MEDICAL PHYSICS CLINICAL APPLICATION OF LINEAR-QUADRATIC MODEL IN REIRRADIATION OF SYMPTOMATIC BONE METASTASES L. REBEGEA 1,2, M. DUMITRU 1, D. FIRESCU 2,3 1 Sf. Ap. Andrei Emergency Clinical Hospital, Galati, Radiotherapy Department, 2 Dunarea de Jos University of Galati, Faculty of Medicine, Clinic Department, 3 Sf. Ap. Andrei Emergency Clinical Hospital, Galati, Surgical Clinic II Corresponding author: Laura Florentina Rebegea E-mail: laura_rebegea@yahoo.com Received December 12, 2013 Radiotherapy is an important and one of the most effective curative and palliative modality of cancer treatment. Symptomatic bone metastases (M1OSS) represent an important problem in oncology. External beam radiotherapy (EBRT) is effective in palliating pain from bone metastases, being rapid treatment without major toxicities. There are many fractionation schemas and a certain percent of patients requires reirradiation. The question arises which treatment schema is more efficient, knowing the equivalence of the three fractionation schemas: TD = 8 Gy/1fraction/1day, TD = 20Gy/5 fractions/5days, dose / fraction = 4Gy and TD = 30Gy/10 fractions, dose/fraction = 3Gy. In order to formulate equivalent fractionation schemes, to get information on acute and late responses and also to calculate additional doses after breaks from radiotherapy, for changing of total time of treatment and for reirradiation cases, the linear quadratic model (LQ) is used. Key words: bone metastases, external beam radiotherapy, reirradiation and linearquadratic model. 1. INTRODUCTION Bone metastases (M1OSS) represent an important oncology problem which can have numerous and debilitating severe effects upon patient including pain, spinal cord compression, hypercalcaemia, pathologic bone fracture [1]. The treatment of bone metastases is a multidisciplinary approach and involves radiologists, radiotherapists, oncologists, surgeons, pain medicine and palliative medicine specialists [1]. External beam radiotherapy (EBRT) reduces the pain symptomatology with partial response in 50 80% and complete response in one third of cases, reducing the risk of spinal cord compression development. There are many fractionation schemas and a certain percent of patients requires reirradiation. The main principles for Rom. Journ. Phys., Vol. 59, Nos. 7 8, P. 785 791, Bucharest, 2014
786 L. Rebegea, M. Dumitru, D. Firescu 2 choosing one or other therapeutic schema include the prognostic factor, risk of spinal cord compression development, radiobiological particularities of irradiated tissues, performance status and the association of visceral secondary lesions. The effects of ionising radiation on the various tissues vary considerably, both in terms of the radiation dose required to produce damage and in the timing of the expression of damage. There are two categories of tissues: early-responding tissues and late-responding tissues. Skin, oral mucosa, intestines, bone marrow, and testis are early-responding tissues and show the effects of radiation damage within a period of days to weeks from irradiation. Lung, kidney, and spinal cord are lateresponding tissues and show their response to radiation damage over months to years after exposure. The damage of early-responding tissues can be healed; the side-effects to the late-responding tissues might be more permanent. The possibility of irreversible late reactions occurring is the main limiting factor on treatment and determine the maximum radiation dose that can be given. Spinal cord is a very low rate of cell turnover tissue and damages are manifested many months to years after treatment. The late-effects may be neurological that eventually may be resolved, in less severe cases, but above a critical dose, the most damaging late effects to the spinal cord, necrosis or permanent radiation myelopathy manifested as paralysis, can occur. The linear quadratic model (LQ) was developed by Douglas and Fowler in 1972 [2], it was assumed that cell death due to ionizing radiation has two components: linear component (αd), directly proportional to dose, D, characterized by linear coefficient, α, corresponding to the cells that cannot repair themselves after one radiation hit and it is important for high-let radiation and quadratic component (βd 2 ) directly proportional to the square of dose characterized by the quadratic coefficient, corresponding to cells that stop dividing after more than one radiation hit, but can repair the damage caused by the radiation and it is important for low-let radiation. The linear coefficient, α indicates the intrinsic cell radiosensitivity, and it is the natural logarithm (log e) of the proportion of cells that die or will die due to their incapacity to repair radiation-induced damage of ionizing radiation. The quadratic coefficient, β