Accounting for respiratory motion in small serial structures during radiotherapy planning: proof of concept in virtual bronchoscopy-guided lung functional avoidance radiotherapy

Abstract

Respiratory motion management techniques in radiotherapy (RT) planning are primarily focused on maintaining tumor target coverage. An inadequately addressed need is accounting for motion in dosimetric estimations in smaller serial structures. Accurate dose estimations in such structures are more sensitive to motion because respiration can cause them to move completely in or out of a high dose-gradient field. In this work, we study three motion management strategies (m1–m3) to find an accurate method to estimate the dosimetry in airways. To validate these methods, we generated a ‘ground truth’ digital breathing model based on a 4DCT scan from a lung stereotactic ablative radiotherapy (SAbR) patient. We simulated 225 breathing cycles with ±10% perturbations in amplitude, respiratory period, and time per respiratory phase. A high-resolution breath-hold CT (BHCT) was also acquired and used with a research virtual bronchoscopy software to autosegment 239 airways. Contours for planning target volume (PTV) and organs at risk (OARs) were defined on the maximum intensity projection of the 4DCT (CT_MIP) and transferred to the average of the 10 4DCT phases (CT_AVG). To design the motion management methods, the RT plan was recreated using different images and structure definitions. Methods m1 and m2 recreated the plan using the CT_AVG image. In method m1, airways were deformed to the CT_AVG. In m2, airways were deformed to each of the 4DCT phases, and union structures were transferred onto the CT_AVG. In m3, the RT plan was recreated on each of the 10 phases, and the dose distribution from each phase was deformed to the BHCT and summed. Dose errors (mean [min, max]) in airways were: m1: 21% (0.001%, 93%); m2: 45% (0.1%, 179%); and m3: 4% (0.006%, 14%). Our work suggests that accurate dose estimation in moving small serial structures requires customized motion management techniques (like m3 in this work) rather than current clinical and investigational approaches.

1. Introduction

There is an urgent need to better understand radiotherapy (RT)-induced airway toxicity, especially in potent regimens like lung stereotactic ablative radiotherapy (SAbR), where very high doses of radiation are delivered to the tumor target in relatively few fractions. Although radiologic manifestations of radiation toxicity of the lung parenchyma have been studied in detail, airway injury pathogenesis is still poorly understood (Kang et al 2015). A number of studies have illustrated bronchial tree toxicity in central airways, reporting narrowing caliber of mainstem bronchi in patients treated with traditional conventionally fractionated radiation after doses ≥73 Gy (Kelsey et al 2006); complete or partial bronchial stricture in patients with central tumors treated with SAbR (Song et al 2009); radiation-induced atelectasis in patients with prescribed SAbR doses of 20–50 Gy in 2–5 fractions (Karlsson et al 2013); or telangiectasia, mild and severe stenosis, and even necrosis in distal regions of central airways, all of them increased by other local treatments and retreatment (van Hoorn et al 2018).

Analogous to the studies reporting radiosensitivity for central airways, there exists a need to estimate the radiosensitivity of airways downstream from the main bronchi. These estimates can then be used to develop treatment plans that spare these airways and therefore preserve the conduits of gas exchange. Functional avoidance in RT planning has been widely studied with the goal of preserving post-RT lung function. Various functional imaging techniques have been proposed to spatially and quantitatively map lung function. Examples include single-photon emission computed tomography (SPECT) lung perfusion (Marks et al 1993, Seppenwoolde et al 2002, Christian et al 2005, St-Hilaire et al 2011), SPECT lung ventilation (Munawar et al 2010, Lukovic et al 2014), positron emission tomography (PET) (Siva et al 2015), magnetic resonance imaging (MRI) (Ireland et al 2007, Rankine et al 2018), and four-dimensional CT (4DCT) (Yaremko et al 2007, Tokihiro et al 2011, Yamamoto et al 2011, Huang et al 2013, Vinogradskiy et al 2013, 2016). Some examples of on-going prospective studies are FLAIR (functional lung avoidance for individualized radiotherapy), which uses hyperpolarized ³He MRI to estimate the functional lung regions (Hoover et al 2014) or clinical trials evaluating the feasibility of CT ventilation functional image guided RT (Vinogradskiy et al 2018, Yamamoto et al 2018).

However, to our knowledge, no clinical studies characterize injury to peripheral airways (defined here as generation 3+), likely because current computed tomography (CT) simulation images used in RT planning do not have sufficient spatial resolution to clearly visualize these fine structures. In a previous study, we described a method based on virtual bronchoscopy that used a high-resolution (HR) breath-hold (BH) CT to spatially map central and peripheral airway segments (down to 3 mm diameter) and estimate their radiosensitivity (Kazemzadeh et al 2018). We found that radiosensitivity was a function of the airway diameter and the maximum point dose, defined as D_{0.01 cc}, i.e. the minimum dose to a voxel within the 0.01 cc volume receiving the highest dose. Based on those findings, we developed a statistical risk-based model of airway collapse. That model was used in the treatment plan to reduce the risk of radiation-induced airway injury by reducing the dose delivered to airways while fulfilling clinical constraints.

A nontrivial problem in performing these dose estimations for individual airway elements is to account for breathing motion. It is well-recognized that respiration-induced organ motion leads to a blurring of dose distributions, the extent of which is dependent on the amplitude and characteristics of the motion (Bortfeld et al 2004). Such geometric and dosimetric errors will be more pronounced in the presence of high dose gradients, large amounts of motion, and small structures (Heath and Seuntjens 2006)—all of which are pertinent to peripheral airways during administration of SAbR.

