The mean lung dose (MLD)

Abstract

Aim

The purpose of this work was to prove the validity of the mean lung dose (MLD), widely used in clinical practice to estimate the lung toxicity of a treatment plan, by reevaluating experimental data from mini pigs.

Materials and methods

A total of 43 mini pigs were irradiated in one of four dose groups (25, 29, 33, and 37 Gy). Two regimens were applied: homogeneous irradiation of the right lung or partial irradiation of both lungs—including parts with lower dose—but with similar mean lung doses. The animals were treated with five fractions with a linear accelerator applying a CT-based treatment plan. The clinical lung reaction (breathing frequency) and morphological changes in CT scans were examined frequently during the 48 weeks after irradiation.

Results

A clear dose–effect relationship was found for both regimens of the trial. However, a straightforward relationship between the MLD and the relative number of responders with respect to different grades of increased breathing frequency for both regimens was not found. A morphologically based parameter NTCP_lung was found to be more suitable for this purpose. The dependence of this parameter on the MLD is markedly different for the two regimens.

Conclusion

In clinical practice, the MLD can be used to predict lung toxicity of a treatment plan, except for dose values that could lead to severe side effects. In the latter mentioned case, limitations to the predictive value of the MLD are possible. Such severe developments of a radiation-induced pneumopathy are better predicted by the NTCP_lung formalism. The predictive advantage of this parameter compared to the MLD seems to remain in the evaluation and comparison of widely differing dose distributions, like in the investigated trial.

Zusammenfassung

Zielsetzung

Es soll unter Reevaluation von Tierversuchsdaten am Minischwein geprüft werden, ob die in der klinischen Praxis zur Beurteilung der Lungentoxizität eines Bestrahlungsregims regelhaft verwendete mittlere Lungendosis (MLD) eine zuverlässige Voraussage der Lungenbelastung erlaubt.

Material und Methoden

Insgesamt 43 Minischweine wurden in vier Dosisgruppen (25, 29, 33 und 37 Gy) entweder mit einer homogenen Bestrahlung der gesamten rechten Lunge oder mit einer Teillungenbestrahlung (jeweils Anteile beider Lungen auch mit niedrigerer Dosis) mit vergleichbarer MLD nach CT-gestützter Bestrahlungsplanung am Linearbeschleuniger in fünf Fraktionen bestrahlt. Die Tiere wurden 48 Wochen nachbeobachtet und in regelmäßigen Abständen sowohl hinsichtlich ihrer klinischen Lungenreaktion (Atemfrequenzerhöhung) als auch der im CT nachweisbaren bildmorphologischen Veränderungen kontrolliert.

Ergebnisse

Es besteht eine klare Dosis-Effekt-Beziehung in beiden Versuchsarmen. Allerdings zeigte sich kein eindeutiger Zusammenhang zwischen der MLD und dem relativen Response hinsichtlich verschiedener Grade der Atemfrequenzerhöhung für beide Versuchsarme. Hierfür scheint ein morphologisch basierter Parameter NTCP_lung besser geeignet zu sein. Der Verlauf dieses Parameters in Abhängigkeit der MLD unterscheidet sich deutlich für beide Versuchsarme.

Schlussfolgerung

Die MLD kann in der klinischen Praxis für die Vorhersage der Lungentoxizität eines Bestrahlungsregims genutzt werden, sofern in Abhängigkeit von der zu applizierenden Dosis nicht mit einer schwereren Nebenwirkung gerechnet wird. Sind jedoch schwerere Lungenreaktionen zu erwarten, so sind Einschränkungen hinsichtlich der Vorhersage der Lungentoxizität mittels MLD möglich. Schwere Radiopneumonitisverläufe werden besser durch einen NTCP_lung-Wert beschrieben. Dieser Vorteil scheint auch bei der Bewertung und dem Vergleich stark differierender Dosisverteilungen, wie im vorliegenden Versuch, erhalten zu bleiben.

Appendices

Appendix

A: Modeling of the dependence of NTCP_lung on the MLD for the investigated trial

Accordingly to the beam arrangements of chapter 2 the MLD for a prescribed dose value D for the regimen A is in principle given by

$$ {\rm{ML}}{{\rm{D}}_A}(D)\, = \,{\rm{D*}}{{\rm{V}}_r}{\rm{/}}{{\rm{V}}_{{\rm{lung}}}} $$

(A1)

with V_r: volume of the right lung,

V_lung: volume of the whole lung, V_lung = V_r + V_l with V_l: volume of the left lung.

