in this study. A total of 20 SBRT lung cancer patients’ 4D-CT and

planning dose data were retrospectively analysed. All the patients had two sets of 4D-CT, one at pre-

treatment and one post treatment. Ventilation distributions were calculated based on the two sets of 4D-CT

for each case. The two ventilation data sets were aligned using DIR. Radiation dose distributions were

resampled to match the resolution of CT images. A ventilation (or ventilation change) and dose values were

thus associated to each voxel of the CT images. A function (ventilation change) – dose – volume surface

was generated for each case. Average ventilation was found degraded in higher than 20 Gy dose regions for

16 out of the 20 cases. This result can be applied in treatment planning to spare functional lung volumes.

1 INTRODUCTION

Lung functional information has been proposed to be

used in radiation therapy (RT) treatment planning to

spare normal functional lung volumes (Lavrenkov et

al., 2007; Shioyama et al., 2007). Conventionally

and clinically, lung functional data are acquired

using nuclear medicine techniques (Petersson et al.,

2004; Suga, 2002). Recently, algorithms have been

developed to derive ventilation distribution matrix

from four-dimensional computed tomography (4D-

CT) images using deformable image registration

(DIR) (Guerrero et al., 2005; Reinhardt et al., 2008;

Zhang et al., 2009). Promising comparison result has

been made between ventilation images using 4D-CT

and a conventional method (Ding et al., 2012). The

advantages of ventilation data derived from 4D-CT

include its quantitativeness, high resolution and low

cost. As 4D-CT is routinely taken for treatment

planning purposes when treating lung cancer

patients using radiotherapy, ventilation data can be

derived from the 4D-CT without any extra imaging

procedure.

Functional lung images were suggested to be

used in treatment planning to spare functional lung

volumes in order to safely escalate radiation dose in

patients and improve disease control (Yaremko et

al., 2007). However, without a thorough

understanding of the effect of radiation dose on lung

functions, it is not meaningful setting up objectives

or constraints in treatment planning. To

meaningfully implement functional lung sparing in

treatment planning in clinical practice, a study of

ventilation change versus radiation dose needs to be

performed.

Ventilation imaging using 4D-CT was proposed

to be used to evaluate the ventilation change due to

radiation therapy by Ding et al in which two

patients’ data were analysed (Ding et al., 2010). This

study uses derived ventilation from 4D-CT scans to

evaluate the effects of radiation treatment on lung

ventilation. Besides more patient data, a different

DIR algorithm and ventilation calculation algorithm

were used in this study. In addition, ventilation data

Latiﬁ K., J. Dilling T., W. Stevens C., Feygelman V., G. Moros E. and G. Zhang G..

Evaluation of the Effects of Dose on Lung Ventilation Calculated from 4D-CT using Deformable Image Registration - An Application of a Ventilation

Calculation Algorithm based on 4D-CT.

DOI: 10.5220/0004719700050011

In Proceedings of the International Conference on Bioimaging (BIOIMAGING-2014), pages 5-11

ISBN: 978-989-758-014-7

 2014 SCITEPRESS (Science and Technology Publications, Lda.)

in this study were normalized to tidal volume for a

more accurate analysis.

2 MATERIALS AND METHODS

The use of patients’ de-identified 4D-CT image and

3D dose distribution data in this retrospective study

using the ventilation calculation algorithm based on

4D-CT and DIR closely followed an institutional

review board (IRB) approved protocol.

Figure 1 shows the flow diagram of the analysis

of ventilation change due to radiotherapy using 4D-

CT and DIR. Two phases, expiration and inspiration,

from each 4D-CT data set were used for ventilation

distribution calculation. DIR was applied 3 times for

each case, one for each ventilation calculation of the

2 data sets and one to map the 2

ventilation data

(post RT treatment) to the 1

one (pre RT

treatment).

Figure 1: Flow chart of the ventilation change – dose

analysis using 4D-CT and DIR. In the diagram, RT =

radiation therapy, exp = expiration, insp = inspiration, DIR

= deformable image registration, FDV = function

(ventilation change) – dose – volume.