Several types of techniques have been introduced to manage respiratory motion during RT (Keall et al 2006). The current standard-of-care to account for breathing motion for treatment planning usually use respiratory-correlated 4DCT. In this method, the patient’s respiratory waveform is recorded during the CT acquisition and used to reconstruct six to ten 3DCT volumes distributed over an average respiratory cycle (Ford et al 2003, Vedam et al 2003, Keall 2004, Rosu and Hugo 2012). These volumes are then combined in the form of a maximum intensity projection CT (CT_MIP, generated by taking the maximum intensity for each voxel from the 3DCT volumes) or an average CT (CT_AVG, generated by averaging all the 3DCT volumes). Usually the CT_MIP is used to estimate the internal target volume (ITV) (Ge et al 2013), which encompasses the super-imposed positions of the target, representing the motion-induced volumetric excursion of the tumor target over the respiratory cycle. The ITV may then be expanded to a planning target volume (PTV) to account for setup uncertainties.

The current paradigm for accounting for respiratory motion in treatment planning is thus focused on maintaining PTV coverage (Admiraal et al 2008, Glide-Hurst et al 2008, Mexner et al 2009, Kim et al 2016). To the best of our knowledge, no studies systematically examine the effects of motion on dosimetric estimations in smaller anatomic structures such as peripheral airways. In this work, we evaluate the accuracy of dose estimations in airways in three methods accounting for breathing motion with different strategies.

2. Materials and methods

In section 2.1, we describe the specific tools used in this work. Section 2.2 describes the patient-based digital breathing model that was developed to serve as ground truth for the evaluation and ranking of the motion management methods. Section 2.3 describes the details of the three motion management methods (m1–m3). In section 2.4 we detail the evaluation of the methods. Note that in this section we will use the term ‘method’ to refer to the motion management methodologies under study in this work, while the term ‘model’ will refer to the digital breathing simulations generated to serve as ground truth for the evaluation of the methods.

2.1. Tools used to estimate dosimetric values

The estimation of the dose delivered in a particular structure during the RT plan is usually obtained by using: (i) a CT image to localize the structure and determine its density and the density of the surrounding organs; (ii) software to segment its volume (manually or automatically); and (iii) a treatment planning system (TPS) to recreate the RT plan and obtain the dose value. In this work, we used different CT images to recreate the RT plan, depending on the strategy to account for breathing motion used in the method under study. The first two methods (m1 and m2) used an average intensity image (CT_AVG) generated from a phase-sorted 4DCT scan with ten breathing phases. Method m3 recreated the plan on each of the 10 phase images of the 4DCT.

To autosegment the individual elements of the bronchial tree we used a high resolution BHCT image (voxel size under 1 mm in the three directions) and a research version of a commercial virtual bronchoscopy system (Archimedes, Broncus Medical; San Jose, CA), (Graham et al 2010). The runtime of the segmentation was 6 min for a BHCT image of 512 × 512 × 486 voxels (voxel size of 0.76 × 0.76 × 0.80 mm³) in an Intel Xeon CPU (8 cores), 2.10 GHz (2 processors), 64 GB of RAM. Given that the native voxel size of the BHCT is under the millimeter, it was likely that the uncertainties for airways smaller than 3 mm in diameter were going to be significantly high. For this reason, we did not use airways smaller than 3 mm in diameter in our analyses.

The PTV and the organs at risk (OARs; i.e. esophagus, heart, spinal cord, and lungs) were manually-contoured on the CT_MIP (used to estimate motion-inclusive margins for the tumor target (ITV) and the other organs) by a radiation oncologist and transferred to the CT_AVG (i.e. overlapped with the CT_AVG), since the CT_AVG was the image used for treatment planning dose calculations. The PTV was defined by isotropically expanding the edges of the ITV by 5 mm. For the dose calculation, the patient’s clinical plan was recreated on a commercial TPS (Eclipse 13.6, Varian Medical Systems; Palo Alto, CA).

2.2. Digital breathing model

We designed a digital breathing model based on patient data to use as a ground truth to evaluate the three methods under study. The key idea was to simulate the breathing motion of a patient during the RT treatment, by generating a digital-patient phantom with a realistic irregular breathing pattern over many breathing cycles. In a real case, the patient would breathe with a nonuniform pattern (different breathing cycles) that, on average, would be represented by the 4DCT. In our model, we recreated this nonuniform pattern by using a patient’s 4DCT and introducing perturbations in the amplitude (cycle-to-cycle) and time (period and time spent at each phase) according to published studies about nonuniform breathing patterns (Dejours et al 1966, Tobin et al 1988, Stromberg and Gustafsson 1996, Modiri et al 2017). In order to differentiate the actual patient’s 4DCT that we use to create our breathing simulation models from the 4DCT generated from our simulation, we will call 4DCT^P (P as in Patient) to the former and 4DCT^M (M as in Model) to the latter from now on. In those cases that we refer to generic data no superscript will be used.

Under Institutional Review Board (IRB) approval, we used the clinical images and plan data of a lung-SAbR patient (75 years-old male, ~4 cm right lower lobe tumor) comprising the 4DCT^P, ${\text{CT}}_{\text{AVG}}^{\text{P}}$, ${\text{CT}}_{\text{MIP}}^{\text{P}}$, and BHCT images, and the segmented structures (i.e. OARs and PTV (contoured on the ${\text{CT}}_{\text{MIP}}^{\text{P}}$ image and transferred to the ${\text{CT}}_{\text{AVG}}^{\text{P}}$)) and bronchial tree elements (autosegmented on the BHCT). The 4DCT^P scan was acquired using a 16-slice Brilliance Big Bore CT (Philips Healthcare US, Andover, MA; 512 × 512 × 204, voxel size of 1.17 × 1.17 × 2.00 mm³). The BHCT was acquired on an Aquilion diagnostic CT scanner (Toshiba America Medical Systems, Inc., Tustin, CA; 512 × 512 × 486, voxel size of 0.76 × 0.76 × 0.80 mm³). This patient was prescribed a 13-beam 3D conformal radiotherapy (CRT) SAbR plan of 5 fractions and 12 Gy per fraction that was originally planned on the ${\text{CT}}_{\text{AVG}}^{\text{P}}$ and delivered to the patient under free breathing conditions.

