To use or not to use the LQ model at “high” radiation doses per fraction

Dr Santam Chakraborty

Assistant Professor, Tata Memorial Hospital, Mumbai

Why are we afraid?

● Singh et al 1970s treated 24 patients with

stage III Ca Cx with 5.8 Gy in 5 fractions

one week apart.

○ Equivalent to NSD of 2 Gy in 20 fractions○ Equivalent acute toxicity

○ Equivalent tumor control

● All patients developed RVF starting 7

months after completion of RT.

Probability Theory

The probability of two mutually

independent events occurring together

is the product of two individual

probabilities.

Probability of getting a “dui chokka” is

1/6 x 1/6 = 1/36

Basics of LQ Model

Cell Kill leads to biological effects

DNA damage primary effect of Radiation

Modelling DNA damage mechanism can model radiation effect

Biggest utility in designing new dose fractionation schedules in a rational way

Mechanistic Basis of LQ Model

DSB

1 2

P ∝ D

Pair of DSB in both strands of chromosome (Dicentric)

Failure of Repair

Mechanistic Basis ...

● Probability of the two double strand breaks interacting in a

chromosome to produce lethal events (e.g. Dicentric) ∝ D x D = D2

● A single radiation track producing lethal lesion

● The probability of this occurrence is ∝ D

Thus,

● Probability of Lethal lesions ∝ D2 + D

● Number of Lethal Lesions (Y) = αD + βD2

Mechanistic basis ...

● The number of lethal lesions due to radiation in a group of cells is

randomly distributed.

● This probability distribution follows a Poisson distribution.

○ Discreet & independent events○ Randomly distributed○ Take place in a certain time interval○ Expected number of events is constant through the time period.

Survival = e-Y

Survival = e-(αD + βD2)

A typical cell survival curve

The initial linear portion of the cell survival curve corresponds to the αD component.

The curved portion (representing “lost dose”) represents the quadratic or the βD2 component.

LQ Model and the 5 R’s of Radiotherapy

1. Based principally on REPAIR of SLD

a. Quadratic component points a wasted dose as damage gets repaired

2. Which other R’s of radiotherapy are linked to the LQ model? =>

INTRINSIC RADIOSENSITIVITY.

3. Does not account for Repopulation, Reassortment and

Reoxygenation.

Advantages of the LQ model

1. It is a mechanistic model

2. Based on sound biological plausibility

3. It is also practical as it has just two parameters

4. Performs as well as other mechanistic models of cell killing

5. Well validated in doses upto 2 - 6 Gy and backed by reasonable

amount of clinical evidence.

What are the key assumptions

1. Assumes that DNA repair is the primary mechanism that explains

the cell survival following radiation.

2. Assumes that pair wise chromosomal aberrations are the only

mechanism mediating cell death

3. Assumes lethal lesions have a Poisson distribution

4. Repair rates reduce at higher dose / fraction

5. Assumes a constant radiosensitivity across all dose fractions

6. Assumes homogenous dose and dose rate

A “Real” Cell Survival Curve

● There is marked deviation of the observed data from the line predicted by the equation at higher doses

● Model predicts higher cell death than what is actually observed.

● Direct use “underestimates” of the dose equivalence

Cytotoxicity at high doses per fraction

High dose Radiation ( > 10 Gy)

Traditional dsDNA Damage mediated mitotic cell death

Stem Cell Programmed

Cell Death

Vascular Endothelial Cell Death

Acid Sphingomyelinase (ASMase) mediated ceramide generation

from cell membrane

ATM mediated direct Ceramide synthesis from

cell membrane

Hypoxia*

*Acute hypoxia abrogates DNA repair and results in cell kill

1 2 3

Murine experiment (Song et al)

1. Irradiated Walker 256 rat tumors to 10 Gy

single fraction.

2. Removed the irradiated tumors at different

time points and plated

3. Survival linked to time at which tumor was

removed after irradiation

4. Excess loss in cell viability linked to

vascular endothelial damage.

Murine experiment (Song et al)

Murine Experiment (Lee et al)

● GK irradiation of C6/LacZ glioma cells in rats to a dose of 20 Gy +

TMZ or Thalidomide

● Both regimens - showed only apoptosis of endothelial cells at 24

hours.

● Both regimens - reduced microvascular density

● Significant reduction in tumor volume with Thalidomide -

suggesting synergistic anti-angiogenic property.