The dose distribution from treatment planning

usually used 2×2×2 or 3×3×3 mm

dose grid. To

calculate the function (ventilation change)-dose-

volume surface and ventilation change versus dose

data, the 3D dose distribution data were resampled

to match the CT resolution, usually about 1×1×3

. The dose distribution was not recalculated in

the treatment planning system with the new dose

grid size. Linear interpolation was applied in the

dose data resampling.

After the DIR and resampling, the two

ventilation distributions and thus the ventilation

change distribution were aligned with the expiration

phase in the pre RT 4D-CT, and so was the dose

distribution. The quantitative analysis was based on

the aligned distribution data.

2.1 Deformable Image Registration

(DIR)

This study uses the diffeomorphic morphons (DM)

DIR method (Janssens et al., 2009). In the validation

of the DM algorithm, the average target registration

error (TRE), for normal end-expiration to end-

inspiration registration in a 4D-CT data set, is

1.4±0.6 mm (Latifi et al., 2013c). DM DIR of the

normal end-expiration and end-inspiration phases of

4D-CT images was used to correlate the voxels

between the two phases.

DM DIR is also used in the 2

ventilation

mapping from the post treatment CT to the pre-

treatment CT. After the mapping, the two ventilation

data sets are aligned on the pre-treatment CT set.

The DIR is performed between the expiration phase

of the post treatment 4D-CT and the expiration

phase of the pre-treatment 4D-CT. The deformation

matrix resulted from the DIR was used to map the

ventilation data from the post treatment CT frame to

the pre-treatment CT frame.

2.2 Ventilation Calculation

This study uses the ΔV ventilation calculation

algorithm (Zhang et al., 2011; Zhang et al., 2009) to

derive ventilation from 4D-CT scans.

Figure 2: (A) A cuboid can be divided into 6 tetrahedrons.

(B) The corresponding 12-face polyhedron (deformed

cuboid) is composed of 6 deformed tetrahedrons.

The ΔV method, which is a direct geometrical

calculation of the volume change, was used to

calculate the local lung expansion or contraction

(Zhang et al., 2009). In the expiration phase of a 4D-

CT data set, each voxel is a cuboid defined by 8

vertices. In the inspiration phase, this cuboid is

changed into a 12-face polyhedron which is still

comprised of the corresponding 8 vertices. Any

hexahedron or 12-face polyhedron can be divided

BIOIMAGING2014-InternationalConferenceonBioimaging

into 6 tetrahedrons (Figure 2). The volumes of the

cuboid and the 12-face polyhedron (deformed

cuboid) are the sums of the volumes of their 6

corresponding tetrahedrons. In the inspiration phase,

DIR calculates the corresponding locations of the 8

vertices that define the cuboid in the expiration

phase. The volumes of each cuboid and the

corresponding deformed cuboid are calculated using

the corresponding vertices of each respective

polyhedron.

The fundamental volume calculation is based on

the volume calculation for each tetrahedron. The

coordinates of the 4 vertices of a tetrahedron are

used to determine its volume:

V = (b - a) · [(c - a) × (d - a)] / 6 (1)

where a, b, c, d are the vertices’ coordinates

expressed as vectors. The volumes of the six

tetrahedrons are summed up to generate the volume

of the given polyhedron.

The ventilation distribution was calculated as the

distribution of

P = ΔV/V

, (2)

where ΔV is the volume change between expiration

and inspiration and V

exp

is the initial volume at

expiration (Simon, 2000).

There is often tidal volume (TV) difference

between two 4D-CT scans of the same patient. The

quantitative ventilation data derived from 4D-CT

depends on the TV, since if TV is different, ΔV for

each local voxel would be different thus ventilation

P is different based on Equation (1). To remove the

ventilation dependence on the TV of the patient’s

respiration, the ventilation change was calculated

using the tidal volume normalized ventilation data

(Du et al., 2013). Tidal volume is calculated by

integrating the local volume change ΔV over the

entire lung volume. For two 4D-CT sets, taken

before and after treatment, there are two TVs from

the ventilation calculations: TV1 from the pre-

treatment data set and TV2 from the post-treatment

one. In the normalization process, the pre-treatment

ventilation distribution is not changed, while the

post-treatment ventilation distribution is normalized

to TV1 by applying a multiplication factor,

TV1/TV2, to every voxel in the lungs. After this

normalization, both ventilation data sets have the

same tidal volume, TV1, thus removing the final

result dependency on the TV. In this study, two sets

of ventilation data were compared using this

normalization method for each patient.