We investigated two breathing models. In breathing model 1 (BM-1), we allowed only amplitude variations. In the second, more complex model (BM-2), we included (i) amplitude variations (identical to those in BM-1), (ii) variations in period (time per respiratory cycle), and (iii) intra- and intercycle variations in time per respiratory phase.

To construct BM-1 we introduced cycle-to-cycle variations in the breathing amplitude using the patient’s 4DCT^P as a nominal reference of uniform breathing pattern. Based on studies reported by Tobin et al (1988) for healthy subjects, Stromberg and Gustafsson et al (1996) for asthmatic patients, and Dejours et al (1966) for resting human subjects, we chose a maximum value of 20% (i.e. ±10%) for the amplitude variations. To generate these perturbations, we registered the BHCT (high resolution) to the ten breathing phases of the 4DCT^P (low resolution), obtaining ten high-resolution phase images (4D-HRCT) and 10 deformation vector fields (DVFs). We used a B-spline deformable image registration (DIR) for the registration, using the software Plastimatch (open source, http://plastimatch.org), previously validated for 4DCT (Kipritidis et al 2014). Subsequently, we generated new respiratory cycles by varying the breathing amplitude per cycle (i.e. cycle-to-cycle amplitude variations). The variation in amplitude per cycle was generated by calculating a factor per cycle, f_Amp, that multiplied the DVFs of all the ten deformations (BHCT → 4DCT^P phases). This factor was calculated by using equation (1):

$$f_{Amp}=1+(\text{rand}([0,1])-0.5)\times \frac{P_{Amp}}{100},$$ (1)

where rand ([0, 1]) is a random number between 0 and 1, both included, and P_Amp (=20% here) is the percentage ±10% of maximum variation in amplitude. Thus, we allowed amplitude variations, which implied a maximum displacement of 14 mm (from exhale to inhale) to peripheral airways. With this strategy, we calculated four amplitude factors to generate four new breathing cycles. These new respiratory cycles, along with the 4D-HRCT itself (f_Amp = 1) were used to generate the breathing model, by randomly selecting them to generate 225 cycles of 4 s.

These new volumetric 4D-HRCT images were then used to calculate the delivered doses in each structure of the digital-patient phantom with breathing motion modeled by BM-1. Because the patient that we used to generate the model was prescribed a CRT treatment planned on the ${\text{CT}}_{\text{AVG}}^{\text{P}}$ and delivered to the patient under free breathing conditions, we recreated the same clinical plan (i.e. same PTV, same beam angles and intensities, same dose constraints, etc) for all the volumetric 4D-HRCT images and variations (10 phases × 5 cycle-to-cycle amplitude variations). In this manner, we were simulating the free breathing during the RT treatment. Therefore, we needed to combine the contribution of the deposited doses at each phase of each cycle in one dose matrix to calculate the total dose delivered to each structure during the treatment. To calculate the final dose matrix, the resulting 50 dose matrices were then deformed to a reference image. We chose the BHCT as the reference image because the airways were defined on this image and that avoided extra deformations that might introduce extra errors. Thus, we performed 50 DIRs from the 10 HR-phase images and its variations to the BHCT and applied the corresponding DVFs to the dose matrices.

Assuming a treatment delivery time of 15 min (225 respiratory cycles of 4 s), we were randomly selecting from the 5 cycle-to-cycle amplitude variations to generate the 225 cycles and adding their corresponding dose matrices (deformed to the reference image) to the final one. We calculated the final dose matrix by summing the 2250 dose distributions (225 cycles × 10 phases) with equal weighting factors for all the phases (i.e. we assumed same time was spent at each breathing phase in BM-1).

Finally, we generated the digital-patient 4DCT (4DCT^M) by averaging the used amplitude variations during the 225 breathing cycles and down-sampling the resulting 4D-HRCT (0.76 × 0.76 × 0.80 mm³ in this study) to the original voxel size of the actual-patient 4DCT^P (1.17 × 1.17 × 2.00 mm³). We also generated the average intensity image (${\text{CT}}_{\text{AVG}}^{\text{M}}$) by averaging the 10 phase images of the 4DCT^M. This digital-patient 4DCT^M and the ${\text{CT}}_{\text{AVG}}^{\text{M}}$ were therefore used to evaluate the three methods.

To construct BM-2 we used the same amplitude variations generated in BM-1 (in the same order in the 225 cycles). In addition, in BM-2 we also included time variations in the respiratory period and in the time per phase. Based on the above-mentioned studies (Dejours et al 1966, Tobin et al 1988, Stromberg and Gustafsson 1996), we chose period variations of 20% (±10%). The variations were included by using equation (2):

$$f_{t_{\mathit{\text{cycle}}}}=(\text{rand}([0,1])-0.5)\times \frac{P_{t_{\mathit{\text{cycle}}}}}{100},$$ (2)

where $P_{t_{\mathit{\text{cycle}}}}$ is the percentage of maximum variation in the time of a cycle. Each variation was created by multiplying the typical time for a breathing cycle, t_cycle, by $f_{t_{\mathit{\text{cycle}}}}$ and adding the result to t_cycle as it is shown in equation (3):

$$t_{\mathit{\text{cycle}}}^{\prime }=t_{\mathit{\text{cycle}}}\times \left[1+f_{t_{\mathit{\text{cycle}}}}\right],$$ (3)

where $t_{\mathit{\text{cycle}}}^{\prime }$ is the new time for the perturbed breathing cycle. We considered t_cycle = 4 s and $P_{t_{\mathit{\text{cycle}}}}=20\%$ , so the cycles used in our model ranged from 3.6 to 4.4 s.

