Cell, Tissue and Tumor Kinetics

Proliferation Kinetics: rate of growth of a popula tion, change in total cell num ber. Adult tissues are in homeo stasis. Children (and tumors) grow.

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I. Quantitative Assessment o f Parts of the Cell Cycle

Mitotic Index (MI): proporti on of cells in m itosis (count di rectly)

MI = T M /T C

where:

T M = time for m itosis

T C = total cell cycle time

Assumes:

 All cells in the population are dividing

 All cells have the same cell cy cle times

 Cells are uniform l y distributed around the cell cy cle (probably not)

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Labeling Index (LI) : proporti on of cells in S phase

LI = T S /T C

 Sam e assum p tions as for MI.

 Can be determ ined by pulse-labeling (10-30 min) cells with DNA precursors ( 3 H-thym idine or with BrdUrd), fixing, st aining as appropriate and counti ng labeled cells.

 Note that both MI and LI are ratios, not actual duration of phases of the cell cycle.

Percent-labeled-mitoses .

L a b e l c e l l s i n o n e p a r t o f t h e cell cycle.

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Observe p a s s a g e o f t h e s e c e l l s through a n o t h e r p a r t o f t h e c e l l c y c l e .

Requires s t a i n i n g a n d scoring m u ltiple sam p l e s f r o m t h e o r i g i n a l population.

b first labeled m itotic figures appear

a b = T G2

bc = T M

bd = T S = c e

T C = p e a k 1 - p e a k 2

T G1 = T C – (T S – T G2 – T M )

Real data show s asymmetric peak s.

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Typical values for duration of parts of cell cycle:

T C 10 h–10 days T G1 1–150 h

T S 6-10 h

T G2 1-2 h

T M 1 h

Cell population has a variety of cell cycle times.

If T C is long, variability is greater; second peak may not be dist inct.

 T S is sim i lar in all cell lines

 T G1 varies widely an d is the m a jor c ontributor to the widely different T C values observed

Grow th Fraction (GF)

Not all cells in a tu mor are actively growing.

 Proliferating cells (P)

 Quiescent cells (Q)

Grow th fraction is ratio of the num ber of proliferating cells (P) to the total num ber of cells.

GF = P/( Q +P)

 Determ ined by conti nuous l a b e l i n g o f c e l l s f o r ~ o n e c e l l c y c l e t i m e ( T C ).

 GF = fraction of cells labeled.

 Growth fraction for experimental anim al tum o r s i s u s u a l l y 3 0 - 5 0 % .

Or use of antibody (Ki-67) tha t binds to a n u c l e a r a n t i g e n i n c y c l i n g c e l l s .

Because not all cells in a tu mor are in th e growth fra ction, the actual (measured)

tumor volume doubling time (T D ) is usually longer than the cell cycle time. Normal adult tissues show no net grow th : growth fraction balanced by cell loss . Flow cytometry

Provi des a direct measure of all phases of the cell cycle.

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P o t e n t i a l D o u b l i n g T i m e ( T pot )

T h e p a r a m e t e r o f m o st immediate rele vance to clinical radiotherapy.

 T pot i s t h e c e l l c y c l e t i m e / f r a c t i on of cycling cells:

T pot = T C /GF

 T pot does not take cell loss into account

T S and LI can be determ ined by the % labe led m itoses approach, but this is not p r a c t i c a l i n humans.

A n a v e r age T pot can be estimated for tumors us ing flow cyto metry with the dual f l u o r e s c e n c e m e t h o d :

T pot = (T S /LI)

 Inject a tracer am ount of BrdUrd

 4-8 hours l a ter obtain tum o r biopsy

 Stain with antibody t o BrdUrd (green)

 Stain DNA with propidium iodide (red)

 Disaggregate for flow cyto metry analysis.

T pot is being studied as a potential predictive assay.

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Objective is to identify pa tients whose tumors are growing ra pidly.

These tu mors m i ght benefit from an accelerated fractionation schedule.

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LI is the p r oportion of cells that show green fluorescence (BrdUrd labeled).

T S is cal culated from mean red fluor escence of S cel l s r e l a t i v e t o G 1 and G 2 c e l l s (assumes DNA content in S p h a s e c e l l s i n c r e a s e s l i n e a r l y t h r o u g h S p h a se).