For the regimen B, the MLD can be expressed by the equation

$$ {\rm{ML}}{{\rm{D}}_B}(D)\, = \,({\rm{D*}}{{\rm{V}}_r}{\rm{/2}}\, + \,{\rm{D/2*}}({V_r}{\rm{/2}}\, + \,{V_l}{\rm{/n}})){\rm{/}}{{\rm{V}}_{{\rm{lung}}}} $$

(A2)

with 1/n: irradiated part of the left lung.

For an animal of regimen A, equation (1) leads to the relation

$$ {\rm{NTC}}{{\rm{P}}_{{\rm{lung,A}}}}(D)\, = \,W(D){\rm{*}}{{\rm{V}}_r}{\rm{/}}{{\rm{V}}_{{\rm{lung}}}} $$

(A3)

For regimen B, the equation (1) is simplified to

$$ {\rm{NTC}}{{\rm{P}}_{{\rm{lung,B}}}}(D)\, = \,(W(D){\rm{*}}{{\rm{V}}_r}{\rm{/2}}\, + \,W({\rm{D/2}}){\rm{*}}({V_r}{\rm{/2}}\, + \,{V_l}{\rm{/n}})){\rm{/}}{{\rm{V}}_{{\rm{lung}}}} $$

(A4)

Although the condition of equal values of the MLD for both regimens was not completely achievable, like stated in the Materials and methods section, the validity of this condition will be used for the following simplified modeling. It should be noted that this modeling is limited to the investigated doses and volumes in the regimens. The condition of equal values of the MLD(D) for equal values of the prescribed dose D for both regimens A and B leads to the following equation (by equating equations (A1) and (A2)):

$$ {\rm{V}}_{\rm{r}} = {\rm{V}}_{\rm{r}}/2 + ({\rm{r}}_{\rm{V}}/2 + {\rm{V}}_{\rm{l}}/{\rm{n}})/2 $$

(A5)

Thus, from Eq.  (A5) one gets for the value n the expression

$$ {\rm{n}}\, = \,2{\rm{*}}{{\rm{V}}_{\rm{l}}}/{\rm{}}{{\rm{V}}_{\rm{r}}} $$

(A6)

Introducing this expression for n into Eq.  (A4) simplifies the formula of NTCP_{lung, B} as follows:

$$ {\rm{NTC}}{{\rm{P}}_{{\rm{lung,B}}}}(D)\, = \,{V_r}{\rm{/}}{{\rm{V}}_{{\rm{lung}}}}*(W(D){\rm{/2}}\, + \,W({\rm{D/2}})) $$

(A7)

Now, one obtains a relation between NTCP_lung and the MLD(D) by applying the condition of equal values of the MLD(D) for both regimens. So Eq.  (A1) leads to

$$ {V_r}{\rm{/}}{{\rm{V}}_{{\rm{lung}}}}\, = \,{\rm{MLD}}(D){\rm{/D}} $$

(A8)

and with this expression substituting V_r/ V_lung in equations (A3) and (A7), the following equations for NTCP_lung are obtained:

$$ {\rm{NTC}}{{\rm{P}}_{{\rm{lung,A}}}}({\rm{MLD}}(D))\, = \,{\rm{MLD}}(D){\rm{/D*W}}(D) $$

(A9)

$$ {\rm{NTC}}{{\rm{P}}_{{\rm{lung,B}}}}({\rm{MLD}}(D))\, = \,{\rm{MLD}}(D){\rm{/D*}}(W(D){\rm{/2}}\, + \,W({\rm{D/2}})) $$

(A10)

For the same value of MLD(D), the values of NTCP_lung for both regimens will only become equal under the condition that

$$ {\rm{W}}({\rm{D}})/{\rm{}}2\, = \,{\rm{W}}({\rm{D}}/{\rm{}}2) $$

(A11)

For a more quantitative modeling, the dependence of W(D) accordingly to Table 3 is approximated by a polynom of grade 3 (for 14Gy < D < 38Gy)

$$ {\rm{W}}\left( {\rm{D}} \right)\, = \, - 0.00005{\rm{*}}{{\rm{D}}^3}\, + \,0.0036{\rm{*}}{{\rm{D}}^{2}}-0.0402{\rm{*D}}\, + \,0.003 $$

(A12)