A reduced lung mask was used in order to avoid

any possible artifacts near the lung boundary due to

sliding motion (Loring et al., 2005). The margin of

the lung mask reduction was 1 mm. The lung masks

were automatically generated by density threshold

method on the CT images using a homemade

computer program.

Ventilation data were calculated and

superimposed on the normal end-expiration phase of

the 4D-CT before and after RT for each case. DM

was also applied to register the two normal end-

expiration phases of the 2 sets of 4D-CT, and the

resulted deformation matrix was used to deform the

ventilation matrix from the after RT data frame to

the before RT data frame. The ventilation change

distribution was then calculated between the

registered ventilation data sets.

Dice similarity coefficient (DSC) index was used

to calculate the similarity between the two

ventilation volumes (Dice, 1945). When volume A

and B are compared, DSC is calculated as

DSC(A,B)







2

(3)

The values of DSC index range between 1.0 and

0.0. A DSC index of 1.0 indicates a complete

overlap of the two volumes examined whereas a

DSC index of 0.0 indicates no overlap between the

volumes examined, and intermediate values describe

proportional amount of overlap. To calculate the

DSC for the two sets of ventilation data in each case,

the ventilation data were converted to relative

percentile ventilation distribution (Castillo et al.,

2010). Similar to the cumulative dose-volume

histogram, if a certain percentage lung volume is

covered by a certain ventilation value and below,

this ventilation value is converted to the

corresponding percentage value of the lung volume

in the percentile distribution. The volumes for the

DSC index were generated based on the percentile

ventilation values. The two aligned ventilation data

sets were compared for the similarity of the higher

50% of ventilation volume.

2.3 Patient Data

As 4D-CT is not clinically taken in patient follow-up

scans after radiotherapy, patient selection has to be

within the group that had second tumor treatment. A

4D-CT is taken for the treatment planning before the

second tumor treatment, which can also serve as the

follow-up 4D-CT of the first tumor treatment.

Among the hundreds of lung cancer patients treated

with stereotactic body radiotherapy (SBRT), 20

patients who had second lung tumor treated were

selected for this study.

4D-CT sets from before and after RT were used

EvaluationoftheEffectsofDoseonLungVentilationCalculatedfrom4D-CTusingDeformableImageRegistration-An

ApplicationofaVentilationCalculationAlgorithmbasedon4D-CT

to derive ventilation for the patients, following an

IRB approved protocol. The resolution in the 4D-CT

was about 1×1×3 mm

. All CT data covered the

lungs completely. Time between end of treatment

and the follow up scan ranged from 1-25 months.

Table 1 lists the statistic data of target volume

and dose level volumes in lungs for the 20 patients.

Notice that the lung and dose level volumes exclude

the gross target volume (GTV). Also, the low dose

volumes (<1Gy) were much larger than the high

dose volumes (>30Gy, 20~30Gy), usually by 2

orders of magnitude. The internal gross target

volume (IGTV) was derived from (at a minimum)

the union of the GTV volumes on two extreme

phases of the 4D-CT scan and the free breathing

scan. The standard IGTV to the planning target

volume (PTV) expansion was 5mm axially and 7mm

superiorly and inferiorly. The treatment plans were

optimized to cover 100% of the IGTV and at least

95% of the PTV by the prescribed dose. Doses

ranged from 40-60 Gy delivered in 4-5 fractions.

Table 1: Target volume and dose level volumes in lungs.

Volume Average SD Median Min Max

Lung 2447.6 1062.1 2338.7 837.0 4599.6

PTV 34.3 28.2 24.9 5.5 106.7

>30Gy 78.1 85.4 53.5 6.7 359.4

20~30Gy 65.1 66.7 38.2 10.2 276.1

10~20Gy 159.8 128.7 139.4 23.3 536.4

5~10Gy 195.6 145.0 145.6 51.4 589.7

1~5Gy 540.5 436.1 391.2 166.1 1737.5

<1Gy 1402.9 614.6 1372.7 418.5 2778.9

Dose and normalized ventilation were

superimposed on the CT volume resulting in each

voxel having a volume, normalized ventilation

change and a dose and therefore leading to a 3-

dimensional histogram, or function (ventilation

change) – dose – volume (FDV) surface. An FDV

surface was generated for each case based on the

aligned data. Accumulating the volumes in different

ventilation change ranges in the FDV surface data,

2D dose – volume histograms for the corresponding

ventilation change range were generated. Mean TV

normalized ventilation within the 1, 5, 10, 20 and 30

Gy regions was calculated before and after RT. The

cases were binned into 3 groups with follow-up time

of less than 5 months (n = 6), 5 months to 1 year (n

= 6) and longer than 1 year (n = 8). The ventilation

change versus dose of different follow-up time was

compared.

