# Dynamics-Adapted Radiotherapy Dose (DARD) for Head and Neck Cancer Radiotherapy Dose Personalization

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## Abstract

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_{DARD}). We also present the results of an in silico trial of this dose personalization using retrospective data from a combined cohort of n = 39 head and neck cancer patients from the Moffitt and MD Anderson Cancer Centers that received 66–70 Gy RT in 2–2.12 Gy weekday fractions. This trial was repeated constraining D

_{DARD}between (54, 82) Gy to test more moderate dose adjustment. D

_{DARD}was estimated to range from 8 to 186 Gy, and our in silico trial estimated that 77% of patients treated with standard of care were overdosed by an average dose of 39 Gy, and 23% underdosed by an average dose of 32 Gy. The in silico trial with constrained dose adjustment estimated that locoregional control could be improved by >10%. We demonstrated the feasibility of using early treatment tumor volume dynamics to inform dose personalization and stratification for dose escalation and de-escalation. These results demonstrate the potential to both de-escalate most patients, while still improving population-level control rates.

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Patient Data

#### 2.2. Mathematical Model

^{−1}], and $K\left(t\right)$ is the tumor carrying capacity [cc], which is defined as the maximum tumor size that the local tissue can support at time t.

#### 2.3. Model Calibration and Fitting

^{−1}for all patients, which was optimized in the original presentation of this model [18]. Patient-specific values for $\delta $ were then determined using the particle swarm optimization toolbox in MATLAB with $\delta $ being bound between 0 and 1, as per the definition of the parameter. Model fit to data was analyzed using normalized root mean square error, <nRMSE>.

#### 2.4. Dose Personalization Framework

_{DARD}, which is the minimum cumulative RT dose predicted for LRC. This was done using a framework that was adapted from the original implementation that was used to forecast patient outcomes with high specificity and sensitivity using a few weeks of on-treatment tumor volume measurements [18]. The framework learns 3 inputs from a training cohort: (1) a function to estimate δ from average weekly tumor volume decrease, $\overline{-\Delta V/\Delta t}$, (2) a prior distribution for δ, and (3) a volume reduction cutoff correlated with the patient outcome of interest, in this case LRC (Figure 2).

_{DARD}. D

_{DARD}is determined by measuring cumulative dose that includes the RT fraction such that all of the forecasted tumor volume trajectories have a tumor volume reduction below the cutoff association with complete LRC.

#### 2.5. Dose Personalization In Silico Trial Design

_{DARD}for the virtual patient. We then further simulated RT to a cumulative dose of 50 Gy, after which the clinically observed tumor volume measurement was compared to the model prediction made at the beginning of week 5 of RT. If the in silico tumor volume trajectories were on the same side of the LRC threshold as the measured tumor volume after 50 Gy of RT, then the in silico treatment was completed to D

_{DARD}. Otherwise, in silico treatment reverted to standard of care, and the virtual patient received the same dose that the original patient received.

## 3. Results

#### 3.1. Model Fitting

^{−1}across all patients, and although the optimization algorithm search for $\delta $ over the whole range of (0,1), the fitted values of $\delta $ were all <0.1 (Figure 4C). The model fitting results were robust across a range of pre-treatment volume dynamics, as captured by the range of PSI values (0.47,1). Notably, we did not account for whether or not the patients received chemotherapy, so the effect of chemotherapy is also captured in the patient-specific fit of the $\delta $ parameter.

#### 3.2. Personalized Dynamics-Adapted Radiation Therapy Dose (D_{DARD})

_{DARD}, to achieve a tumor volume reduction below the trained cutoff for locoregional control. Compared to the clinically delivered total dose, D, D

_{DARD}indicates candidates for dose escalation if D

_{DARD}> D, or de-escalation if D

_{DARD}< D (Figure 5A). D

_{DARD}ranges from 8–186 Gy (Figure 5B) and suggests that 77% (n = 30) of patients treated with standard of care were overdosed by an average dose of 39 Gy, and 23% (n = 9) underdosed by an average dose of 32 Gy (Table 1). One patient was predicted to not achieve the necessary tumor volume reduction for LRC within 20 weeks of in silico RT to a cumulative total dose of 200 Gy.

