Conventional dose rate spatially-fractionated radiation therapy (SFRT) treatment response and its association with dosimetric parameters – A preclinical study in a Fisher 344 rat model

Purpose To identify key dosimetric parameters that have close associations with tumor treatment response and body weight change in SFRT treatments with a large range of spatial-fractionation scale at dose rates of several Gy/min. Methods Six study arms using uniform tumor radiation, half-tumor radiation, 2mm beam array radiation, 0.3mm minibeam radiation, and an untreated arm were used. All treatments were delivered on a 320kV x-ray irradiator. Forty-two female Fischer 344 rats with fibrosarcoma tumor allografts were used. Dosimetric parameters studied are peak dose and width, valley dose and width, peak-to-valley-dose-ratio, volumetric average dose, percentage volume directly irradiated, and tumor- and normal-tissue EUD. Animal survival, tumor volume change, and body weight change (indicative of treatment toxicity) are tested for association with the dosimetric parameters using linear regression and Cox Proportional Hazards models. Results The dosimetric parameters most closely associated with tumor response are tumor EUD (R2=0.7923, F-stat=15.26*; z-test=−4.07***), valley/minimum dose (R2=0.7636, F-stat=12.92*; z-test=−4.338***), and percentage tumor directly irradiated (R2=0.7153, F-stat=10.05*; z-test=−3.837***) per the linear regression and Cox Proportional Hazards models, respectively. Tumor response is linearly proportional to valley/minimum doses and tumor EUD. Average dose (R2=0.2745, F-stat=1.514 (no sig.); z-test=−2.811**) and peak dose (R2=0.04472, F-stat=0.6874 (not sig.); z-test=−0.786 (not sig.)) show the weakest associations to tumor response. Only the uniform radiation arm did not gain body weight post-radiation, indicative of treatment toxicity; however, body weight change in general shows weak association with all dosimetric parameters except for valley/min dose (R2=0.3814, F-stat=13.56**), valley width (R2=0.2853, F-stat=8.783**), and peak width (R2=0.2759, F-stat=8.382**). Conclusions For a single-fraction SFRT at conventional dose rates, valley, not peak, dose is closely associated with tumor treatment response and thus should be used for treatment prescription. Tumor EUD, valley/min dose, and percentage tumor directly irradiated are the top three dosimetric parameters that exhibited close associations with tumor response.

292 arms decrease at different rates, which can introduce biases due to unbalanced sample sizes in 293 the study. Hence, Day 17 was chosen for the linear regression association studies because at 294 this timepoint there is a good compromise between the number of animals available for statistical 295 consideration and the magnitude of radiation effects. We also fit a more robust Cox Proportional 296 Hazards (CoxPH) model to the full data set that includes all animals.

297
Animal body weight change on Day 17 is used as an indicator of treatment toxicity. Animal 298 body weight change is a gross assessment on treatment toxicity, especially in this study where 299 tumors were implanted in the rodent flank, near the lower gastro-intestinal tract (including the 300 rodent anus, rectum, colon, and cecum) and parts of the upper gastro-intestinal tract (including 301 portions of the small bowel). We speculate that some treatment arms may induce more GI toxicity 302 that others. We subtracted the tumor weight from the measured body weight and regard this "net" 303 animal body weight change as an indication, not confirmation, of treatment toxicity. To confirm 304 any lower GI toxicity, additional tissue histological staining or organ function examination studies 305 would be necessary, both of which are beyond the scope of this work.

307
We computed Product-Limit (Kaplan-Meier) Estimator and Logrank (Mantel-Haenszel) 308 test for statistical significance of survival difference between each pair of treatment arms (30).
309 Multiple simple linear regression models (31) were used to study the association between 310 dosimetric parameters with animal body weight and percentage survival within treatment group 311 on Day 17. R 2 (square of the Pearson correlation) coefficient is computed to estimate the 312 proportion of variance explained in each of the linear regression models. In general, the greater 313 the magnitude of the test statistic (t or F), the more closely associated the dosimetric parameter 314 studied is with the treatment response (survival or body weight).

315
In addition to linear regressions, we fit Cox Proportional Hazard (CoxPH) models with 316 individual animal survival as the time-to-event outcome, which used data from all dates including 317 Day 17. This allowed us to calculate the hazard ratio associated with the impact of dosimetric 318 parameters on treatment response. We also used a Pearson Correlation matrix to show the cross-319 correlation between each pair of the dosimetric parameters. All data collected were analyzed 320 using R (version 3.5.3) statistical software available from R Core Team.  Table S1). Peak dose (R 2 =0.04472, F-stat=0.6874 (not sig.)) and AVG     470 S1 Table). This observed association between tumor treatment response with tumor 471 valley/minimum dose and tumor EUD dose in this preclinical study is consistent with their known 472 association in tumor treatment response seen in clinical conventional uniform dose radiation 473 therapy.

474
Our data suggests that valley/minimum dose or Tumor EUD are more appropriate than 475 peak dose for SFRT treatment prescription. When tumor control is the endpoint, we suggest that 476 equal valley or minimum dose be used for comparative study between a uniform radiation and 477 SFRT therapy or among different SFRT treatments.
478 479 PVDR 505 sig.)). In a synchrotron microbeam brain study using multiple beams Serduc et al. kept valley 506 dose constant while varying peak width and peak dose. They concluded that the latter two 507 parameters have strong influence therapeutic ratio (39).

Volume-averaged dose and peak dose 509
This study is designed to scrutinize the association of volume-averaged dose with tumor 510 treatment response (Fig 1). The four study arms sharing very similar volume-averaged doses (20 511 or 18 Gy) exhibited very different tumor treatment responses (Fig 6 and 7) showing the survival 512 rate at day 17 varied from 100% to 33%. Therefore, the association between volume-average 513 dose and tumor treatment response is weak.

514
We found that peak dose has little to no association with tumor treatment response 515 (R 2 =0.04472, F-stat=0.6874 (not sig.)) (Fig 7, S1 Table, Table 2). This finding is significant 516 because peak dose has been used for treatment prescription in practically all SFRT treatments 517 (8) (9). Although the linear regression analysis on day 17 showed a weak association between 518 peak dose and survival that was not statistically significant, the CoxPH analysis using the entire 519 survival data set did show a modest association with survival.

SFRT dosimetric association with normal tissue toxicity 521
We did not study treatment induced normal tissue toxicity directly in this study. We used 522 body weight change post radiation (targeted to the flank, lower abdominal region of the animal) 523 as an indicator, not an evidence of normal tissue toxicity. We did not see a strong association 524 between animal body weight change and any of the eight dosimetric parameters studied, except 525 a modest association with valley/minimum dose.

Valley dose 527
The strongest association we observed is a weak one between body weight change and 528 valley/min dose (R 2 =0.3814, F-stat=13.56**) (  1 and Fig 6). The 20GyUniform arm 559 has the best tumor treatment response and the worst body weight change. Our data indicated the 560 2mm wide beam array is a kV photon SFRT pattern that has the potential for high therapeutic 561 ratio SFRT and deserves further investigation.