Download Document

Biologically conformal
radiation therapy
author: Urban Simončič
advisor: doc. dr. Robert Jeraj
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=riVi

Number of clonogen cells after DT is
N i DT   N i 2
DT
Td
 N i e i DT
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 mass
D=DE/Dm

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 hits
Si  e
D  D 2
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 statistics
TCP  e
N
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 r

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
Si  e

 i DT
Killing the cells after irradiation
Si  e
 i D
Local tumor control probability

Taking into account growth and kill
Si  e  i D  i DT

Initial number of clonogen cells in individual
volume element is
Ni=riVi

Recalling equation for TCP from Poisson
statistics
N
TCPi  e
fin a l
i
Local tumor control probability

Probability to eliminate all cells in i-th
volume element
TCPi  e

 riVi e i D iDT
DT in interval between RT fractions
Global TCP maximization

TCP for whole tumor is product of TCPs for
each voxel
TCP   TCPi
i

Total dose to the tumor is constrained
m D  E
i

i
t
To maximize TCP, we construct Lagrangian
LTCP1 ,..., TCPi ,...  TCPi    mi Di  Et 
Solution of the optimization
problem


We assume that all volume elements are equal
We choose reference radiobiological parameters
rref, ref, ref and reference dose Dref that would
give sensible TCP
L
0
TCPi
 ref
1
1   ref r ref
D i  
Dref   ref   i DT 
ln 
i
i
 'i   i ri
T
0



Special cases

Constant radiobiology parameters implies
uniform dose


Not a surprise, just gives us confidence that
method may be correct 
Variable clonogen density r
1  r ref 

D i   Dref 
ln 
 'i  ri 
T
0
Dose increases
logarithmically
with clonogen
density.
Another two special cases

Nonuniform radiosensitivity 
 ref
1   ref
D i  
Dref 
ln 
i
 'i   i
T
0




Dose is approximately
inversely proportional
to the radiosensitivity.
Nonuniform proliferation rate 
D i   Dref 
T
0
1
i

ref
  i DT
Dose increases
linearly with
proliferation rate.
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.