3 RESULTS

Figure 3 shows an example of the dose and

calculated ventilation change distributions

overlapped on the expiration phase of the 4D-CT.

More negative ventilation change, or ventilation

degradation, around the tumor (high dose region)

can be seen in this example.

Figure 3: A coronal view of an example of the dose (A)

and ventilation change (B) distributions overlapped with

the expiration phase of the pre-treatment 4D-CT.

Figure 4 shows a typical FDV surface. Since

most of the lung volume is under low dose coverage

(Table 1), the surface is peaked close to 0 dose. The

maximum value of % volume (vertical axis) in this

figure is set at 0.1% to make the high dose surface

visible.

Figure 5 shows a typical ventilation change

versus dose histogram. For sixteen out of 20 cases,

ventilation after treatment was lower within the high

dose region compared to that before treatment,

which is reflected by the “get worse” curve being

BIOIMAGING2014-InternationalConferenceonBioimaging

higher than “get better” curve in the high dose

region in Figure 5.

Figure 4: A typical function (ventilation change)-dose-

volume (FDV) surface. The volume of the lungs is

normalized to 100%. The maximum value of the %

volume (vertical axis) is set to 0.1% to make the high dose

surface visible. In the figure, dv = ventilation change.

Figure 5: A typical ventilation change versus dose

histogram. Curve “get worse” is the volume integration at

a certain dose level for lower (worse) ventilation after

treatment and “get better” is the volume for higher (better)

ventilation. In the figure, worse than 0.1 means the TV

normalized ventilation decreased more than 10%

after

treatment.

Table 2: Ventilation change versus dose over the 20 cases.

Region Average SD Median Min Max

<1Gy 0.0002 0.0178 -0.0010 -0.0339 0.0376

1~5Gy 0.0075 0.0365 0.0035 -0.0444 0.1403

5~10Gy 0.0096 0.0522 -0.0004 -0.0427 0.2051

10~20Gy -0.0074 0.0491 0.0026 -0.1293 0.0764

20~30Gy -0.0189 0.0664 -0.0091 -0.1805 0.1100

>30Gy -0.0239 0.0529 -0.0188 -0.0927 0.1448

Figure 6 demonstrates that the trend of the

average ventilation change is less dependent on

dose. In other words, the average ventilation change

versus dose tends to be flattened with time.

Table 2 lists the statistical ventilation change

data over the 20 cases. The trend is that the average

ventilation degrades with dose when the dose is

greater than 20 Gy. The ventilation change

difference was statistically significant in the dose

regions covered by < 1 Gy and > 30 Gy (p = 0.006).

Figure 6: The median values of average ventilation

changes in various dose level regions of different groups

of follow-up time.

Mean DSC index for the above 50% ventilation

volume was 0.60 ± 0.04 (1 SD) with a range 0.52 to

0.69.

For lung tissue regions receiving more than 20

Gy, a decrease in ventilation was observed in 16 of

20 patients. For the 16 cases ventilation within the

20 Gy dose was reduced by an average of 6.4%

(range 0.3 to 18.1%). For regions receiving more

than 30 Gy, 15 out of 20 patients had an average

decrease of ventilation by 4.4% (range 0.6 to 9.3%).

Four patients had an average increase of ventilation

of 4.1% within the 20 Gy and five patients had an

average increase of 3.8% within the 30 Gy region.

