Yue Ning, Chen Zhe, Nath Ravinder
Department of Therapeutic Radiology, Yale University School of Medicine, New Haven, CT 06520-8040, USA.
Phys Med Biol. 2002 Apr 7;47(7):1185-204. doi: 10.1088/0031-9155/47/7/313.
Edema caused by the surgical procedure of prostate seed implantation expands the source-to-point distances within the prostate and hence decreases the dose coverage. The decrease of dose coverage results in an increase in tumour cell survival. To investigate the effects of edema on tumour cell survival, a bio-mathematical model of edema and the corresponding cell killing by continuous low dose rate irradiation (CLDRI) was developed so that tumour cell surviving fractions can be estimated in an edematous prostate for both 125I and 103Pd seed implants. The dynamic nature of edema and its resolution were modelled with an exponential function V(T) = V(p)(1 + M exp(-0.693T/ T(e))) where V(p) is the prostate volume before implantation, M is the edema magnitude and T(e) is edema half-life (EHL). The dose rate of a radioactive seed was calculated according to AAPM TG43, i.e. D = SkAg(r)phi(an)/r2, where r is the distance between a seed and a given point. The distance r is now a function of time because of edema. The g(r) was approximated as 1/r(0,4) and 1/r(0.8) for 125I and 103Pd, respectively. By expanding the mathematical expression of the resultant dose rate in a Taylor series of exponential functions of time, the dose rate was made equivalent to that produced from multiple fictitious radionuclides of different decay constants and strengths. The biologically effective dose (BED) for an edematous prostate implant was then calculated using a generalized Dale equation. The cell surviving fraction was computed as exp(-alphaBED), where alpha is the linear coefficient of the survival curve. The tumour cell survival was calculated for both 125I and 103Pd seed implants and for different tumour potential doubling time (TPDT) (from 5 days to 30 days) and for edemas of different magnitudes (from 0% to 95%) and edema half-lives (from 4 days to 30 days). Tumour cell survival increased with the increase of edema magnitude and EHL. For a typical edema of a half-life of 10 days and a magnitude of 50%. the edema increased tumour cell survival by about 1 and 2 orders of magnitude for 125I and 103Pd seed implants respectively. At the extreme (95% edema magnitude and an edema half-life of 30 days), the increase was more than 3 and 5 orders of magnitude for 125I and I03Pd seed implants respectively. The absolute increases were almost independent of TPDT and the prostate edema did not significantly change the effective treatment time. Tumour cell survival for prostate undergoing CLDRI using 125I or 103Pd seeds may be increased substantially due to the presence of edema caused by surgical trauma. This effect appears to be more pronounced for 103Pd than 125I because of the shorter half-life of 103Pd. If significant edema is observed post implantation, then a boost to the prostate using external beam radiotherapy may be considered as a part of the treatment strategy.
前列腺粒子植入手术所引发的水肿会扩大前列腺内部源点到靶点的距离，进而降低剂量覆盖范围。剂量覆盖范围的减小会导致肿瘤细胞存活率上升。为了研究水肿对肿瘤细胞存活的影响，我们构建了一个水肿生物数学模型以及连续低剂量率照射（CLDRI）对应的细胞杀伤模型，这样就能够估算出在植入¹²⁵I和¹⁰³Pd粒子的水肿前列腺中肿瘤细胞的存活分数。水肿的动态特性及其消退过程采用指数函数V(T) = V(p)(1 + M exp(-0.693T / T(e)))进行建模，其中V(p)是植入前的前列腺体积，M是水肿程度，T(e)是水肿半衰期（EHL）。放射性粒子的剂量率根据美国医学物理师协会（AAPM）TG43进行计算，即D = SkAg(r)phi(an)/r²，其中r是粒子与给定靶点之间的距离。由于水肿，距离r现在是时间的函数。对于¹²⁵I和¹⁰³Pd，g(r)分别近似为1/r(0,4)和1/r(0.8)。通过将所得剂量率的数学表达式在时间的指数函数泰勒级数中展开，使剂量率等同于由不同衰变常数和强度的多个虚拟放射性核素产生的剂量率。然后使用广义戴尔方程计算水肿前列腺植入的生物等效剂量（BED）。细胞存活分数计算为exp(-alphaBED)，其中alpha是存活曲线的线性系数。针对¹²⁵I和¹⁰³Pd粒子植入，以及不同的肿瘤潜在倍增时间（TPDT）（从5天到30天）、不同程度的水肿（从0%到95%）和水肿半衰期（从4天到30天），计算肿瘤细胞存活率。肿瘤细胞存活率随水肿程度和EHL的增加而升高。对于半衰期为10天、程度为50%的典型水肿，¹²⁵I和¹⁰³Pd粒子植入时，水肿分别使肿瘤细胞存活率提高约1个和2个数量级。在极端情况下（水肿程度为95%且水肿半衰期为30天），¹²⁵I和¹⁰³Pd粒子植入时，增加幅度分别超过3个和5个数量级。绝对增加量几乎与TPDT无关，前列腺水肿也未显著改变有效治疗时间。由于手术创伤导致的水肿，使用¹²⁵I或¹⁰³Pd粒子进行CLDRI治疗的前列腺肿瘤细胞存活率可能会大幅提高。由于¹⁰³Pd半衰期较短，这种效应在¹⁰³Pd上似乎比¹²⁵I更明显。如果植入后观察到明显水肿，那么可以考虑使用外照射放疗对前列腺进行补充照射，作为治疗策略的一部分。