shows cell repair mechanisms, and it is the natural logarithm of the proportion of repairable cells due to their ability to repair the radiation-induced effect of ionizing radiation. In order to formulate equivalent fractionation schemes, to get information on acute and late responses and also to calculate additional doses after breaks from radiotherapy the LQ model is used. The early and late-responding tissues distinction is very important as a result of the recognition that time dose relationships are systematically different between them. The α/β ratio is dose for which the number of acutely responding cell deaths is equal to the number of late-responding cell deaths (the dose for which the linear and quadratic components of cell death are equal). For tumors and acute effects
3 Clinical application of linear-quadratic model 787 response in normal tissues, the mean α/β ratio is 10Gy [range 7 20 Gy]. For late effects in normal tissues, α/β ratio range from 0.5 to 6 Gy [3]; the α/β ratio is not constant, may differ among tumor types and its value should be carefully chosen [3]. 2. MATERIAL AND METHOD Our retrospective study analyzed 56 bone metastases patients who performed reirradiation on secondary bone lesions, between 1 st January 2000 and 31 st December 2012 in Sf. Ap. Andrei Emergency Clinical Hospital, Galati, Radiotherapy and Oncology Department. The following parameters were analyzed: histological type, site of primary tumor, systemic disease, the retreated site bone metastases, fractionation schemas used at the first and second irradiation, pain control, and time interval of reirradiation (table 1). EBRT was performed of Rokus M 40 and Theratron Elite 100 radiotherapy units, in isocentric technique, using direct fields for spine M1OSS and parallelopposed fields pelvic and long bones M1OSS. In cases of inferior lumbar spine, lumbosacral or pelvis irradiation, inevitably, a certain volume of gastrointestinal tract was included in treated volume. In order to prevent the adverse effects (nausea, vomiting and diarrhoea) we utilized personalized lead blocks and we administrated adequate antiemetic drugs. In our lot we did not find pathological bone fractures and 3 patients presented spinal cord compression syndrome (5.36%). All patients performed treatment with bisphosphonates zolendronic acid. Table 1 Clinical parameters Parameters Nr. patients (%) N = 56 Age (years) mean (range) Sex Feminine Masculine Medium of life Urban Rural Primary tumour site Breast Lung Prostate Multiple myeloma Non-Hodgkin lymphoma with big cells Colon M1OSS with unknown primary site 59.51 (21-78) 34 (60.71) 22 (39.29) 40 (71.43) 16 (28.57) 34 (60.71) 5 (8.93) 12 (21.43) 1 (1.79) 2 (3.57) 1 (1.79) 1 (1.79)
788 L. Rebegea, M. Dumitru, D. Firescu 4 Table 1 (continued) Bone metastases site Spine Thoracic Lumbar Sacral Pelvis Femur Tibia Systemic disease M1Oss multiple M1Oss+PUL M1Oss+M1HEP M1Oss+M1Lym supra-clavicle 44 (78.57) 21 (37.5) 15 (26.79) 8 (14.29) 3 (5.36) 7 (12.5) 2 (3.57) 44 (78.57) 8 (14.29) 18 (32.14) 2 (3.57) 2.1. STATISTICAL ANALYSIS Statistical analysis was done by XLSTAT Software. Chi-square and independent samples t-tests were used for comparison between the patient groups. Mann Whitney test was done for independent samples to compare the time of retreatment. 3. RESULTS External beam radiotherapy was performed for pain control. From 56 patients, 53 (94.64%) performed reirradiation one the same bone site and 3 patients (5.36%) performed EBRT on two different bone segments. Complete and partial response achieved 30% and respective 60% of cases; the last category of patients received analgesic medication. Patients with low performance status (10.71% of cases) performed palliative single fractioned radiotherapy, TD = 8Gy/1fr./1day, D/fr. = 8Gy; these patients required reirradiation at shorter time range, 3 months, without statically significance, comparative with patients receiving multiple treatment fractions, TD = 20Gy/5fr/5 days, with reirradiation time of 22 months, p = 0.17 and TD = 30Gy/10fr.D/fr. = 3Gy, with reirradiation time of 18 months, p = 0.28 (table 2). We did not finned gastrointestinal toxicities in our lot and the skin fibrosis occurred in 70% of cases. In 5 cases (8.93%) was necessary the second reirradiation. In 4 of 5 cases, the primary tumour was prostate cancer and in 1 of 5 cases, the primary tumour was the multiple myeloma (table 3). Fractionation schemas administrated at the second reirradiation was stated conforming to linear-quadratic model (LQ), taking into consideration the following parameters: normal tissues tolerance, specially the spinal cord radiation tolerance, time of reirradiation, repairing cell time, α/β ratio for each tissue, patient s performance status, systemic disease and life expectancy.