Table 3 Probability W for the induction of a morphological lung complication dependent on dose D based on the dose–response curve of the CT investigations (Fig. 2). The half dose values were applied in the cranial part of the right lung and the caudal part of the left lung of the animals of the regime B

Using this expression for W(D) in equations (A9) and (A10) and the matching pairs of values of D and MLD_mean(D) from Table 1 leads to the results of Fig. 5a. These results are quite similar to the behavior of the individual relations of NTCP_lung dependent on MLD for both regimens shown in Fig. 4, thereby supporting the clearly different but approximately parallel directions of the graphs for both regimens in this figure. To obtain an estimation of the behavior of the NTCP_lung beyond the investigated dose range, the D–MLD_mean pairs of Table 1 are extended towards lower and higher doses. D is decreased to 10 Gy and increased to 45 Gy. The matching value of MLD_mean is estimated as 0.58 * D, the average ratio one gets from Table 1. According to Eq.  (A1) this ratio describes the mean value of the ratio of V_r/ V_lung of all animals in the trial. Repeating the NTCP_lung calculations with this extended dose range leads to the results presented in Fig. 5b. Here one detects the fundamental sigmoidal character of the NTCP_lung graphs with the linear part in the investigated dose range of the trial. The graph for regimen A will reach a maximum value of 0.58 if the alone irradiated right lung has a probability W equal to 1 (maximum complication), which refers to Eq. (A3) with the above mentioned ratio of V_r/ V_lung. The graph for regimen B will further increase with MLD_mean, but for this range the approximation of Eq.  (A12) is not valid. Even so, one will expect that the NTCP_lung graph of regimen B in Fig. 5b will reach and intersect the NTCP_lung graph of regimen A at its plateau value of 0.58. Thus, Fig. 5b indicates that—beyond the part of the linear and nearly parallel behavior with the strong separation of both graphs—dose regions exist where both graphs are approaching: for MLD_mean < 10 Gy and MLD_mean of about 30 Gy. These are the dose regions where condition (A11) is fulfilled, here the NTCP_lung is either near to zero or very high.

Fig. 5

a Modeling: Dependence of NTCP_lung on MLD for both regimens of the trial and for the applied range of the MLD (characterized by a linear behavior). The functions of the linear regressions and the RSQ function (R ², Excel) are also given. b Modeling: Dependence of NTCP_lung on MLD for both regimens of the trial and for an extended range of the MLD

Fig. 6

Relative isodoses in a coronal plane for an animal of regimen A

Fig. 7

Relative isodoses in a coronal plane for an animal of regimen B

B: Extension of this model to a clinical fractionation pattern

Conventional curative irradiation of a lung tumor could be done by applying 33 fractions with 2 Gy per fraction to a dose reference point in the target. The overall value of the MLD in this case will commonly be limited to a maximum value of about 20 Gy what is equal to a MLD per fraction of about 0.6 Gy. To compare the fractionation pattern of the investigated trial with this clinical case the prescribed doses D of the trial are transformed to overall doses D_0.6Gy(D) that will result in the same response to the lung like the dose D, given in five fractions, but with a dose per fraction of 0.6 Gy. This transformation is done using the well-established linear-quadratic (LQ) model [8] with a value of α/ β = 3Gy. Table 4 shows this values D_0.6Gy(D), further the value of D/2 and additionally the probabilities W(D)/2 and W(D/2) according to condition (A11), presenting very different values for both probabilities. To characterize the mentioned curative lung tumor irradiation, the value of D_0.6Gy(D) = 19 Gy is used in Table 4. This clinical dose constraint corresponds in the used model to a prescribed dose D = 12.5 Gy, given in five fractions. This dose value is much lower than the applied doses D in the trial. For this pair of doses D_0,6Gy(D) = 19 Gy and D = 12.5 Gy the probability values W of both regimens of the trial in Table 4 are equal to zero, thereby indicating that there is no difference between the NTCP_lung values for the two regimens but also showing that for this dose no complication will expected in the used score (see Table 3).

Table 4 Equivalent overall doses D_0.6Gy (based on 0.6 Gy per fraction), which result in the same lung response like the prescribed doses D (given in five fractions). The values of D_0.6Gy(D) are calculated using the LQ-model with an α/β of 3 Gy. For the evaluation of the condition (A11) two different probabilities W for the induction of a lung complication are calculated, using the approximation (A12). The values that were used in the trial are shown in the cells with normal print. The cells printed in bold contain the values for the curative fractionation pattern, what is explained in the part B of the appendix