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Microdosimetry in ion-beam therapy for beginners

Wiener Neustadt, 9-10 October 2019

Giulio Magrin

Welcome

• Unique synchronism (the momentum of Microdosimetry for therapy)

• Unexpected response (from young and experienced researchers)

• The idea was born after yet another unsuccessful EU program submission. The idea is stolen from the Marie Skłodowska Curie Grants

• Unusual implementation (Reciprocal support to make it successful in the short run and hopefully in the long run)

… for beginners

Agenda of these two half days:

• Introducing ourselves, why our institute is having a microdosimetric program.

• Background:• Microdosimetry and ion-beams therapy (Paolo Colautti, tentative title) • From conventional microdosimetry to ion-beam therapy microdosimetry (Giulio Magrin)

• Hands-on:• Linearization of the response of the electronic components• Collection of single-event spectra

• Computation:• Self-calibration process• Obtaining microdosimetric spectra and lineal energy mean values

• Outreach and plan for a (possible) future collaborations:• Experiments: Metrological approach and sharing of microdosimetric data. • Computations: Microdosimetry and Monte Carlo codes • Methodologies: A multi-centric approach?

Introducing ourselves

• Current activity in microdosimetry

• Why

do we think to link microdosimetry and ion-beam therapy

• How

Experiments

TheorySimulations

How the participants identify their activities in MICRODOSIMETRY:

9 October 2019

Topics (to be) discussed in the community…… missing additional experimental data or missing agreement

• Conceptual decisions:• Best shape: is the sphere STILL the most significant?• Best material: is water the most convenient?• What parameter for characterizing the radiation quality in ion-beam therapy?

LET OR lineal energy? Spectra OR Averages (L OR ӯ)? • The role of the size of the Sensitive Volume

• Consolidations of experimental topics:• Equivalence of shapes, Equivalence of materials• Self calibration parameters: maximum chord, maximum LET, interpolating sigmoid• Extrapolation below noise-cutoff threshold

• Reach out the users:• Correlation microdosimetric spectra and LET spectra

• Different use of LET averages in radiobiological data: LT OR LD• Separate IN-target from OUT-of-target. • Under what conditions using the saturation values of lineal energy, y*• For IN-target use Lin-Lin representation (not Log-Lin)?

General concepts described by Paolo

f(y)

d(y)

𝑦𝐹 = 0

∞

𝑦 · 𝑓 𝑦 ⅆ𝑦

𝑦𝐷 =1

𝑦𝐹 0∞𝑦2 · 𝑓 𝑦 ⅆ𝑦= 0

∞𝑦 · ⅆ 𝑦 ⅆ𝑦

All these 4 terms are used to specify the radiation quality:

the discussions in the community in using one of them instead of another as a specification of the radiation quality are open.

Experimental spectra

0∞𝑓 𝑦 ⅆ𝑦 = 1 ≅ 𝑖

𝑖𝑀𝑎𝑥 𝑓𝑖 · (𝑦𝑖+1−𝑦𝑖) = 1

𝑦𝐹 = 0∞𝑦 · 𝑓 𝑦 ⅆ𝑦 ≅ 𝑖

𝑖𝑀𝑎𝑥 𝑦𝑖 · 𝑓𝑖 · (𝑦𝑖+1−𝑦𝑖)

The fundamental equation of microdosimetry

The quantities:• The energy deposit in a single collision: εi• The energy imparted, ε, to the matter in a volume is the summation is performed over

all energy deposits, εi in that volume (the εi can refer to different particles):

𝜀 =

𝑖

𝜀𝑖

• The energy imparted in a single event ε1 (for simplicity from now on we ignore the subscript ‘1’) is the energy imparted from a single ionizing particle.

• Speaking of distributions, sometimes ‘energy imparted’ is omitted: single event spectra. However single event spectra can refer also to spectra of lineal energy, y, which are by definition related to single particles.

• The chord length: l

• The Lineal Energy Transfer: L

The fundamental equation of microdosimetry

(*) The three assumptions for writing ε1 = l · L

• Assumption 1. The energy straggling is negligible.

The energy straggling is linked to two stochastic characteristics of energy deposition, the probability of a electronic collision and the energy exchanged in that collision.

In the ideal case for assumption 1, the distance between to collision coincides with the mean free path, and the secondary electrons have all the same energy.

The fundamental equation of microdosimetry

(*) The three assumptions for writing ε1 = l · L

• Assumption 2. The LET at the entrance of the sensitive volume is the same of the LET at the exit

The fundamental equation of microdosimetry

(*) The three assumptions for writing ε1 = l · L

• Assumption 3. There is no escape of delta rays.

• Plus the general condition: the particles cross the SV of the detector in strait lines

The fundamental equation of microdosimetry

(*) The three assumptions for writing ε1 = l · L

• Additional assumption 4, for (therapeutic) ion beams: the particles cross the SV of the detector in strait and parallel lines

The fundamental equation of microdosimetry

Site

L is the density of energy

l is the chord length

ε1 = l · L

is energy imparted

The fundamental equation of microdosimetry

1st use of the fundamental equation:Finding the maximum value of ε1

ε1,max = Lmax · lmax

ymax = Lmax · lmax / 𝒍

The fundamental equation of microdosimetry

density distribution of L: t(L)

density distribution of l: g(l)

the distributions g(l) and t(L) combine to generate the density distribution of ε1: f(ε1)For simplify the notation let us drop the subscript ‘1’

The transition from single values to DISTRIBUTIONS of values:

The fundamental integral of microdosimetry

𝐹 ε = 0

+∞

𝑡 L ∙ 𝐺 𝑙 dL = 0

+∞

𝑡 L ∙ 𝐺ε

LdL

ε = l · L

The fundamental integral of microdosimetry

• From the fundamental equation to the fundamental integral.