Proof in HPE

● Szeifert et al evaluated the histological

changes in 18 cerebral metastases treated

with Radiosurgery (14 - 20 Gy)

● Observed a brisk inflammatory response

in irradiated tumor volume

● Severe vasculopathy (progressive as a

function of time)

Computer Simulation

● Kocher fitted a computer simulation model to the effect of 20 Gy SRS

on brain metastases (90 patient data)

● Tumor size, oxygenation, cell division, vascularization and vascular

occlusion modelled

● Simulation could predict tumor control only if a vascular effect was

included in which 99% of the vessels surrounding the tumor were

obliterated

● Vascular effect contributed approximately 1/3rd of the effect of

single dose radiosurgery.

The story in AVMs

● Karlsson et al treated 28 AVMs with 3.5

Gy twice a week to a total dose of 41 -

50 Gy

● LQ-BED = 88.8 - 108.3 Gy3

● LQ-BED of 15 Gy SRS = 90Gy3

● Obliteration rate < 10%.Obliteration rate of AVM as a function of the

marginal dose using SRS. Flickinger et al

Effect of High Doses on Stem Cells (Ch’ang)

● Gastrointestinal response to whole body radiation assayed in mice

● Between doses of 8 - 13 Gy stem cells regenerate the normal mucosa

despite endothelial injury

● Beyond 14 Gy death occurs due to gastrointestinal symptoms

● Deletion of Smpd1 gene (which produces ASMase) is protective till

17 Gy (blocks endothelial apoptosis)

● Blocking Ceramide synthase activity abrogates cell death response

at doses > 17 Gy

Effect of High Doses on Stem Cells (Ch’ang)

Effect on Immune Cells

M. A. Postow et al., Immunologic correlates of the abscopal effect in a patient with melanoma. N. Engl. J. Med. 366, 925–931 (2012).

In-situ Vaccination by RT

1. Immunogenic Cell Death is induced:

a. Extracellular release of ATP and HMGB1 (High mobility group protein B1)b. Cell surface exposure of Calreticulin

2. High dose (> 10 Gy) results in activation of CD8+ T cells via activated

dendritic cells.

3. Expression of chemokines that attract effector T cells (CXCL16).

4. Upregulation of MHC Class I antigen on tumor

CD8+ Cells are required for RT ablation

Mice injected with B16 Melanoma cells and tumor

volume measured after 20 Gy whole body RT

Nude mice injected with B16 Melanoma cells and tumor

volume measured after 20 Gy whole body RT

Mice injected with B16 Melanoma cells and

tumor volume measured after 20 Gy whole body RT in presence of CD8

inhibition

Alternative Models

● The LQ model is a special case of a general multi-target model

● It became popular as the multi-target model predicted a zero cell kill

at low doses which is not correct.

● Several alternative models have been proposed to the LQ model.

○ Linear Quadratic Linear Model (Guerrero et al)○ Universal Survival Curve (Park et al) - hybrid of LQ and multi-target models○ Generalized Linear Quadratic Formula (Wang et al)

Generalized Linear Model

● Proposed specifically for the uncertainties in LQ model at high

doses.

● Accounts for the fact that amount of SLD is reduced at higher doses

as sublethal damage converts to lethal damage. - “Repair

Saturation Assumption”

● Also accounts for variable dose rate during treatment (e.g. SRS /

HDR)

● Unlike LQ model α/β estimates are not dose range dependant.

Generalized Linear Model

ɑ/β estimates from low dose range

Back to the LQ Model ...

● LQ model fits the high dose data when LQ estimates are derived

from the entire dose range.

● LQ model can incorporate the dose rate independent mechanisms

of cytotoxic effects in the linear term. - can account for cell death

mechanisms like apoptosis.

● A higher ɑ/β ratio can “straighten” the LQ curve beyond a

threshold.

Back to the LQ Model ...

● Repair mechanisms may not get saturated at higher dose per

fraction.

● Utility of an empirical model diminishes with additional terms.

● The newer models also do not account for the additional cytotoxic

processes observed

Looking to the Future ...

1. Basal gene expression

profiles may determine the

LQ model parameters.

2. Seo et al investigated LQ

model parameters based

on basal gene expression

in 52 NCI-60 cancer cell

line panel.L

ow

ɑ

Hig

h β

Conclusions

● LQ Model is a well tested and validated model

● Clinical data exists that shows that LQ model can predict the effect at

higher doses (esp 5 - 10 Gy)

● While newer models have higher accuracy they need clinical data to

support them

● The real need of the hour is to not to abandon the LQ model but to

integrate it with modern molecular biology

● Appreciate that the story does not end with understanding the

cancer cell response

Thank You