5 Clinical application of linear-quadratic model 789 Table 2 Fractionation schemas performed at first irradiation, la reirradiation and the time of retreatment No. patients (%) N=56 TD initial (Gy) 6 (10.71) TD = 8Gy/1fr. D/fr. = 8Gy 41(73.21) TD = 20Gy/5fr, D/fr. = 4Gy 9 (16.07) TD = 30Gy/10fr, D/fr. = 3Gy Mean time in months of reirradiation [range] TD reirradiation (Gy) 3 [2 6 ] TD = 8Gy/1fr./1zi D/fr. = 8Gy 22 [2 85] TD = 20Gy/5fr; D/fr. = 4Gy 18 [1 41] TD = 20-24Gy/ 5-12fr, D/fr. = 2-4Gy Table 3 Fractionation schemas performed at first and the second reirradiation and the time between them Primary tumour site/ irradiated bone site sacroiliac+l5 Multiple myeloma / thoracic spine sacroiliac+l5 Fractionation schemas at first reirradiation TD = 16Gy/8fr; D/fr. = 2Gy α/β = 2Gy, BED = 32Gy TD = 10Gy/5fr; D/fr. = 2Gy α/β = 2Gy, BED = 20Gy TD = 27Gy/9fr; D/fr. = 3Gy α/β = 2Gy, BED = 67.5Gy Mean time of reirradiation [months] p 0.17 0.28 Fractionation schemas at second reirradiation 18 TD = 16Gy/4fr; D/fr = 4Gy α/β = 2Gy, BED = 48Gy 25 TD = 10Gy/5fr D/fr. = 2Gy α/β = 2Gy, BED = 20Gy 27 TD = 24Gy/8fr; D/fr. = 3Gy α/β = 2Gy, BED = 60Gy sacroiliac sacroiliac TD = 20Gy/5fr; D/fr = 4Gy, α/β = 3.5Gy, BED = 43Gy TD = 21Gy/7fr.; D/fr = 3Gy α/β = 3.5Gy, BED = 39Gy 28 TD = 4Gy/1fr.; D/fr. = 4Gy α/β = 3.5Gy, BED = 9Gy 7 TD = 10Gy/5fr D/fr. = 2Gy α/β = 3.5Gy, BED = 16Gy In order to evaluate and to avoid the possible radiation damages of the spinal cord, we estimated the biological effective dose (BED) for each reirradiation case, conforming to the formulae (1) and (1.1). BED is a measure of the effect of a fractionated or continuous radiotherapy; having the units of dose, it is expressed in grays (Gy) [2, 3]. BED d = n d 1 + α / β (1)
790 L. Rebegea, M. Dumitru, D. Firescu 6 n d = TD (1.1) where, n = fraction number d = fraction dose BED = biological effective dose TD = total dose α/β = the value of α/β ratio for each concerning tissue; We chose α/β for spinal cord, 2Gy and α/β for skin = 3.5Gy [3]. 4. DISCUSSIONS AND CONCLUSIONS Repeating EBRT rate after single fractioned treatment is 20% comparative with multifractioned EBRT, where the reirradiation percent reach up to 8% [4]. ASTRO recommends that any time is possible, we have to take into consideration the disease condition, spinal cord compression risk, adverse effects, late toxicities, characteristics and performances of radiotherapy units (IMRT < thomotherapy < stereotactic radiotherapy), neurosurgical opportunity (vertebroplasty), bisphosphonates use [5]. Randomized trials evidenced that all fractionation schemas reached an excellent pain control with minimal adverse effects. The longer course of treatment, with TD = 30Gy/10 fractions, has the advantage in pain relief, decreased risk of pain recurrence, or a decrease in the risk of pathologic fracture (i.e. a fracture caused by the tumor); but single-fraction EBRT is logistically much easier accepted by the patient, their families, for health service (with higher cost/benefit ratio comparative with other prolong fractionation schemas), having also the advantage of reduced hospitalization [6, 7]. These advantages are most applicable if the shorter course of treatment is as effective as the longer course of treatment [6]. Randomized trials from different areas in the world have demonstrated that single-fraction radiation therapy is sufficient to achieve palliation of painful bone metastases with optimized convenience for both caregivers and patients. A single dose of 8 Gy/1fr. is consider the standard treatment, however, patients receiving short-course radiotherapy may receive remarkably more re-irradiations [8]. The most recent studies report a great variety of fractionation schemas used in palliative bone metastases radiotherapy: single fractioned EBRT: TD = 8Gy/1fr./1day, D/fr. = 8Gy or multiple fractioned EBRT: TD = 20Gy/5fr, D/fr = 4Gy; TD = 24Gy/6fr. D/fr. = 4Gy, TD = 30Gy/10fr, D/fr = 3Gy, in different clinical scenarios. The main criteria which influence the choosing of one or other therapeutically schemas include the prognostic factor, spinal cord compression occurring, performance status, secondary visceral lesions association [9]. The speciality literature did not identify any protocol for reirradiation and were administrated different treatment schemas in single or multiple dose fractionations