To introduce variations in the amount of time spent at each breathing phase, we randomly chose a breathing time pattern for each cycle from the ten reported breathing patterns in Modiri et al (2017). The values of percentage of time spent in each phase ranged from 3.3% to 29.2%.

We generated 225 respiratory cycles using the same amplitude variation as in BM-1 but including the time variations. Therefore, in BM-2, the weighting factors of the dose matrices at each breathing phase were proportional to the amount of time spent at that phase and that cycle to quantify the relative contribution to the final dose distribution. Figure 1 illustrates an example of the lung volume as a function of the time for eight consecutive cycles from the 225 simulated cycles to generate the two breathing models.

Figure 1.

Example of eight consecutive cycles from the 225 simulated for the two digital breathing models (blue and orange lines) overlapped with the initial 4DCT^P (dashed black line, repeated eight times, one per cycle). The total lung volume in milliliters at each phase of each cycle is shown as a function of the time in seconds, assuming 4 s as a typical time for one cycle. The blue line represents BM-1, where variations in the amplitude of 4DCT phases were performed. The orange line represents BM-2, which includes, in addition to the same variations in amplitude as in BM-1, variations in the time of each of the 4DCT phases and in each cycle.

Finally, we needed to generate the digital-patient 4DCT^M for this model. However, note that, this digital-patient 4DCT^M was identical to that generated in BM-1, because in both cases, the 4DCT was generated by phase-binning; i.e. the time-per-phase (which was the difference between BM-1 and BM-2) was not considered.

2.3. Motion management methods

The aim of each of these methods was to recreate the clinical RT treatment delivered to the patient and estimate the mean dose (D_mean) and maximum point dose (D_max) in each structure of interest. Therefore, the same clinical plan (i.e. beam arrangements, dose constraints, etc) was used as the starting point in all the methods. In order to validate the results of the methods using the breathing models as the ground truth, we used the same clinical plan as used to generate the breathing models (a 13-beam conformal SAbR plan, 5 fractions, 12 Gy per fraction) as well as the 4DCT^M and the ${\text{CT}}_{\text{AVG}}^{\text{M}}$. The CRT plan was optimized using Eclipse and the volume-dose constraints for the PTV and the OARs. No dose-constraints were included in the optimization for the airways.

2.3.1. Method m1: dose estimation using the CT_AVG in the RT plan

In current clinical practice, RT plans that account for respiratory motion usually use an average CT (CT_AVG) derived from the individual phases of the 4DCT and an ITV to define a motion-inclusive volume for the tumor target, which may then be expanded to a planning target volume (PTV) to account for setup uncertainties. To quantitatively characterize how this approach worked in the estimation of the dosimetry of the airways, we designed m1 using the CT_AVG image for recreating the RT plan and all the structures defined on (or deformed to) this ‘average phase’.

Because the airway structures were segmented on the BHCT, we needed to perform a DIR from the BHCT to the ${\text{CT}}_{\text{AVG}}^{\text{M}}$ (figure 2(a); step 1) and apply the DVFs of this registration to the bronchial tree airways (step 2). The resulting deformed BHCT image from step 1, a high-resolution ${\text{CT}}_{\text{AVG}}^{\text{M}}$ image (${\text{HRCT}}_{\text{AVG}}^{\text{M}}$), was then used to recreate the clinical plan (step 3) along with the PTV structure (defined on the ${\text{CT}}_{\text{AVG}}^{\text{M}}$). For the D_mean and D_max calculation, we multiplied each structure mask defined on the ${\text{CT}}_{\text{AVG}}^{\text{M}}$ by the dose matrix (step 4).

Figure 2.

Workflows of methods m1 and m2. The numbers in the circles indicate the step numbers of the method. Note that in m2 steps 2 and 3 must be repeated 10 times, once per breathing phase. (a) Method m1: dose estimation using the CT_AVG in the RT plan. Step 1: DIR (BHCT → CT_AVG); step 2: deformation of the bronchial tree using the DVFs from step 1; step 3: RT plan recreation using the HRCT_AVG image from step 1 and the PTV structure (defined on the CT_AVG); step 4: D_mean and D_max calculation by multiplying each structure mask defined on the CT_AVG by the dose matrix. (b) Method m2: dose estimation using the CT_AVG and the union of the airway structures from the 10 4DCT phases in the RT plan. Step 1: DIR (BHCT → CT_AVG); step 2: DIR (BHCT → 4DCT (10 times, ne per breathing phase)); step 3: deformation of the bronchial tree using the DVFs from step 2 (10 times, one per breathing phase); step 4: generation of the contour of each airway as the union of the 10 structures of this airway at the ten breathing phases; step 5: RT plan recreation using the HRCT_AVG image from step 1 and the PTV structure (defined on the CT_AVG); step 6: D_mean and D_max calculation by multiplying each structure mask defined on the CT_AVG by the dose matrix.

