Test the Effectiveness of Quantitative Linear-Quadratic-Based (qLQB) Model on Evaluating Irradiation-Induced Liver Injury (ILI) Against Normal Tissue Complication Probability (NTCP).

OBJECTIVES: To test the effectiveness of quantitative linear-quadratic-based (qLQB) model on evaluating irradiation-induced liver injury (ILI) and establish the relation between the damaged ratio/percent (DRP) in qLQB model and normal tissue complication probility (NTCP).
MATERIALS AND METHODS: We established the qLQB model to calculate the ratio/percent (RP) between damaged cell/functional subunit (FSU) and entire cell/FSU of liver for radiation dose response, tested the qLQB against the Lyman-Kutcher-Burman (LKB) model, and established relation between the RP and NTCP through analyzing the dose of 32 patients with cancer of abdominal cavity who were treated with radiation therapy at our department. Based on varied α/β and varied parameters for NTCP, we put the calculated results into varied arrays for the next analysis. We named the 2 groups of RPs: RP1 (α/β = 3.0, α = 0.03) and RP2 (α/β = 8.0, α = 0.26), and named the 2 groups of NTCPs: NTCP1 (n = 0.32, m = 0.15, TD50(1) = 4000 cGy) and NTCP2 (n = 1.10, m = 0.28, TD50(1) = 4050 cGy).
RESULTS: Spearman correlation analysis was used to analyze the correlations among the groups, the results were as follows: RP1 vs NTCP1, rs = 0.83827, p < 0.0001; RP1 vs NTCP2, rs = 0.83827, p < 0.0001; RP2 vs NTCP2, rs = 0.79289, p < 0.0001; and RP2 vs NTCP1, rs = 0.79289, p < 0.0001.
CONCLUSIONS: There is a significant correlation between RP value and NTCP for evaluating ILI, and there is no difference between qLQB model and LKB model on evaluating ILI.

Introduction

The liver is an important organ that needs to be protected during radiotherapy for tumors in the lower abdomen.[1,2] The liver is relatively slow to renew, and the average lifetime of liver cells is about 1 year. However, under the strong stimulation of partial liver resection or fatal injury, all liver cells will quickly enter the period of proliferation. Radiation to an abdominal tumor is bound to damage the liver, and slight damage can lead to some dysfunction, but not any functional consequences.[3,4] When the liver is exposed to a relatively high dose of radiation or has serious damage occurrence, the liver tolerates well in the first few months, but then the liver develops progressive degeneration, due to the normal functional activity of irradiated liver cells but the inability to divide.

In the clinical practice, Vx or Dx% (Vx is the percentage between the volume receiving the dose equal to and greater than x and the total organ volume. The Vx and Dx% can be converted into each other, and for example, the information expressed by D50% = 30.0 Gy and V30 = 50.0% is the same.) is usually used to evaluate the radiotherapy physical plan (RPP) and predict the degree of irradiation-induced liver injury (ILI). However, when using Vx to evaluate and optimally select RPP, 2 problems are often encountered. One is that there are many Vx related to ILI. Liang et al. showed that mean dose to normal liver (MDTNL) >23.0 Gy and V > 86.0%, V > 68.0%, V > 59.0%, V > 49.0%, V > 35.0%, V > 28.0%, V > 25.0% and V > 20.0% were all risk factors for ILI.[5] Dawson et al. found that mean liver dose > 31.0 Gy was the risk factor for ILI. If the probability of occurrence of ILI was 5.0%, 1/3 of the liver receiving the dose of > 90.0 Gy and 2/3 of the liver receiving the dose of > 47.0 Gy were also the risk factors for ILI.[6] It can be seen that ILI is a complex problem. And the other is that using different Vx to select RPP will get different results. For example, the imaginary and full lines in Figure 1 represented Plan1 and Plan2 designed for the same liver tumor patient, respectively. When using V to optimally select RPP, the Plan1 will be selected, and when using V to optimally select RPP, the Plan2 will be selected.

Figure 1.

DVH display of 2 plans.

In order to overcome the difficulties encountered by using Vx to evaluating plan, our research team based on irradiation-induced lung injury established linear-quadratic-based (LQB) model and quantitative LQB (qLQB) model, and verified the effectiveness of the 2 models on evaluating irradiation-induced lung injury. In this study, we tested the effectiveness of qLQB model on evaluating ILI against LKB model, and then established the relation between the RP in qLQB model and NTCP of ILI for the qLQB model to be applied to all parallel organs in the body.

Materials and Methods

Patients’ Base Data

A total of 32 postoperative patients with cancer of abdominal cavity who were treated with radiation therapy at our department from June 2015 to February 2016 were enrolled in this study. Each patient underwent Siemens computed tomography scan with 120 kV and 80 mA and reconstructed with 2.5mm-layer, and was transferred to treatment planning system (TPS). Among 32 patients, 8 patients had gastric carcinoma, 18 patients had liver carcinoma, and 6 patients had pancreatic carcinoma. The plan data set consisted of 32 IMRT plans with 5-7 fields based on Pinnacle TPS 9.6 and Varian IX with 80 pairs of multi-leaf collimator. Dose calculation grid size was set 2.5 mm for every plan.