7 Clinical application of linear-quadratic model 791 [9]. Patients who did not initial respond to treatment can perform reirradiation. Even that, reirradiation is less frequent, probably due to the late toxicities [10]. From radiobiological point of view, single-fraction EBRT, TD = 8Gy/1fr./1 day, D/fr. = 8Gy is equivalent with multiple-fraction EBRT, TD = 20Gy/5fr; D/fr. = 4Gy; TD = 30Gy/10fr, D/fr. = 3Gy, for α/β ratio of Gy [11]. In clinical practice, the radiotherapeutic management of patients with locoregional recurrence in an anatomical site that necessitates re-irradiation of a tissue or organ which is previously treated is a specific problem [2]. The clinical assessment of the re-irradiation tolerance must to include some clinical aspects: life expectancy of the patient respect of latent period of late side-effects and the prospect for long-term benefit from the re-treatment. The BED formulae provide a convenient and simple modality of calculating isoeffective irradiation schemas [2]. Our study confirms the importance of radiobiological information into clinical practice especially in the management of the re-irradiation cases. In our study, single fraction radiotherapy proved efficiency, the therapeutically response occurring after second irradiation, aspect confirmed by speciality literature 60% of reirradiated patients achieved pain control after single-fractioned retreatment. REFERENCES 1. A. G. Horvat, V. Kovač, P. Strojan, Radiotherapy in palliative treatment of painful bone metastases, Radiol Oncol. 43(4), 213 224 (2009). 2. S. M. Beyzadeoglu, G. Ozyigit, C. Ebruli, Basic Radiation Oncology, Springer-Verlag Berlin Heidelberg 2010, pp. 145 173. 3. G.G. Steel, Basic Clinical Radiobiology 3 rd Edition, Arnold, London 2002, pp. 105 157. 4. Bone Pain Trial Working Party, 8 Gy single fraction radiotherapy for the treatment of metastatic skeletal pain: randomised comparison with a multifraction schedule over 12 months of patient follow-up, Radiother Oncol., 52, 111 21 (1999). 5. S. Lutz, L. Berk, E. Chang, et al., Palliative Radiotherapy for Bone metastases: an ASTRO evidence-based guideline, Int J Radiat Oncol Biol Phys., 79, 965 976 (2011). 6. W.F. Hartsell, C. Scott, D.W. Bruner, et al., Randomized trial of short- versus long-course radiotherapy for palliation of painful bone metastases, J Natl Cancer Inst., 97, 798 804 (2005). 7. E. Steenland, J.W. Leer, H. van Houwelingen, et al., The effect of a single fraction compared to multiple fractions on painful bone metastases: a global analysis of the Dutch Bone Metastasis Study, Radiother Oncol., 52,101 109 (1999). 8. Yu-jia Zhu, Palliative radiotherapy for painful bone metastases: Short-course or long-course? Ann Palliat Med. 1(1), 78 80 (2012). 9. A. Fairchild, E. Barnes, S. Ghosh, et al., International patterns of practice in palliative radiotherapy for painful bone metastases: Evidence-based practice? Int J Radiat Oncol Biol Phys., 75, 1281 628 (2009). 10. N.P. Mithal, P.R. Needhan, P.J. Hoskin, Re-treatment wiht radiotherapy for painfull bone metastases, Int J Radiat Oncol Biol Phys., 29, 1011 1014 (1994). 11. B. Jeremic, Y. Shibamoto, L.J. Acimovic, et al., A randomized trial of three single-dose radiation therapy regimens in the tratment of metastetic bone pain, Int J Radiat Oncol Biol Phys., 42, 161 167 (1998).