2.3.2. Method m2: dose estimation using the CT_AVG and the union of the airway structures from the 10 4DCT phases in the RT plan

Method m2 was designed per m1 but using for each airway the union of the airway structures from the ten breathing phases of the 4DCT. We investigated this methodology for defining the airways in order to analyze which definition of the average shape of the airways, the one studied in m1, or the one proposed in m2, provided more accurate dose values. Figure 3 shows the shape of the airway structures used in m1 (figure 3(a); airways deformed from the BHCT to the CT_AVG) and the ones used in m2 (figure 3(b); airways as union of the structures at the 10 phases).

Figure 3.

Bronchial tree elements defined at the ‘average phase’ (${\text{CT}}_{\text{AVG}}^{\text{M}}$image) using two methods. (a) Bronchial tree generated by applying the DVFs of the DIR from the BHCT to the ${\text{CT}}_{\text{AVG}}^{\text{M}}$ (structures used in m1). (b) Bronchial tree generated as the union of the bronchial tree elements at the ten breathing phases (structures used in m2).

Hence, in addition to the DIR from step 1 of m1 to obtain ${\text{HRCT}}_{\text{AVG}}^{\text{M}}$ (figure 2(b); step 1 in m2), we performed 10 more deformations of the BHCT to each of the 10 phases of the 4DCT^M (step 2). Subsequently, we applied the DVFs of each phase to the airways (step 3), obtaining ten deformed bronchial trees. After that, we calculated the contour of each airway as the union of the ten structures of this airway at the ten breathing phases (step 4). Finally, steps 5 and 6 were similar to steps 3 and 4, respectively, in m1 but used the new airway structures.

2.3.3. Method m3: dose estimation using the 10 breathing phases of the 4DCT

In method m3 we investigated an approach based on using the breathing motion derived from the 4DCT to estimate the dosimetric values. Thus, the dose delivered to each structure was estimated in each breathing phase of the 4DCT and averaged over the ten phases.

The first step of this method was to perform 10 DIR from the BHCT to the ten phases of the 4DCT^M (figure 4; step 1), obtaining in this way a 4D-HRCT^M. Then, using these 10 HR^M phase images, we recreated 10 exactly equal clinical plans (i.e. same beam angles and intensities, same dose constraints, etc), using the same PTV (defined on the ${\text{CT}}_{\text{AVG}}^{\text{M}}$) but using the corresponding HR phase image in each case (step 2). In this manner, we obtained one dose matrix per respiratory phase. To obtain the final dose matrix, we needed to refer each of the 10 dose matrices to the same reference system, to add their contribution to the final dose in the correct spatial location. Therefore, we needed to deform all the dose matrices to a reference image. Usually the reference image is one of the phases of the 4DCT, generally the end exhalation phase, because patients usually spend most of their respiratory cycle in this phase (Modiri et al 2017). However, in this case we chose the ‘BHCT phase’ as the reference image because we wanted to avoid the errors introduced while deforming the airways. Choosing the BHCT as the reference image avoids such deformation.

Figure 4.

Workflow of method m3 (dose estimation using the 10 phases of the 4DCT). The numbers in the circles indicate the step numbers of the method. Note that some steps (1, 2, 3, and 4) must be repeated 10 times, once per breathing phase. Step 1: DIR (BHCT → 4DCT (10 times, one per breathing phase)); step 2: RT plan recreation at each 4D-HRCT phase (10 exactly equal clinical plans, using the same PTV (defined on the CT_AVG)); step 3: DIR (4D-HRCT → BHCT (10 times, one per breathing phase)); step 4: deformation of the dose matrices applying the DVFs from step 3 (10 times, one per breathing phase); step 5: calculation of the final dose matrix as the average of the 10 deformed dose matrices assuming the breathing phases as equally timed; step 6: DIR (CT_AVG → BHCT); step 7: deformation of the OARs and the PTV applying the DVFs from step 6; step 8: D_mean and D_max calculation by multiplying the averaged dose matrix by the different structure masks defined at the reference image (BHCT).

Thus, to deform all the dose matrices to the reference image (BHCT), we performed 10 DIRs (step 3) from the 10 HR^M phases to the BHCT (the inverse transformations of step 1) and applied the corresponding DVFs to the dose matrices (step 4). Because no extra information about the amount of time spent at each breathing phase is usually available, we assumed the phases were equally timed and averaged the dose matrices at the reference image without any weighting factors (step 5). To obtain the OARs at the BHCT image we performed an extra DIR form the ${\text{CT}}_{\text{AVG}}^{\text{M}}$ to the BHCT (step 6), applying the DVFs to the OARs and the PTV (step 7). Finally, we calculated D_mean and D_max (step 8) by multiplying the averaged dose matrix by the different structure masks defined at the reference image (BHCT).

2.4. Evaluation of the motion management methods

As it was discussed in the previous sections, the evaluation of the three motion management methods was performed by using the data generated from the breathing models (BM-1 and BM-2). In this manner, we used the same clinical plan as used to generate the breathing models (a 13-beam conformal SAbR plan, 5 fractions, 12 Gy per fraction) as well as the 4DCT^M and the ${\text{CT}}_{\text{AVG}}^{\text{M}}$ as input data in the three motion management methods. Since the digital breathing models were a simulation of a realistic respiration, and we had the information of the deposited dose at every phase of all the 225 simulated breathing cycles, the results obtained in each breathing model served as the ground truth to estimate the accuracy of the results from the methods under study.

We performed two evaluations, one per breathing model, because we wanted to investigate the performance of the methods while (i) having only amplitude perturbations in the respiration (BM-1), and (ii) having amplitude perturbations and not equally timed respiratory phases and cycles (BM-2), which is the most realistic situation. The second evaluation was especially interesting for m3, because we wanted to study how assuming equal timed breathing phases in this method affected to the dose estimations while the breathing phases are not equally timed.