_{DARD}—D) for the remaining 38 patients are summarized in Figure 5C. Although the small size of the cohort limits statistical comparisons with clinical characteristics, we visualized the distribution of the primary tumor site, T-stage, p16 viral status, and the originally delivered RT dose for the predicted escalation and de-escalation cohorts. Interestingly, there were patients with T4 tumors in both the escalation and de-escalation subgroups. The 9 patients predicted for dose escalation had a variety of disease sites (tonsil [3], oral cavity [2], tongue [1], base of tongue [1], oropharynx [2]). Of interest, 4 predicted escalation patients (44%) were p16-, 4 were p16+, and 1 unknown. Similarly, of the patients with de-escalation D

_{DARD}, 18 were p16+ (60%) and 6 were p16- (20%; 6 with unknown p16 status), suggesting that HPV status alone may not be a clear indicator for HNC dose personalization.

#### 3.3. ${D}_{\mathit{DARD}}^{*}:$Dose Personalization within Restricted Dose Range

_{DARD}suggests a widespread of personalized radiation doses. As most of the D

_{DARD}values are far outside the current standard of care prescription dose of 66–70 Gy for HNC, which may be unrealistic to test in initial clinical trials, we tested a restricted personalized dose range of (54,82) Gy based on upper and lower limits tested in previous clinical trials of locally advanced HNC and HPV-associated oropharyngeal cancer [21,22,23]. Thus, we mapped D

_{DARD}< 54 Gy to ${D}_{\mathrm{DARD}}^{*}$ = 54 Gy and D

_{DARD}> 82 Gy to ${D}_{\mathrm{DARD}}^{*}$ = 82 Gy (Figure 6A) and repeated the in silico trial with ${D}_{\mathrm{DARD}}^{*}$. The results of this trial are summarized in Figure 6B.

## 4. Discussion

## 5. Patents

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**

**Patient tumor volume trajectories and correlation with locoregional control (LRC).**(

**A**) Longitudinal tumor volume trajectories for all 39 patients normalized by initial patient tumor volume at start of RT with one measurement before the start of RT and weekly measurements during the course of treatment. Patients with eventual locoregional failure are highlighted in purple. The indicated median volume reduction (−ΔV = 32.2%) at week 4 of RT perfectly separates the patients with locoregional control (LRC) and locoregional failure. (

**B**) Kaplan–Meier survival plot for locoregional control (LRC) separated by percent tumor volume reduction (−ΔV = 32.2%) at 4 weeks of RT.

**Figure 2.**

**RT Dose personalization framework for D**The framework is divided into three phases: Pre-measurement based on the historical cohort, measurements for the i-th patient, and patient-specific dose personalization. The squares represent information learned from the training cohort; circles represent information measured or calculated for an individual patient.

_{DARD}.**Figure 3.**

**Flowchart description of in silico trial sequence.**The trial has three major phases: (1) Leave-one-out initialization, where model parameters are calibrated from the training cohort and combined with tumor volume data from before the start of RT to week 4 of RT, (2) Personalized dose estimation, and (3) Safety check for model agreement with measured tumor volume after in silico treatment up to 50 Gy.

**Figure 4.**

**Model fit to longitudinal tumor volume data.**(

**A**) Representative model fits for three patients arranged in order of increasing PSI values. Red dots are measured pre-treatment tumor volumes; black dots on-treatment tumor volumes; the dashed green curves are the calculated pre-treatment tumor growth trajectory; the solid green curves are the fitted on-treatment tumor volume trajectories; and the thin red line indicates the calculated value of the tumor carrying capacity both before and during treatment. (

**B**) Correlation of measured tumor volumes and fitted tumor volumes for all 39 patients with indicated average normalized root mean square error (<nRMSE>). Green dots indicate individual weekly tumor volumes. (

**C**) Parameter distributions for all 39 patients. Volumetric tumor growth rate, λ = 0.13 day

^{−1}, was fixed for all patients.