Relative Movement (RM)

RM = ( F L-FG1)/(FG2-FG1)

FL = the mean red f l uorescence o f t h e B r d U r d l a b e l e d c e l l s

FG1 and FG2 are the m e an red fluores c e n c e o f t h e G 1 a n d G 2 p o p u l a t i o n s

T S 

0 . 5 t RM  0 . 5

Cell Loss

 Tum o rs usually grow m u ch m o re slow ly than predicted by knowledge of T C and GF because of cell loss.

 Tu m o r growth is the net result of cell growth and cell loss.

 Cells can be lost due to death from:

o inadequate nutrition (necrosis, hypoxia, reflects inability of the vascular suppl y to keep up with tum o r growth)

o apoptosi s

o imm unological surveillance

o metastasis

o exfoliation.

Cell loss factor,  :

 = 1 – (T pot /T D ) or T D = T pot /(1 -  )

Example:

If T C = 22h, GF = 0.6, and  = 0.9, the T D = 366 hrs

 In experimental ani m al tu mors, ce ll loss factors range from 0 to 90%.

 Carcinomas tending to have high cell loss factors (>70%) and sarcom as tending to have low cell loss factors (<30%).

 This m i ght be attributable to the or igin of carcinomas from continuously renewing epithelial tissues, where the cell loss factor is 100%.

 This m i ght also account for t h e di ffering responses of sarcom as and carcinomas to radiation.

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S u m m a r y :

Potential doubling time

T pot

 T C GF

T pot

 T S

L I

( flow cytometry)

Cell loss

  1  T pot

T D

Tumor do ubling time

T D 

T pot

( 1   )

V. Volume Doubling Time, T D

Three f act ors determine tumor growth

 Cell cycle time of proliferating cells

 Growth fraction

 Cell loss fraction

Cell cycle times for tum o r cells ( T C ) ~ 1-5 days Tum o r volume doubling tim es ( T D ) ~40-100 days

Example:

Initial tumor diameter = 0.5 cm. V = (4/3)  r 3 100 days l a ter the tum o r had grown to 4 cm .

What is the tum o r doubling time?

Cal culation:

 Diameter i n creased b y a factor of 8.

 8 3 = 512-fold increase in tum o r volum e.

 How many doublings occurred during t h e 100 days?

 2 n = 512;

 n = 9 doublings

 Nine doublings in 100 days = 1 doubli ng every 11 days

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Relationship between tum o r weight, num ber o f c e l l s i t c o n t a i n s , and the num ber of doublings per cell. (assumes 10 9 cells per gram tissue)

T u m o r g r o w th tends to be Gompert z i an

Doubling time of the tum o r i n c r e a s e s p r o g ressively as the tum o r gets bigger. Cell cycle time is probably constant

T h i s i m p l i e s t h a t G F , c e l l l o s s f a c t o r , vary as a function of tum o r size.

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Kinetics of Human Tumors

S o m e parameters

 T C usually between 15 and 125 h, m odal value of 48 h

 T S usually between 10 and 24 h, m odal value of 16 h.

 T C usually 3 x T S , s o L I g i v e s a n a p p r o x i mate value of GF.

 LI varies between 0.1% and 40%, so G F v a r i e s b e t w e e n 0 . 3 % a n d 1 0 0 % .

 Cell loss factors high, usually in exce ss of 50%. Thus, cell loss may be the m o st im po rtant factor in determ ining th e pattern of growth of hum an tum o rs.

 Volume doubli ng ti mes range from 18 to over 200 days, with an average median doubling time estimated to be 66 days.

Generally, the cell cy cle time of m a lignant ce lls is sh orter than that of their norm a l tissue counterparts.

Metast ases appear to grow mo re rapidly than the primaries in the same in dividual.

 Tu m o rs with high GF tend to be m o re radiosensitive.

 GF, LI, cell loss factor determ ine re sponse to chemotherapy (acting on S phase cells)

 Chem otherapy cures observed only in t u m o rs with high LI.

Kinetics After Irradiation

I f c e l l s a r e g r o w i n g n o r m ally and have adequate nutri tion, etc. (e.g., exponentially g r o w i n g c e l l s i n c u l t u r e o r i n a t u m o r), i m m e d i a t e l y a f t e r i r r a d i a t i o n t h e i r c e l l c y c l e w i l l i n c r e a s e , l a r g e l y d u e to division delay.

 Subsequently, the loss of som e cells in a tum o r or non-growing norm a l tissue may cause the rem a ining cells to show accelerated growth or repopulation .

 This m a y result from shorteni ng of the T C , i n c r e a s e d g r o w t h f r a ction, and/or decreased cell loss.

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Tu m o r behavior after irradia tion will depend, at least in part, on the cell loss factor, GF and T C of the tumor.