To quantitatively evaluate the accuracy of the methods, we calculated the percent errors in D_mean and D_max in the 239 airways, the OARs, and the PTV, where D_max was defined as D_{0.01 cc}, i.e. the minimum dose to a voxel within the 0.01 cc volume receiving the highest dose. The percent errors were calculated as

$${\Delta }_j{D}_{\text{mean }}^{m_i}[\%]=\frac{|D_{\text{mean }}^{m_i}-D_{\text{mean }}^{BM-j}|}{D_{\text{mean }}^{BM-j}}\times 100,$$ (4)

where $D_{\text{mean }}^{m_i}$ is the mean dose for one structure in method m_i (i ∈ [1, 2, 3], $D_{\text{mean }}^{BM-j}$ is the mean dose for the same structure in model BM-j (j ∈ [1, 2]), and ${\Delta }_j{D}_{\text{mean }}^{m_i}$ is the percent error of the mean dose for that structure in method m_i evaluated with the model BM-j . The same expression was used for calculating the percent error for D_max. Note that the result of equation (4) is an absolute value. It does not provide information about the under- or overdose compared to the ground truth. The reason of choosing an absolute value was because we wanted to study the cumulative average error in the airways. Using a non-absolute value would result in smaller average values because overdose values would cancel out the underdose ones.

3. Results

Figure 5 shows the errors in D_max for individual airways as a function of the airway inner diameter in millimeters in four intervals, (3, 3.5], (3.5, 4], (4, 5], and (5, 18]. We represent the errors in D_max as a function of the diameter, because in our previous work, D_max and the airway diameter were found to be the two parameters of interest to estimate the radiosensitivity of the airways (Kazemzadeh et al 2018). Figure 5 illustrates the evaluation of the three methods using BM-1 (amplitude variations) as the ground truth in figure 5(a) and using BM-2 (amplitude and time variations) in figure 5(b). Note that some outliers with very high values were left outside the representation for better visualization of the boxplots.

Figure 5.

Percent errors in D_max for the airways as a function of the airway inner diameter in millimeters in four diameter intervals. (Note that the mathematical notation (X, Y] symbolizes that X is not included in the interval while Y is included.) (a) Evaluation of the three methods (m1–m3) using the breathing model BM-1 (breathing model with amplitude variations) as the ground truth; (b) error values for the best ranked method (m3) evaluated with BM-1. (c) Evaluation of the three methods (m1–m3) using the breathing model BM-2 (breathing model with amplitude and time variations). (d) Error values for the best ranked method (m3) evaluated with BM-2.

We observe that the methods that used the CT_AVG image in the RT plan obtained worse results, providing higher performance in method m1, with median values from 13% to 28% for m1 and 27% to 46% for m2 (evaluation using BM-1) and 14% to 31% for m1 and 28% to 48% for m2 (evaluation using BM-2). The best-ranked method for both model evaluations was m3, with median values ranging from 2% to 3% for the evaluation using BM-1, and 3% to 4% while using BM-2. The results for the errors in D_mean followed the same distribution as the errors in D_max with slightly lower values (around 7% lower on average).

A general summary of the minimum, maximum, mean, and standard deviation of the dose errors computed for the airways for both D_mean and D_max is listed in tables 1 (with BM-1 as the ground truth) and 3 (with BM-2 as the ground truth). For the max, mean, and standard deviation of the dose errors, we also show the values calculated without considering the outliers (we label them in the table as max*, mean*, and std*, respectively); defining outliers as the values outside the 95% percentile. We also present the errors obtained in the OARs and PTV dosimetry, with values considerably lower for all the methods in tables 2 (with BM-1 as the ground truth) and 4 (with BM-2 as the ground truth).

Table 1.

Summary of the dosimetric errors in the 239 airways obtained with the three evaluated methods (m1–m3) using for the evaluation the BM-1 (breathing model with amplitude variations). Max*, mean*, and std* are the maximum, mean, and standard deviation calculated without using the outliers (>95% percentile).

Method	Percent error in Dmax (%)							Percent error in Dmean (%)
	min	max	max*	mean	mean*	std	std*	min	max	max*	mean	mean*	std	std*
ml	0.001	179.6	85.7	24.7	19.8	29.0	18.8	0.001	165.6	99.2	27.7	22.7	31.3	22.3
m2	0.1	429.2	177.5	53.7	43.0	64.1	42.1	0.04	193.5	109.5	31.9	25.9	36.0	24.6
m3	0.03	16.4	7.5	3.0	2.5	2.9	1.8	0.002	14.5	7.8	2.9	2.5	2.6	1.7

Table 2.

Dosimetric errors in the OARs and PTV obtained with the three evaluated methods (m1–m3) using for the evaluation the BM-1 (breathing model with amplitude variations).

		Percent error (%)
Method		Dmax	Dmean
m1	PTV	2.8	9.2
	Esophagus	5.4	3.9
	Heart	7.7	7.9
	Spinal cord	2.9	2.3
	Lungs	3.9	3.9
m2	PTV	2.8	7.7
	Esophagus	5.4	0.4
	Heart	7.7	3.9
	Spinal cord	2.9	5.9
	Lungs	3.9	1.3
m3	PTV	2.5	2.1
	Esophagus	1.7	1.4
	Heart	2.5	1.7
	Spinal cord	2.7	3.8
	Lungs	2.7	1.8

4. Discussion

In this work, we evaluated the performance of three motion management methods to investigate how to account for breathing motion in small serial structures such as airways and which method should be used to provide more accurate dose estimates. To design the motion management methods, the RT plan was recreated using different images and structure definitions. Methods m1 and m2 used the average intensity image (CT_AVG) of the 10 breathing phases of the 4DCT. In method m1, airways were deformed to the CT_AVG. In m2, airways were deformed to each of the 4DCT phases, and union structures were transferred onto the CT_AVG. Method m3 recreated the RT plan at the 10 breathing phases calculating the final dose matrix as the average of the 10 phases, assuming equally timed breathing phases.