**Figure 5.**

**Dose personalization and trial results using D**(

_{DARD}.**A**). Example calculations of finding minimum RT dose for locoregional control, D

_{DARD}, for two patients using 4 tumor volume measurements (1 before start of RT and 4 from weeks 1–4 of RT). Black dots are normalized tumor volume measurements; blue curves the 100 projected tumor volume forecasts; horizontal dashed line the volume reduction threshold associated with LRC; and the vertical dashed line D

_{DARD}, the minimum dose where all 100 trajectories are below the LRC threshold. (

**B**). Histogram of calculated D

_{DARD}values for all 39 patients. (

**C**). Waterfall plot of difference between D

_{DARD}and the actual dose received in the clinic, where ΔD > 0 indicates dose escalation and ΔD < 0 indicates dose de-escalation for the 38 patients on the trial. Individual patient characteristics of interest (primary tumor site, p16 status, T-stage, cumulative dose received in the clinic, and D

_{DARD}) are indicated for each patient below the waterfall plot.

**Figure 6.**

**Dose adjustment to**${D}_{\mathrm{DARD}}^{*}$

**and subsequent in silico trial results.**(

**A**) Scatter plot of ${D}_{\mathrm{DARD}}^{*}$ and D

_{DARD}limited to the moderate escalation/de-escalation range of (54,82) Gy for 38 patients. A histogram of the D

_{DARD}is projected above the scatterplot. (

**B**) Waterfall plot of difference between ${D}_{\mathrm{DARD}}^{*}$ and the actual dose received in the clinic, where ΔD > 0 indicates dose escalation and ΔD < 0 indicates dose de-escalation for the 38 patients that remained on the trial. Individual patient characteristics of interest (primary tumor site, p16 status, T-stage, cumulative dose received in the clinic, and ${D}_{\mathrm{DARD}}^{*}$) are indicated for each patient below the waterfall plot.

$\mathbf{Clinical}\mathit{D}$ | ${\mathit{D}}_{\mathbf{DARD}}$ | ${\mathit{D}}_{\mathbf{DARD}}^{*}$ | |
---|---|---|---|

Mean Escalation (Gy) | 0 | 38.9 | 12.4 |

Mean De-Escalation (Gy) | 0 | 32.0 | 10.7 |

LRC Rate | 84.6% | 100% | 94.9% ^{1} |

^{1}Estimated based on number of escalated patients for whom ${D}_{\mathrm{DARD}}^{*}={D}_{\mathrm{DARD}}$

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**MDPI and ACS Style**

Zahid, M.U.; Mohamed, A.S.R.; Caudell, J.J.; Harrison, L.B.; Fuller, C.D.; Moros, E.G.; Enderling, H.
Dynamics-Adapted Radiotherapy Dose (DARD) for Head and Neck Cancer Radiotherapy Dose Personalization. *J. Pers. Med.* **2021**, *11*, 1124.
https://doi.org/10.3390/jpm11111124

**AMA Style**

Zahid MU, Mohamed ASR, Caudell JJ, Harrison LB, Fuller CD, Moros EG, Enderling H.
Dynamics-Adapted Radiotherapy Dose (DARD) for Head and Neck Cancer Radiotherapy Dose Personalization. *Journal of Personalized Medicine*. 2021; 11(11):1124.
https://doi.org/10.3390/jpm11111124

**Chicago/Turabian Style**

Zahid, Mohammad U., Abdallah S. R. Mohamed, Jimmy J. Caudell, Louis B. Harrison, Clifton D. Fuller, Eduardo G. Moros, and Heiko Enderling.
2021. "Dynamics-Adapted Radiotherapy Dose (DARD) for Head and Neck Cancer Radiotherapy Dose Personalization" *Journal of Personalized Medicine* 11, no. 11: 1124.
https://doi.org/10.3390/jpm11111124