Treatment Planning. G. Battistoni INFN Milano

Transcription

1 Treatment Planning G. Battistoni INFN Milano

2 The treatment planning process Individual patient Radiotherapy treatment units Patient data: CT scan, outlines Beam data: radiation quality, PDD, profiles,... Localization of tumor and critical structures Optimization of source or beam placement Simulation Dose calculation Preparation of treatment sheet and record and verify data

3 About the patient: Target location Target volume and shape Secondary targets - potential tumor spread Location of critical structures Volume and shape of critical structures Radiobiology of structures 3

4 About the machine: Beam description (quality, energy) Beam geometry (isocentre, gantry, table) Field definition (source collimator distance, applicators, collimators, blocks, MLC) Physical beam modifiers (wedges, compensator) Dynamic beam modifiers (dynamic wedge, arcs, MLC IMRT) Normalization of dose 4

5 Treatment Planning in hadrontherapy (Effective) Dose Optimization Imaging: Electron density CT scan and/or PET-CT) Treatment Planning Nuclear Physics: System Dose vs Depth hadrone/nucleus scattering: fragments etc. Radiotherapist: identification of Target Volume and of Organs at Risk Radiobiology: RBE parameters OER (not yet ) Intensity, position and energies to be delivered to patient

6 Input: Inverse planning per scansione attiva Hounsfield numbers (dalla CT) dei voxels in cui è suddiviso l intero volume anatomico Identificazione da parte del clinico del volume da trattare e la dose da somministrare e degli organ-at-risk (OAR) e la dose massima Si può scrivere la funzione-costo da minimizzare e come esempio si può usare la seguente: Χ 2 = i m T b 2 b [ Di DT ] + [ Di DOAR i OAR ove la somma si esegue su tutti i voxels di interesse ( m T e OAR) e D i b rappresenta la dose biologica fornita al voxel i-esimo ] 2

7 Esempio 1-D Parecchi fasci contribuiscono su un medesimo voxel: da fasci che arrivano dal medesimo campo di irraggiamento da differenti campi

8 Per cui la funzione-costo si riscrive come: Χ 2 = cond i V l [ RBEi ( di fl ) DT d i l è la dose fisica unitaria rilasciata dal fascio l-esimo sul voxel i- esimo f l è la fluenza (da determinare) del fascio l-esimo l RBE i è il relative biological effectiveness sul voxel i-esimo mediato su tutti i fasci che rilasciano dose sul voxel i-esimo ] 2

9 2 2 ] [ T cond V i i S S = Χ Si può riscrivere la funzione-costo in termini di sopravvivenza piuttosto che di dose: ove S i rappresenta la sopravvivenza dello i-esimo voxel mediata su tutti i fasci che rilasciano dose sul medesimo voxel. Assumendo: relazione fra sopravvivenza e dose del tipo lineare-quadratica: ) exp( 2 D D S β α = le seguenti relazioni per mediare a e b sui campi misti = l l l i l l l i l i i f d f d α α = l l l i l l l i l i i f d f d β β

10 Passando al ln la funzione da minimizzare è: ] ) ( [ T X T X l l i l i cond V i l l l i i D D f d f d + = Χ β α β α fluenze: incognite da determinare dose unitaria rilasciata nel voxel i-esimo radiobiologia radiobiologia dei raggi X per la linea cellulare

11 GSI treatment planning package TRiP98

12 Water Equivalent Path Lenght (WEPL) Approximation Conventional one-dimensional scaling of pencil beam If the two ionization potentials are nearly the same z m : depth in the medium z w : depth water. z m can be expressed using the Water Equivalent Path Length approach: If the ratio of stopping power between water and the medium S w m z w is assumed to be independent of the proton energy one easily derives the scaling relation: This 1D path length scaling, is transferred to the lateral fluence L m (r,z,e 0 ) accounting for multiple Coulomb scattering:

13 Treatment Planning System TPS is directly related to scanning modality and RBE evaluation model Need to include management of moving organs and integration of in-room imaging (TPS used at CNAO)

14 Syngo TPS calculation (HIT) Thanks to A. Mairani A cube 3x3x3 cm 3 in water starting at a depth of 7 cm

15 protons Beam spacing ΔX, ΔY is 3 mm, ΔZ is 2 mm 15 slices (energies) from to MeV 121 beams/slice Total no. of particles: E+09 Last slice ( MeV) at ~10 cm of depth: σ x,y = 1.37 cm at isocenter E+09 total particles, E+07 particles/beam (1.2780e+08 particles in 0.3 cm x 1 cm 2 ) First slice (97.53 MeV) at ~7 cm of depth: σ x,y = 1.61 cm at isocenter E+08 total particles, 1.412E+06 particles/beam (1.0807e+07 particles in 0.3 cm x 1 cm 2 )

16 protons No. of Particles Particles vs Slice Slice Numb.