For the evaluation, we designed a digital breathing model with nonuniform breathing cycles based on patient data, which served as the ground truth to compare with the dosimetry of the three methods. Irregularities in the breathing cycles were introduced in terms of cycle-to-cycle respiratory amplitude variations (BM-1) and cycle-to-cycle respiratory amplitude and time variations (BM-2). We analyzed the dosimetric accuracy in 239 airways, the OARs, and the PTV by calculating the percent errors in D_mean and D_max, the latter being of special interest in the airways because it was demonstrated in a previous work to play an important role in the radiosensitivity of these structures (Kazemzadeh et al 2018). We observed lower dose errors, but with very slight differences, in the evaluation using BM-1 rather than BM-2 as ground truth. This result is especially interesting for m3, meaning that assuming equally timed breathing phases is not a bad approximation for airways dosimetry (or the rest of the organs) if no information about time spent at each phase is available.

The results showed that the dose errors in the methods that used the CT_AVG image to recreate the RT plan (m1 and m2) were reasonable for the OARs and PTV, with errors <11%. However, the errors were remarkably higher in peripheral airways, with mean dose errors around 20% in m1 and 30%–40% in m2. The reason for these higher errors is that, although the CT_AVG image accounts for respiration-induced geometric variations in the different structures, it does not account for the fact that the tissue density at a specific location changes over the respiratory cycle. As a result, the CT_AVG provides only an average value of the density of the different structures that took up the same space at different moments during the respiration cycle time. This idea was already pointed out by Glide-Hurst et al (2008) while studying the effect of the breathing motion on the PTV, and it was studied by several groups by recreating the RT plan with the mid-ventilation image (Wolthaus et al 2008, Mexner et al 2009) or using the average intensity from the 4D breathing phases (Admiraal et al 2008, Glide-Hurst et al 2008). The conclusion of all these studies was that the overall effect of the density variations in the PTV was small, even in the presence of large movements, suggesting that using some ‘average’ anatomy/location for planning could ensure sufficiently accurate dose evaluation. These findings were also confirmed in our present study, where the dose errors for the PTV were <11% for both m1 and m2. However, our work demonstrated that, when it comes to smaller serial structures such as airways, this average image-based approach is inadequate. E.g. the apparent density of the airway lumen in the averaged structure is higher than the actual lumen density (i.e. air = −1024 HU) because breathing motion blurs the actual value with the density of the airway wall (~ −500 HU) and/or that of lung tissue (~ −800 HU), which can lead to errors in estimating mean and point doses. This effect was amplified in m2 because the airway structures used were wider, explaining the higher dosimetric errors.

The method that used the ten breathing phases to recreate the RT plan (m3) provided very accurate dose estimates, with mean values of the dose error ≤4% for the evaluation using both breathing models. Therefore, this work highlights the need to use a full 4D dose calculation in order to obtain accurate dose values in small serial structures. It is worth mentioning that, although this strategy entails a more complicated workflow than the actual protocols used in most radiotherapy clinics, it is designed to be fully automatic when eventually implemented. Therefore, the impact on clinical workflow is likely to be minimal, even for treatment techniques such as IMRT and VMAT.

It is important to mention that the ground truth used in this work provided a way to rank the methods, allowing us to select the appropriate one to obtain more accurate dose estimations. However, the obtained dose errors should be taken as illustrative values, because several simplifications were included to generate the model and some sources of error were not considered in the calculation of those values.

Among the simplifications adopted to generate the model, we used only five distinct cycles with different amplitude variations in each cycle (four actual variations and the initial 4DCT^P), which were randomly picked to generate each of the 225 cycles to simulate the respiration of the digital-patient phantom. Therefore, the digital 4DCT^M, calculated by averaging the used amplitude variation images during the 225 breathing cycles, used only five distinct amplitude variations per 4DCT^M phase, weighted by the number of times that each variation was repeated in the 225 cycles. Furthermore, unlike a clinical 4DCT, which is generated by binning groups of slices (slabs) acquired in different respiratory cycles, our model-derived 4DCT (4DCT^M) was binning-free (and therefore binning artifact-free) because it was generated using the entire volume corresponding to a respiratory phase. In other words, the model 4DCT^M represented a ‘scan’ acquired with a CT detector width that can image the whole torso of the patient in one rotation, thus ignoring binning artifacts.

Another simplification adopted in the model was that the delivery of the dose was not time-dependent because the beam-specific temporal information of the dose delivery was not available and, therefore, could not be included in the model. Thus, we assumed the 13 beams of the plan to be simultaneously active. Nevertheless, because the final dose matrix was calculated as the average of all the dose matrices at each phase of each cycle (deformed to a reference phase), in the end the differences average out.