• To understand the process it is better to combine cumulative and density distributions.

• For what events the imparted energy is equal to or lower than 𝜺?

ε = l · L

The fundamental integral of microdosimetry

𝐹 ε = 0

+∞

𝑡 L ∙ 𝐺 𝑙 dL = 0

+∞

𝑡 L ∙ 𝐺ε

LdL

For what events the imparted energy is equal to or lower than 𝜺?

ε = l · L

The fundamental integral of microdosimetry

𝐹 ε = 0

+∞

𝑡 L ∙ 𝐺 𝑙 dL = 0

+∞

𝑡 L ∙ 𝐺ε

LdL

ε = l · L

𝑓 ε ≝ⅆ𝐹 ε

ⅆεε =

0

+∞

𝑡 L ∙ⅆ𝐺εLⅆεdL =

0

+∞

𝑡 L ∙ gε

L∙1

LdL

For what events the imparted energy is equal to or lower than 𝜺?

Applications of the integral

ε𝑛 = 0

+∞

ε𝑛 · 𝑓 ε dε = 0

+∞

ε𝑛 0

+∞

𝑡 L ∙1

Lgε

LdL dε =

= 0

+∞

0

+∞

𝐿𝑛 ·ε𝑛

𝐿𝑛𝑡 L ∙1

Lgε

LdL dε =

0

+∞

0

+∞

𝐿𝑛𝑡 L dL ∙ε𝑛

𝐿𝑛gε

Ldε

L

=𝑳𝒏

= 𝒍𝒏

𝜺𝑛 = 𝑳𝒏 · 𝒍𝒏

Applications of the integral

𝜺𝑛 = 𝑳𝒏 · 𝒍𝒏 ⇒ 𝑦𝑛 =𝜀𝑛

𝑙𝑛 = 𝐿

𝑛 · 𝑙𝑛

𝑙𝑛

Theoretical introduction to transformation

𝐹 𝑦 = 0

+∞

𝑡 L ∙ 𝐺𝑦 · l

𝐿dL

If we consider slab detectors and we make the further assumption that particles are unidirectional we obtain:

𝑓(𝑠𝑙𝑎𝑏) 𝑦 = 𝑡 L

This identities are the key element that allows spectra conversions for different detector, considering both differences, of MATERIAL, and of detector SHAPES.

𝐹(𝑠𝑙𝑎𝑏) 𝑦 = 𝑇 L

Material conversion: y(diamond) = L(diamond) = S(E) (diamond)

The electronic stopping power function S, and its inverse S-1 , are used to assign the bin value of lineal energy to the new material. S and S-1 are provided by lookup tables.

A lineal energy value registered on the spectrum of the diamond detector can be transformed to the value that the same particle would produced in the spectrum in propane.

S(E)diamond

S(E)propane

Carbon-ion Energy/keV

S(E)

(dia

mo

nd

)

Elec

. Sto

pp

ing

po

wer

of

C-i

on

s in

Dia

mo

nd

/(k

eV·µ

m-1

)

S(E)

(dia

mo

nd

)

Elec

. Sto

pp

ing

po

wer

of

C-i

on

s in

Pro

pan

e /(

keV

·µm

-1)

y(propane) =S(propane)(S-1

(diamond) (y(diamond)))

Note: The choice of the appropriate Electronic Stopping Power lookup tables is fundamental

Theoretical introduction to transformation

𝐹(𝑐𝑦𝑙𝑖𝑛𝑑𝑒𝑟) 𝑦 = 0

+∞

𝑓(𝑠𝑙𝑎𝑏) 𝐿 ∙ 𝐺(𝑐𝑦𝑙𝑖𝑛𝑑𝑒𝑟)𝑦 · l

𝐿dL

Shape conversion:

Considering discrete distributions, the algorithm to convert the spectrum in slab to the spectrum in cylinder is the following:

𝐹(𝑐𝑦𝑙𝑖𝑛𝑑𝑒𝑟) 𝑦𝑗 =

𝑖

𝑓(𝑠𝑙𝑎𝑏) L𝑖 ∙ 𝐺 ly𝑗

L𝑖∆L𝑖

𝑓(𝑐𝑦𝑙𝑖𝑛𝑑𝑒𝑟) 𝑦𝑗 = l

𝑖

𝑓(𝑠𝑙𝑎𝑏) L𝑖

y𝑖∗∙ 𝑔 ly𝑗

L𝑖∆L𝑖

Theoretical introduction to transformation

Consequently:Following the two-step process it is possible to convert the spectrum of a slab detector to the spectrum of a detector different in shape and in material. This result can be used to compare the experimental data collected with different detectors and to initiate the ‘consolidation’ of the microdosimetric data.

Theoretical introduction to transformation

The consequence:

If the 3 + 1 assumptions are fulfilled (and only in that case) than we can correlate lineal energy quantities, y, and LET quantities:

1. We can use the correlation 𝑦𝑒𝑑𝑔𝑒 =𝑙𝑚𝑎𝑥 𝑙𝐿𝑚𝑎𝑥

2. We find the correlation 𝑦𝐹 = 𝐿𝑇

3. We know the correlation 𝑦𝐷 = 𝑙2

𝑙 2𝐿𝐷

4. We know how to transform the spectrum collect a spectrum with a particular detector to the spectrum that would be collected with a detector different if shape and material

The next steps

1. Specifying in what experimental conditions the 3+1 assumptions are fulfilled

2. Look at all sources of uncertainties, which play a role in the experimental assessments