17 12 C Beam spacing ΔX, ΔY is 2 mm, ΔZ is 2 mm 14 slices (energies) from to MeV/u 225 beams/slice Total no. of particles: E+08 Last slice ( MeV/u) at ~10 cm of depth: σ x,y = 0.64 cm at isocenter E+07 total particles, E+05 particles/beam (8.345E+06 particles in 0.2 cm x 1 cm 2 ) First slice ( MeV) at ~7 cm of depth: σ x,y = 0.69 cm at isocenter E+06 total particles, E+04 particles/beam (8.07E+05 particles in 0.2 cm x 1 cm 2 )

18 12 C No. of Particles Particles vs Slice Slice Numb.

19 Un esempio di calcolo su un vero caso paziente The complete plan is composed by 2 opposed fields, 12 C. Dose prescription as calculated by Syngo TPS Beam1 = particles Beam2 = particles

20 Energy Slice [n] Nominal Beam Spots per Energy [MeV/u] Slice [n]: Treatment Description: Beam 1 Energy Nominal Beam Spots per Slice [n] Energy [MeV/u] Slice [n]: Total no. of spots: 4542

21 Gross tumor volume or GTV Clinical target volume or CTV Planning target volume or PTV Organ at risk or OAR

22 The GTV is the gross demonstrable extent and location of the tumor. The CTV is a volume of tissue that contains a demonstrable GTV and/or subclinical malignant disease with a certain probability of occurrence considered relevant for therapy. The PTV is a geometrical concept introduced for treatment planning and evaluation. It is the recommended tool to shape absorbed-dose distributions to ensure that the prescribed absorbed dose will actually be delivered to all parts of the CTV with a clinically acceptable probability, despite geometrical uncertainties such as organ motion and setup variations. The OAR or critical normal structures are tissues that if irradiated could suffer significant morbidity and thus might influence the treatment planning and/or the absorbed-dose prescription.

23 Target delineation ICRU 50 & 62 Gross Tumor Volume (GTV) = clinically demonstrated tumor Clinical Target Volume = GTV + area at risk (eg. potentially involved lymph nodes) 23

24 Need to keep in mind Always a 3D problem Different organs may respond differently to different dose patterns. Question: Is a bit of dose to all the organ better than a high dose to a small part of the organ? 24

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26 the correct dose to the correct volume Volume (%) Critical organ Comparison of three different treatment techniques (red, blue and green) in terms of dose to the target and a critical structure Target dose Dose (Gy) Dose Volume Histograms are a way to summarize this information

27 The ideal DVH Tumor: High dose to all Homogenous dose Critical organ Low dose to most of the structure 100% 100% dose dose 27

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29 TCP modelling TCP = long-term local control ~ sigmoidal D50 = local control dose for 50% of cases (also called TDC50) γ50 proportional to slope od TCP vs Dose calculated at D50 γ 50 = D dtcp dd D=D50 Example: TCP curve for D50 = 60 Gy, γ50 = 1.5 For standard fractioning: D50 : 20 Gy to 100 Gy γ50: 1-4 Gy

30 TCP Poisson Model Hyp: Only clonogenic cells can regrow the tumor N = number of clonogenes; SF(D) = fraction of clonogens surviving at dose D TCP ~e N SF(D) TCP ~e N SF 2D/2 TCP ~e N e αd { 1+d/ α } β LQ D50 ~ γ 50~ Log2 2 2 Log Log2 N Log SF2 ( ) Log N Log2

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33 Problemi Soft tissue cell density ~ 10 9 cells/cc Detectable tumors 1 cc (100 cc tumors are common) if N ~ number of cells N 10 9 γ Observations: γ50 ~ 2 2 possibile solution (not utually excluive!!) 1. TCP is controlled by a few radioresistent clonoves 2. TCP is a population averge: (inter-tumor) different tumors have different radiosensitivity (intra-tumor) clonoges within a tumor vary in radiosensitivity

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36 Summary of radiation effects Target in radiotherapy is bulk tumour and confirmed and/ or suspected spread Need to know both effects on tumour and normal tissues Normal tissues need to be considered as a whole organ Radiation effects are complex - detailed discussion of radiation effects is beyond the scope of the course Models are used to reduce complexity and allow prediction of effects...

