Radiation Therapy Radiation Therapy (RT)(RT)

What is cancer?

Failure of the mechanisms that control growth and proliferation of the cells

Uncontrolled (often rapid) growth of the tissue

Formation of the tumor Metastasis; spread to distant

locations

Tumor biology

Tumors consist mainly from fully functional

(mature) cells

Clonogenic (stem) cells are capable of

infinite proliferation and therefore

responsible for tumor growth

Dividing stem cells divides continuously and

tumor is growing exponentially

Tumor biology

Growth rate described by doubling time Td

Potential doubling time (cell cycle period)

Real doubling time (cell loses; up to 90%)

Initial number of clonogen cells in individual

volume element is Ni=iVi

Number of clonogen cells after T is

TT

T

d

ieN2NTN iii

Cancer treatment Cancer usually treated by:

Chemotherapy Surgery Radiation therapy

Treated also by Hyperthermia Hormone therapy Molecular targeted therapy

Ionizing radiation effects Standard physical effects

take place first Chemical reactions follows

them Biological consequences Damage to the cell is

mainly due to DNA damage

Cell is considered to survive if unlimited reproductive potential is preserved

Dosimetry

Dose (actually absorbed dose) is defined as energy absorbed per unit massD=E/m

Biological effects not due to increased temperature Lethal dose increases temperature by

approximately 0.001 degree C

Radiobiology

LQ survival curve Death from single

hit

Death from multiple

sublethal hits2DDi eS

Number of clonogen cells

Survival curve predict average number N of survived cells after irradiation of the cells

One of the hypothesis says that All clonogen cells has to be eliminated to

cure the tumor Cells follow Poisson statisticsNeTCP

Radiation therapy

Use of ionizing radiation to kill cancer cells, while delivering as low dose as possible to normal tissue

How the systems look today…

How the systems work today…

Conventional radiotherapy uses uniform beams that results uniform dose

Technique that uses

nonuniform beams

can produce arbitrary

dose distribution in

tumor (IMRT)

How we plan today…

Despite IMRT capabilities, uniform dose distribution is demanded

How we will plan in the future…

Customized nonuniform dose distributions on a patient specific basis

Planning and imaging

We may image Anatomy Functions or molecular processes

Molecular imaging maybe gives us an answer how to shape the dose

Positron emission tomography

Nuclear medicine medical imaging technique

Produces a 3D image of molecular processes in the body

How PET works

Production of radioisotope

Bounding of radioisotope to some bioactive compound

Injecting patient by that radiolabeled compound

Imaging of spatial distribution of that compound

PET usage

Delineation of the tumor volume and its stage (past and present use)

In the future, probably very important tool for the assessment of: tumor clonogen cells density distribution oxygen status of the tumor tumor response to the radiation

treatment

BCRT Planned dose distribution in target

volume is not uniform, but tailored on patient specific basis

Integral tumor dose is constrained Planned dose distribution should result

highest probability to eliminate tumor

Planned dose conforms to the spatial tumor biology distribution

Spatial biology distribution

The only missing link in the BCRT chain Properties are phenomenologically

characterized by: Clonogen density Radiosensitivity

Redefined =’[1+’/’ D]; ’, ’ are LQ parameters

Proliferation rate

Local tumor kinetics

Parameters for one volume element!

Si is number of cells after something

happens, relative to initial number

Growth of the cells with time

Killing the cells after irradiation

Ti

ieS

Di

ieS

Local tumor control probability

Taking into account growth and kill

Initial number of clonogen cells in

individual volume element is

Ni=iVi

Recalling equation for TCP from Poisson statistics final

iNi eTCP

TDi

iieS

Local tumor control probability

Probability to eliminate all cells in i-th volume element

T in interval between RT fractions

TiDiii eV

i eTCP

Global TCP maximization

TCP for whole tumor is product of TCPs for each voxel

Total dose to the tumor is constrained

To maximize TCP, we construct Lagrangian

i

iTCPTCP

tii EDm

tiiii EDmTCPTCPTCPL ,...,...,1

Solution of the optimization problem

We assume that all volume elements are equal We choose reference radiobiological

parameters ref, ref, ref and reference dose Dref that would give sensible TCP

ii

refref

iiref

iref

i

refT

i

TDiD

TCP

L

ln'

11

0

0

Special cases Constant radiobiology parameters

implies uniform dose Not a surprise, just gives us confidence

that method may be correct Variable clonogen density

i

ref

iref

T DiD

ln'

10

Dose increases logarithmically with clonogen density.

Another two special cases

Nonuniform radiosensitivity

Nonuniform proliferation rate

i

ref

iref

i

refT DiD

ln'

10

TDiD irefi

refT

1

0

Dose increases linearly with proliferation rate.

Dose is approximately inversely proportional to the radiosensitivity.

Conclusions

The formalism proposed here is questionable because is based on an LQ model

Not valid for high doses Presumes uniform dose distribution

Formalism does not take into account Redistribution of the cells through cell cycle Reoxygenation of hypoxic cells

It presumes that spatial distribution of biological parameters is known

Conclusions

Formalism gives a rough overview how to optimally shape the dose distribution

Simplistic (beginners) approach to the patient specific radiation therapy, which is believed to be future of RT by many renowned researchers.