The targets, which included high-risk clinical tumor volume (CTV1) and low-risk clinical tumor volume (CTV2) and OARs for areas that included the normal liver, spinal cord, small intestine, kidney, et al. were delineated. CTV1 and CTV2 were expanded with 5.0 to 8.0 mm margin and for high-risk planning tumor volume (PTV1) and low-risk planning tumor volume (PTV2), respectively. The institutional planning criteria for cancer treatment were applied according to RTOG0615, and the prescription dose should cover at least 95% of the PTV. The recommended dose, 50Gy/25F and 45Gy/25F, 50Gy/25F and 60Gy/25F, 50Gy/25F and 56Gy/25F acted as prescription for GC’s PTV1 and PTV2, LC’s PTV1 and PTV2, PC’s PTV1 and PTV2, respectively. A significant dose gradient was observed between the target and normal tissues in all cancers. The dosimetric constraints recommended for the organs were according to RTOG0615 and RTOG0225.

qLQB Model

The qLQB model was established and applied based on the following 3 assumptions:

The parallel organs in human body, such as lung, liver and kidney, et al. were ideal parallel organs, that is, all function subunits (FSUs) were parallel and independent, and FSU was evenly distributed in the volume of the whole organ. Under the condition of a certain number of cells losing proliferation capacity, normal tissues will have acute and chronic radiation effect.

In all dose ranges, the survival fraction (SF) and dose (D) of the cells always met the formula SF = e- αD- βD ^2.

The relationship between survival of cells and the survival of FSU was rectilinear correlation.

The liver is a parallel organ, and the probability of radiation complications is closely related to the volume ratio of damage. Liver is assumed to be an organ of uniform density, volume ratio is the percentage of cell damage. Based on the above 3 assumptions, we have established the qLQB model to calculate the ratio/percent (RP) between damaged cell/FSU and entire cell/FSU of liver for radiation dose response, test the qLQB against the Lyman-Kutcher-Burman (LKB) model and establish relation between the RP and NTCP. The qLQB model can be described by a formulae[7]:

Here, A is the number of cells in a unit; Vs is the integral volume of normal liver; Dmax is the maximum dose which is exposed on normal liver per fraction in the plan. f 1(D) is the percentage volume of liver which is exposed at dose D. V is the integral exposed volume of liver.αandβare dimensionless parameter, which are determined by the organ character. The process of the qLQB establishment and brief descriptions of the LKB model are given in the Appendix A.

RP and NTCP Calculation

To calculate the RP value, the author obtains D and it’s corresponding f 1(D) from dose-volume statistical table of differential diagram of dose-volume histogram (dDVH). From D = 0 to D = Dmax, the auther abtains all D value by step of 1 cGy, because by step of <1 cGy the value of RP is almost constant. Exposed volume of liver is determined with the low limit of dose. If the low limit of dose is too low, for example 0.1cGy/F, 0.05cGy/F, et al., the whole liver is involved in every radio therapy even if the tumor is in the choracic cavity. To avoid this state, the author sets the low limit of dose at 1cGy/F, the causes are as follows: 1) If step being <1 cGy the value of RP is almost constant. 2) The injury brought about by <1 cGy which can be repaired before the next treatment.

Liver is often considered an organ, but up to date, it’s radiotherapic parameters aren’t acknowledged completely. To avoid the study enter into a 1-sided result, in this study the author employed 2 groups of α, β values for calculating RP: α/β = 3.0,α = 0.03,[8] and α/β = 8.0, α = 0.26.[9,10] And employed 2 groups of TD50(1), m, n values for calculating NTCP in LKB model: n = 0.32, m = 0.15, TD50(1) = 4000cGy,[11] and n = 1.10, m = 0.28, TD50(1) = 4050cGy.[12]

Results

To conveniently discuss, the author named the 2 groups of RPs (each group of RPs has 32 values corresponding to 32 patients): RP1 (α/β = 3.0, α = 0.03) and RP2 (α/β = 8.0, α = 0.26), and named the 2 groups of NTCPs (each group of NTCPs has 32 values corresponding to 32 patients): NTCP1 (n = 0.32, m = 0.15, TD50(1)= 4000 cGy) and NTCP2 (n = 1.10, m = 0.28, TD50(1)= 4050 cGy). Then the Spearman correlation was used to analyze values above 4 groups, the results are as follows: RP1 vs NTCP1, rs = 0.83827, p < 0.0001; RP1 vs NTCP2, rs = 0.83827, p < 0.0001; RP2 vs NTCP2, rs = 0.79289, p < 0.0001; and RP2 vs NTCP1, rs = 0.79289, p < 0.0001. So, there is a positive correlation between qLQB model and LKB model for evaluating ILI, and this correlation are displayed in Figures 2, 3, 4 and 5.

Figure 2.

Relationship between RP value and NTCP. When calculated RP value and NTCP, the parameters were selected as follows: α/β = 3.0, α = 0.03; n = 0.32, m = 0.15, TD50(1) = 4000 cGy.