37 normal tissues Sparing of normal tissues is essential for good therapeutic outcome The radiobiology of normal tissues may be even more complex as the one of tumours: different organs respond differently there is a response of a cell organization not just of a single cell repair of damage is in general more important

38 Different tissue types Tissues may be considered to have functional subunits (FSU), where each subunit performs some of the function of that organ. Serial organs Parallel organs (e.g. lung) each FSU is critical for the function of other FSUs. Each FSU is critical for the function of other FSUs. These organs are considered serial, and include the spinal cord and gastrointestinal tract. each FSU performs its function relatively independently of the others. Such tissues are considered parallel, and examples include the lung, liver and kidney.

39 Different tissue types Effect of radiation on the organ is different Serial organs Parallel organs In these tissues, it is vital that radiation dosage dose not exceed tolerance at any point. For example, loss of one FSU of the spinal cord will lead to loss of all FSUs caudal to that point. In these tissues, the total volume irradiated is very important in determining the outcome. For example, the liver is capable of sustaining life even if half its volume is made nonfunctional by radiation.

40 Disclaimer Warning: the concept of serial and parallel arrangement of FSUs is not entirely correct, as many tissues have both serial and parallel components. For example, the lungs rely on the trachea and airways (serial arrangement) to function. The FSUs of the brain have both serial and parallel components. It is possible to lose part of the occipital cortex and still have vision, but if that part is the fovea then function will be critically impaired.

41 Dose Volume effects The more normal tissue is irradiated in parallel organs the greater the pain for the patient the more chance that a whole organ fails Rule of thumb - the greater the volume the smaller the dose should be In serial organs even a small volume irradiated beyond a threshold can lead to whole organ failure (e.g. spinal cord)

42 Equivalent Uniform Dose The concept of equivalent uniform dose (EUD) (Niemierko 1997) provides a single metric for reporting non-uniform tumor dose distributions. It is defined as the uniform dose that, if delivered over the same number of fractions as the nonuniform dose distribution of interest, yields the same radiobiological effect. Phenomenological formula referred to as the generalized EUD, or geud: geud = a v i D i v i is the fractional organ volume receiving a dose Di and a is a tissue-specific parameter that describes the volume effect. For a, geud approaches the minimum dose; thus negative values of a are used for tumors. For a +, geud approaches the maximum dose (serial organs). For a = 1, geud is equal to the arithmetic mean dose. For a = 0, geud is equal to the geometric mean dose. i geud is often used in plan evaluation and optimization because the same functional form can be applied to both targets and OARs with a single parameter capturing the dosimetric essence of the biological response. 1 a

43 Classification of radiation effects in normal tissues Early or acute reactions Skin reddening, erythema Nausea Vomiting Tiredness Occurs typically during course of RT or within 3 months Late reactions Telangectesia Spinal cord injury, paralysis Fibrosis Fistulas Occurs later than 6 months after irradiation 43

44 Classification of radiation effects in normal tissues Early or acute reactions Late reactions Late effects can be a result of severe early reactions: consequential radiation injury

45 Late effects Can occur many years after treatment Can be graded - lower grades more frequent

46 The Linear Quadratic Model Cell survival: single fraction: S = exp(-(αd + βd 2 )) (n fractions of size d: S = exp(- n (αd + βd 2 )) Biological effect: E = - ln S = αd + βd 2 E = n (αd + βd 2 ) = nd (α + βd) = D (α + βd)

47 Biological effectiveness E/α = BED = (1 + d / (α/β)) * D = RE * D BED = biologically effective dose, the dose which would be required for a certain effect at infinitesimally small dose rate (no beta kill) RE = relative effectiveness

48 BED useful to compare the effect of different fractionation schedules Need to know α/βratio of the tissues concerned. α/β typically lower for normal tissues than for tumour

49 The linear quadratic model Probability of cell survival cell kill (low α/β) cell kill (high α/β) Dose (Gy)

50 The linear quadratic model Probability of cell survival cell kill (low a/b) cell kill (high a/b) Beta determines curvature Alpha determines initial slope Dose (Gy)

51 Rule of thumb for α/β ratios Large α/β ratios α/β = 10 to 20 Early or acute reacting tissues Most tumours Small α/β ratio α/β = 2 Late reacting tissues, e.g. spinal cord potentially prostate cancer

52 The effect of fractionation Probability of cell survival cell kill (low a/b) cell kill (high a/b) fractionated (low a/b) fractionated (low a/b) Dose (Gy)

53 Fractionation Tends to spare late reacting normal tissues - the smaller the size of the fraction the more sparing for tissues with low α/β Prolongs treatment

54 A note of caution This is only a model Need to know the radiobiological data for patients Important assumptions: There is full repair between two fractions There is no proliferation of tumour cells - the overall treatment time does not play a role.

