Clinical Investigation
The Radiation Dose–Response of the Human Spinal Cord

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Purpose

To characterize the radiation dose–response of the human spinal cord.

Methods and Materials

Because no single institution has sufficient data to establish a dose–response function for the human spinal cord, published reports were combined. Requisite data were dose and fractionation, number of patients at risk, number of myelopathy cases, and survival experience of the population. Eight data points for cervical myelopathy were obtained from five reports. Using maximum likelihood estimation correcting for the survival experience of the population, estimates were obtained for the median tolerance dose, slope parameter, and α/β ratio in a logistic dose–response function. An adequate fit to thoracic data was not possible. Hyperbaric oxygen treatments involving the cervical cord were also analyzed.

Results

The estimate of the median tolerance dose (cervical cord) was 69.4 Gy (95% confidence interval, 66.4–72.6). The α/β = 0.87 Gy. At 45 Gy, the (extrapolated) probability of myelopathy is 0.03%; and at 50 Gy, 0.2%. The dose for a 5% myelopathy rate is 59.3 Gy. Graphical analysis indicates that the sensitivity of the thoracic cord is less than that of the cervical cord. There appears to be a sensitizing effect from hyperbaric oxygen treatment.

Conclusions

The estimate of α/β is smaller than usually quoted, but values this small were found in some studies. Using α/β = 0.87 Gy, one would expect a considerable advantage by decreasing the dose/fraction to less than 2 Gy. These results were obtained from only single fractions/day and should not be applied uncritically to hyperfractionation.

Introduction

Radiation injury to the spinal cord is among the most easily studied experimental models of radiation injury and probably is the most fully documented clinical radiation complication. It has been studied in mice, rats, guinea pigs, dogs, pigs, and monkeys, and it was the subject of more than 400 clinical reports. Nonetheless, owing to its rare clinical manifestation, the clinical dose response has not been established for radiation myelopathy, and the dose–response function at 2-Gy/fraction has been established in animal models only by use of the top-up dose technique (1). This study combines reported data from the literature to establish the parameters of the dose–response function for clinical radiation myelopathy, including the median tolerance dose (D50), and the α/β ratio from the linear-quadratic (LQ) model.

Section snippets

Methods and Materials

In an experimental setting, dose–response data consist of a number of animals at risk and the number of responders at each dose point. For late radiation responses of normal tissues in humans, time to onset of injury must also be known. However, it is possible to circumvent this requirement if the survival experience of the population is known or can be approximated (2). In addition, one must also know the distribution of latent periods (time to onset) for the injury in question (2). In this

Results

A good fit to the combined cervical and thoracic cord data was not possible. Therefore, the different levels were analyzed separately.

Results of the fit of the cervical cord data in Table 1 were D50 = 69.4 Gy, k = 18.8, and α/β = 0.87 Gy. Pearson's chi-square statistic was 2.1 with 5 df, indicating a good fit of the model to the data. The 95% CI for D50 was 66.4–72.6 Gy. The 95% CI for α/β was 0.54–1.19 Gy. The 95% CI for k was 13.3–27.4. Data and the dose–response function are shown in Fig. 1.

Discussion

Values of D50 and calculated values for D05 (the dose at which P = 0.05), P(45 Gy), and P(50 Gy) are in reasonable agreement with previously published estimates based not on statistical analysis, but on extrapolation from animal models combined with some clinical data (24). The dose–response parameters also agree well with large-animal data (21).

The estimated incidence of myelopathy at 45 and 50 Gy seems to fit well with the collective experience. Whereas there are a number of cases of

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    This work was supported in part by National Institutes of Health Grant CA 73766.

    Conflict of interest: none.

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