Figure 3.

Relationship between RP value and NTCP. When calculated RP value and NTCP, the parameters were selected as follows: α/β = 3.0, α = 0.03; n = 1.10, m = 0.28, TD50(1) = 4050 cGy.

Figure 4.

Relationship between RP value and NTCP. When calculated RP value and NTCP, the parameters were selected as follows: α/β = 8.0, α = 0.26; n = 0.32, m = 0.15, TD50(1)= 4000 cGy.

Figure 5.

Relationship between RP value and NTCP. When calculated RP value and NTCP, the parameters were selected as follows: α/β = 8.0, α = 0.26; n = 1.10, m = 0.28, TD50(1)= 4050 cGy.

Discussion

The fundamental goal of radiotherapy is to give the tumor a therapeutic dose while minimizing the risk of normal tissue complications. Until now, the commonly used indicator for assessing the risk of liver complication has Vx, which is an agency of radio-biological responses and does not directly reflect liver complication risk. Several studies had reported that partial volume irradiation of the liver is feasible.[13,14] And it is well known that the tolerance of the liver to external beam irradiation depends on the volume of liver irradiated, few data exist which quantify this dependence. Radiation-induced liver disease is one of ILI, a well-established concept, a serious hepatic toxicity caused by irradiation of 30-35 Gy to the whole liver.[15] Although clinical practice indicates that the level of ILI is related with exposed-volume of liver and dose exposed on the volume, we haven’t knowed their specific relation.

The early NTCP model was mainly derived from clinical observation, and generally included 2 factors, overall treatment time and fractionation. In order to calibrate the differences caused by these 2 factors, the formulas such as nominal standard dose (NSD), cumulative radiation effect (CRE) and time, dose and fractionation (TDF) were proposed.[16] Later, with the development of radiobiology and the update of radiotherapy technology, multiple NTCP models were proposed in attempts to quantify dependence of tolerance effect for a certain radiation effect on the size of the treated region.[17,18] Although, up to now, we still haven’t found a model, and the calculated results are completely consistent with the clinical results because of the uncertainty of models’ parameters and the complexity of clinical practice. However, it is undeniable that these models provide a good reference for us to evaluate the plan.

LKB model is good and widely used model, which can be used to analyze ILI not considering Vx. We test the effectiveness of the qLQB model against the LKB model, acquiring rs > 0.79 (0.793, 0.837) and p < 0.0001, indicating there is a abvious positive correlation between RP values in qLQB model and NTCP values in LKB model, and use of the LKB model or the LQ-based model will obtain the same results for evaluating level of ILI.

The model established by Lyman can be used to describe dose response only when the absorbed dose is uniform dose. But the precise radiotherapy increases rapidly non-uniform degree of normal organs absorbed dose. Although Kutcher and Burman had improved the model, non-uniform dose must be converted some uniform dose before using the integral model. But qLQB model is based on LQ model, which can be used to describe dose response directly using non-uniform dose. Secondly, LKB model is a experiential model based on 4 parameters, and the base of qLQB model, LQ model, was from a radiation biology experiment, which is more reliable than experiential parameters. Thirdly, qLQB is not only based on in vitro LQ model but also based on in vivo LQ model, which can increase consistency between calculation base on qLQB model, if which is based on in vivo LQ model, and clinical outcomes in the future. Fourthly, the LKB model only contains information on the total dose, without the total treatment time and fractionation, which are important factors for biological effects. The qLQB model can reflect fractionation and other information through the LQ model, because we can convert a physical radiotherapy planning to a biological radiotherapy planning.[19] Fifthly, LQ model is widely used in clinical practice,[19-23] indicating that the qLQB model based on LQ model has the potential possibility to be widely used in clinical practice. Finally, the established process of qLQB model provides us a method, by which we can convert the laws (models) obtained from radiobiology into practical models available in clinical practice.

Although an α/β ratio of 3 could be used to calculate for most of the parallel organ which is widely acknowleged,[8] the α/β ratio of normal liver is unknown. Various ranges of α/β ratio were used with respect to various different criteria of ILI in previous studies. To calculate the BED delivered to the normal liver, α/β ratio of 2 was used for grade 3 or worse CTCAE hepatic toxicity.[24] Son et al. used α/β ratio of 2, 4, 6, 8 or 10 for 2 groups, Group A (45-50 Gy, 4.5-5.0 Gy) and Group B (36-60 Gy, 2.5-3.0 Gy), of liver patients. And then suggested that α/β ratio of normal liver is 8.[10] Dawson et al. used an α/β ratio of 2 or 2.5 for cases of classic RILD.[24,25]

Although the qLQB model overcomes limitations of Vx and has some advancement than LKB model, there are several problems requiring more attention and further study regarding the use of qLQB model in the clinic setting. The qLQB model is based on the LQ model, but the LQ model is obtained in vitro. So, actual RP in vivo should be more lower than calculated RP based on qLQB model in this paper, because of proliferation in vivo.