55 3. The 4 Rs of radiotherapy R Withers (1975) Reoxygenation Redistribution Repair Repopulation (or Regeneration)

56 Reoxygenation Oxygen is an important enhancement for radiation effects ( Oxygen Enhancement Ratio ) The tumour may be hypoxic (in particular in the center which may not be well supplied with blood) One must allow the tumour to re-oxygenate, which typically happens a couple of days after the first irradiation

57 Redistribution Cells have different radiation sensitivities in different parts of the cell cycle Highest radiation sensitivity is in early S and late G2/M phase of the cell cycle G2 M (mitosis) G1 S (synthesis) G1

58 Redistribution The distribution of cells in different phases of the cycle is normally not something which can be influenced - however, radiation itself introduces a block of cells in G2 phase which leads to a synchronization One must consider this when irradiating cells with breaks of few hours.

59 Repair All cells repair radiation damage This is part of normal damage repair in the DNA Repair is very effective because DNA is damaged significantly more due to normal other influences (e.g. temperature, chemicals) than due to radiation (factor 1000!) The half time for repair, t r, is of the order of minutes to hours

60 Repair It is essential to allow normal tissues to repair all repairable radiation damage prior to giving another fraction of radiation. This leads to a minimum interval between fractions of 6 hours Spinal cord seems to have a particularly slow repair - therefore, breaks between fractions should be at least 8 hours if spinal cord is irradiated.

61 Repopulation Cell population also grows during radiotherapy For tumour cells this repopulation partially counteracts the cell killing effect of radiotherapy The potential doubling time of tumours, T p (e.g. in head and neck tumours or cervix cancer) can be as short as 2 days - therefore one loses up to 1 Gy worth of cell killing when prolonging the course of radiotherapy

62 Repopulation The repopulation time of tumour cells appears to vary during radiotherapy - at the commencement it may be slow (e.g. due to hypoxia), however a certain time after the first fraction of radiotherapy (often termed the kick-off time, T k ) repopulation accelerates. Repopulation must be taken into account when protracting radiation e.g. due to scheduled (or unscheduled) breaks such as holidays.

63 RepopulationRegeneration Also normal tissue repopulate - this is an important mechanism to reduce acute side effects from e.g. the irradiation of skin or mucosa Radiation schedules must allow sufficient regeneration time for acutely reacting tissues.

64 The 4 Rs of radiotherapy: Influence on time between fractions, t, and overall treatment time, T Reoxygenation Redistribution Repair Repopulation (or Regeneration) Need minimum T Need minimum t Need minimum t for normal tissues Need to reduce T for tumour Cannot achieve all at once-optimization of schedule for individual circumstances

65 Time, dose and fractionation Need to optimize fractionation schedule for individual circumstances Parameters: Total dose Dose per fraction Time between fractions Total treatment time

66 Extension of LQ model to include time: E = - ln S = n * d (α + βd) - γt γ equals ln2/t p with T p the potential doubling time note that the γt term has the opposite sign to the α + βd term indicating tumour growth instead of cell kill

67 The potential doubling time the fastest time in which a tumour can double its volume depends on cell type and can be of the order of 2 days in fast growing tumours can be measured in cell biology experiments requires optimal conditions for the tumour and is a worst case scenario

68 Extension of LQ model to include time: E = - ln S = n * d (α + βd) - γt Including T k ("kick off time") which allows for a time lag before the tumour switches to the fastest repopulation time: BED = (1 + d / (α/β)) * nd - (ln2 (T - T k )) / αt p

69 Evidence for kick off time Part 3, lecture 2: High doses in radiation therapy 69

70 Use of the LQ model Calculate equivalent fractionation schemes Determine radiobiological parameters Determine the effect of treatment breaks e.g. Do we need to give extra dose for the long weekend break?

71 Calculation of equivalent fractionation schemes Assume two fractionation schemes are identical in biological effect if they produce the same BED BED = (1+d 1 /(α/β))n 1 d 1 = (1+d 2 /(α/β))n 2 d 2 This is obviously only valid for one tissue/ tumour type with one set of alpha, beta and gamma values Example at the end of the lecture