Among the sources of error not considered in the analysis, we did not simulate baseline shifts in our nonuniform respiration model (i.e. irregular motion involving substantial displacement resulting from changes in the breathing pattern, producing abrupt shifts, and mean position drift (Balasubramanian et al 2017)). Another source of error not fully taken into account was the uncertainty related to the B-spline DIRs. The order of magnitude of these uncertainties may vary depending on the software used and the size and location of the structure. For example, Motegi et al (2019) reported average target registration errors of ~4 mm at the centroid of the prostate, bladder, rectum, and seminal vesicles (SVs) ROIs, and ~2 mm for multiple evaluation points using the RayStation hybrid DIR. Slightly higher errors were found while using the MIM Maestro hybrid DIR, with 2 mm for the prostate and bladder, about 6 mm for the rectum and SVs, and more than 6 mm for multiple evaluation points. In the case of the B-spline DIRs using Plastimatch (the algorithm used in this work), Kipritidis et al (2014), estimated that the accuracy of this algorithm between different 4DCT phases (in the lung area) was ~2 mm uncertainty on average (1.8 ± 1.5 mm). These errors would have been considered in the analysis if the breathing model used as ground truth had not also been affected by the use of the DIRs in its generation. Certainly, the DVFs used for the breathing model were different from the ones used for m3; however, some uncertainties might have been obscured. Furthermore, in this study, we did not impose an invertibility constraint on the DIR, which could also be a potential source of uncertainty, and we did not conduct an explicit sensitivity analysis on the impact of DIR errors on our methods.

It is also worth mentioning that, for ultimate treatment delivery, ensuring that what was planned will be accurately delivered into the smallest peripheral airways (diameters ~3 mm) can be challenging. To the best of our knowledge, it is not possible to visualize peripheral airways in the treatment room. In current clinical practice there is no real time volumetric-based imaging modality with enough spatial and temporal resolution. Usually a cone beam CT (CBCT) is used for the generation of 3D image sets that can be overlaid onto the simulation CT scan for matching. CBCTs significantly increase target accuracy and reduce patient setup and correction of positional errors (Higgins et al 2009), with patient setup errors of ~2 mm (Corradetti et al 2013) and they are thus recommended for treatment using SAbR in early stage non-small cell lung cancer (Molitoris et al 2019). Therefore, these setup uncertainties are within the same order of magnitude as the smallest airways considered in this study.

Taking these limitations into account along with the above-mentioned registration uncertainties, we estimate that there is a 5 mm-threshold for the amplitude of the breathing motion above which the benefits of all the steps involved in methods like m3 are worth the effort. This threshold is still far from typical respiratory amplitudes in a breathing cycle, which are around 10–12 mm. Furthermore, as it was shown in a previous work (Kazemzadeh et al 2018), it is possible to meet the clinical constraints for the PTV and the usual OARs (esophagus, heart, spinal cord, and lungs) when the airways are included as organs at risk in the treatment planning. Thus, in our opinion, it is worthwhile to use methods to estimate airway dose more accurately with the goal of preserving these structures in order to prevent lung injury. Moreover, with the increased interest in MR-linacs, there are intriguing possibilities of monitoring the airway motion during intra-fraction delivery, such as registering the airways with real time imaging, e.g. MRI dataset etc, and then modifying the delivery/aperture real-time to spare the airways/OARs. However, with the current clinical MRI systems, it is still challenging to visualize airways with diameters of 3–5 mm, especially during free-breathing.

In addition, at this initial stage, we used data (239 airways) from a single patient. Future works would benefit from the use of data from multiple patients and therefore multiple RT plans.

5. Conclusions

This work demonstrates the importance of accounting for breathing motion for dosimetric estimations in peripheral airway elements. These initial findings indicate that the current clinical motion management paradigm of using an ‘average’ anatomy/location for planning, to account for patient’s respiration differences from the simulation to the treatment delivery and from cycle to cycle, is likely to be inadequate for dose estimation in moving peripheral airways. Therefore, this study suggests the use of techniques like m3 in this work to account for breathing motion in order to obtain accurate dosimetric values in small structures, such as the airways. Although this method may be cumbersome with currently available clinical tools, the basic framework can be largely automated for eventual clinical implementation. Beyond the current scope, the technique m3 to account for motion described here may also be of interest when calculating dose to other small serial structures affected by motion, such as the pulmonary vessels and/or cardiac substructures.

Table 3.

Summary of the dosimetric errors in the 239 airways obtained with the three evaluated methods (m1–m3) using for the evaluation the BM-2 (breathing model with amplitude and time variations). Max*, mean*, and std* are the maximum, mean, and standard deviation calculated without using the outliers (>95% percentile).

Method	Percent error in Dmax (%)							Percent error in Dmean (%)
	min	max	max*	mean	mean*	std	std*	min	max	max*	mean	mean*	std	std*
m1	0.001	182.8	93.0	26.0	21.0	29.8	19.4	0.001	168.5	94.8	29.1	23.4	31.9	21.9
m2	0.1	493.9	179.3	56.8	45.4	68.8	44.7	0.01	195.8	119.4	33.9	27.8	37.2	26.1
m3	0.006	22.6	14.4	4.3	3.6	4.1	2.9	0.01	18.4	12.0	4.1	3.5	3.5	2.6

Table 4.

Dosimetric errors in the OARs and PTV obtained with the three evaluated methods (m1–m3) using for the evaluation the BM-2 (breathing model with amplitude and time variations).

		Percent error (%)
Method		Dmax	Dmean
m1	PTV	2.8	10.3
	Esophagus	5.1	1.9
	Heart	7.6	5.5
	Spinal cord	2.8	3.2
	Lungs	3.7	3.2
m2	PTV	2.8	10.3
	Esophagus	5.1	1.9
	Heart	7.6	5.5
	Spinal cord	2.8	3.2
	Lungs	3.7	3.2
m3	PTV	2.5	0.8
	Esophagus	1.5	2.0
	Heart	2.4	1.8
	Spinal cord	2.9	5.3
	Lungs	2.5	2.1