4 DISCUSSION

The use of normalized ventilation data in the

comparison is to remove the tidal volume

dependence. However, the normalization gives

prominence to the relativity feature of the ventilation

data. In other words, the ventilation change is

relative after normalization. If ventilation gets better

in some regions, there must be some regions where

ventilation gets worse, since the total volume change

in each data set must be the same tidal volume, or

the total ventilation change over the whole lung

must be zero between two normalized data sets. This

EvaluationoftheEffectsofDoseonLungVentilationCalculatedfrom4D-CTusingDeformableImageRegistration-An

ApplicationofaVentilationCalculationAlgorithmbasedon4D-CT

relativity feature is the reason that the FDV surface

often shows symmetry with ventilation axis (Figure

4). Here is an easy example to help understanding

the relativity feature. Assuming half of a uniformly

ventilated lung becomes no ventilation (half A) and

the other half is still uniformly ventilated (half B).

After normalization, half A gets worse by 100%

while half B gets better by 100% since half B is

normalized to the tidal volume of before the change.

Without normalization, the comparison would really

depend on how deep the subject breathes (tidal

volume dependence).

To spare functional lung volumes in treatment

planning for SBRT, an objective or constraint thus is

suggested that good ventilation regions derived from

the pre-treatment 4D-CT should avoid radiation dose

of higher than 20 Gy, based on this study.

Based on the linear-quadratic model, the

biological effective dose (BED) of 4 Gy × 5

fractions = 20 Gy isodose line in the normal lung

tissue is the same of 35 Gy isodose line in the

conventional treatment of the prescription dose 2 Gy

× 35 fractions = 70 Gy, and the 30 Gy isodose line

in the SBRT is equivalent to 58 Gy isodose line in

the conventional treatment. In the above calculation,

the α/β ratio for the normal lung tissue is set at 3.1

Gy (Dubray et al., 1995). The analysis on the 20 and

30 Gy dose levels thus can be applied to the

conventional treatment at dose levels of 35 and 58

Gy.

A related study evaluated whether dose to the

highly ventilated regions in the lung resulted in

increased incidence of clinical toxicity, in which

only the pre-RT 4D-CT was used for each patient to

generate ventilation distribution and dose-ventilation

histogram (Vinogradskiy et al., 2013). By

comparison, our study used two sets of 4D-CT, one

pre-RT and the other one post-RT, for each patient

to directly calculate dose-induced ventilation

change, which generated more statistically

significant results.

For each case, there are two calculated

ventilation data sets. The DSC is a measure of the

similarity between the two data sets. The DSC data

showed that there are some changes between the two

data sets. The ventilation changes mostly are

because of the radiation therapy treatments.

However, the errors introduced in ventilation

calculation may cause some ventilation variation.

Although the reproducibility of ventilation derived

from 4D-CT has been shown good in some studies

(Du et al., 2013; Du et al., 2012), and the

comparison between this method and other standard

modality is good (Ding et al., 2012), some other

studies also show that the ventilation calculation

depends on DIR algorithm and ventilation

calculation algorithm (Latifi et al., 2013a). The

reason for the dependence is deemed that different

algorithms handle 4D-CT artifacts differently.

Artifacts in 4D-CT could cause errors in DIR

(Zhang et al., 2008), which in turn introduces errors

in the derived ventilation data. To minimize the

errors introduced by artifacts in 4D-CT, data sets

with obvious mushroom artifacts in the diaphragm

region, which are usually caused by irregular

diaphragm motion, were excluded in this study.

Since this is a retrospective study, this kind of

exclusion would cause exclusion of clinical cases. If

this method is used in a prospective study, timely

review the 4D-CT data before the patient getting off

the table is recommended. If obvious mushroom

artifacts are present, re-scan with a slower

respiration should be performed.

Quantum noise is another source of DIR errors.

High quality 4D-CT is essential for accurate

ventilation data (Latifi et al., 2013b).

5 CONCLUSIONS

Lung ventilation prior to and following radiotherapy

can be measured using 4D-CT and DIR techniques.

Changes in ventilation were observed with a

correlation between ventilation change and radiation

dose of greater than 20 Gy. These data suggest that

ventilation calculated from 4D-CT may be a reliable

tool for measuring/predicting the effects of dose on

ventilation. Incorporating 4D-CT calculated

ventilation in treatment planning would aid in

avoiding well ventilated regions and possibly

preventing lung injury.

ACKNOWLEDGEMENTS

This work was partially supported by a research

grant from Varian Medical Systems, Inc., Palo Alto,

CA. We thank Kenneth Forster for his involvement

in the early stages in this project.

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