From the Pathology and Laboratory Medicine Service,
Veterans Affairs Maryland Health Care System, Baltimore, Maryland [1];
Department of Pathology, University of Maryland Medical System,
Baltimore, Maryland [2]; and
Department of Pathology, The Johns Hopkins Medical Institutions,
Baltimore, Maryland [3].
Send comments and correspondence to:
George.Moore4@va.gov
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0. DISCLAIMER.
DISCLAIMER. United States Government Work, uncopyrighted,
public-domain, DRAFT COPY ONLY. This document does not necessarily
represent the views or policies of any United States Government agency.
This document is provided "as is", without warranty of any kind, express
or implied, including but not limited to the warranties of merchantability,
fitness for a particular purpose and non-infringement. In no event shall the
authors be liable for any claim, damages or other liability, whether in an
action of contract, tort or otherwise, arising from, out of, or in connection
with the document or the use or other dealings made with the document.
1. ABSTRACT.
Studies showing the clonal identity of various tumors have led to the
belief that most tumors originate from a single cell. It is shown by
Monte Carlo computer simulations that monoclonality can evolve from
minor differences either in cell cycle time or in the probability of
cell death in a polyclonal `founder' population. If cells divide continuously
without cell death (exponential clonal growth), a tri-clonal population
with three starting cells (cell cycle times 0.9 days, 1 day,
and 1.1 days) converges to near-monoclonality in 100
generations. For cell cycle times of 0.9 days, 1.1 days, and
1.1 days, and cell death probabilities of 0.45 and 0.46,
populations tend toward monoclonality while the tumor is still small
(<3 mm3)
Key words: monoclonal, tumor origin, polyclonal, Monte Carlo, cell death
2. INTRODUCTION.
Although little is understood about the early cellular events in
carcinogenesis, many observers have concluded that most tumors arise from
a single cell. Since it is impossible to observe a tumor grow from the
single cell stage to a clinically evident tumor mass, our understanding
of the origins of tumors have been inferential. Many tumors have a clonal
phenotype (e.g., cells of an antibody-producing myeloma produce monotypic
antibodies; neoplastic cells of chronic myelogenous leukemia may all have
the identical abl-bcr tumor marker). When all cells in a tumor have the
same genetic characteristics, one concludes that all cells in the tumor
are descended from a single cell (7,16). However, it cannot be concluded
that only one neoplastic cell was present at the tumor's origin. Any number
of non-clonal neoplastic cells may have been present (and even necessary)
during the evolution of the tumor, only to be lost through selection as the
tumor enlarged. A polyclonal theory for the origin of tumors has been
proposed by Alexander (1) and others
(12, 17).
We propose that over generations, polyclonal populations tend toward
monoclonality when there is variation in the growth properties of the
original cells in the original population. We employ the Monte Carlo method
to simulate the growth of cell clones with different probabilities of
cell death (2,
4, 11).
The Monte Carlo method obtains a single outcome for a function containing
a probability value by selecting a pseudorandom number, comparing it to the
probability value, and substituting 0 or 1, depending on
whether the selected number exceeds the probability value. By repeating
the simulation many times, a distribution of outcomes is obtained.
Monte Carlo simulations are particularly useful in predicting outcomes
where a simple set of initial conditions results in a large number
of possible outcomes, from which it is too difficult or cumbersome to derive
analytic solutions. By performing repeated trials and observing
the distribution of outcomes that evolve through time, one can predict
the behavior of complex systems.
3. MATERIALS AND METHODS.
Cell proliferation models were programmed on an IBM PC/AT compatible computer
(COMTEX, 30368 microprocessor, 25MHz, 330 Mb Priam hard disk), using American
National Standard MUMPS (MGlobal, Inc., Houston, TX), and the public-domain
File Manager (FileMan) database management system of the United States
Department of Veterans Affairs (5).
We assume that tumors begin as populations of genetically distinct
and independently dividing cells, each with the potential for unbounded
growth with a constant cell cycle time per generation, t,
and a constant, inherited death probability, p. For the case
in which there is no cell death (deterministic model), the number of cells
at the nth generation is 2n.
In a Monte Carlo simulation, a pseudorandom number is substituted
for the probability value to obtain a single outcome. The calculation
is then repeated many times to obtain a distribution of outcomes.
For example, in a clone beginning as a single founder cell with a death
probability of 0.45, the cell divides, and each of the two daughter cells
is assigned an independent pseudorandom number between 1 and 100,
inclusive. If a daughter cell obtains a pseudorandom number at most
45, then it dies without dividing. If a daughter cell obtains
a pseudorandom number at least 46, then it is capable of at least
one additional mitosis. The process continues until no daughter cells
can divide further (extinction), or until the experiment is arbitrarily
terminated (in this report, at the 100th generation).
Table 1
shows the source code in American National Standard MUMPS for calculating
a cell growth simulation from a single founder cell. The output
is arbitrarily terminated after generation 100. In this report,
the program was executed 500 times apiece at each cell death
probability and each cell cycle time shown in subsequent tables and figures,
yielding a distribution of outcomes for that cell death probability and
cell cycle time. A single Monte Carlo simulation using this program
is shown in Figure 1. Although the outcome
of each single simulation may vary widely, the outcomes of 500
such simulations can be regarded as a statistical sample of simulations.
8. RESULTS.
Figure 2 shows the relative contributions
to a population that began with three cells in a deterministic model
(i.e., zero cell death probability), each dividing with cell cycle times
of 0.9 days (solid), 1 day (checkered), or 1.1
days (crosshatched). Even with only this 10% difference in cell cycle
time, the population at 60 days is composed almost entirely
of descendants of the fastest growing cell. At day 40, the cells
derived from the slowest growing cell contributed only 0.3%
of the total population.
Table 2 shows the results of a Monte Carlo
simulation of 1500 founder cells, all growing with a constant
0.47 probability of cell death per generation. Five hundred
starting cells apiece have a cell generation time of 1.1 days,
1 day, and 0.9 days. At the end of 100 days, most founder
clones have become extinct. Only 251 (17%) of the original
1500 clones have survived (84 dividing every 1.1 days,
88 dividing every day, and 79 dividing every 0.9
days). The mean size of clones surviving at 100 days is 2053
cells for a 0.9 day cell cycle time, 31% higher than
the mean clone size of 1569 cells for a 1 day cell cycle time,
and 159% higher than the mean clone size of 792 cells for
a 1.1 day cell cycle time. The number of clones surviving to
100 days is a fairly constant feature of the cell death probability,
whereas the mean clonal size at 100 days varies according to
cell cycle time. At cell death probabilities below 0.50, a certain
proportion of clones, once established, tend to persist, with larger clone
sizes at 100 days resulting from shorter cell cycle times.
Table 3 shows the results of a Monte Carlo
simulation of the growth of clones of cells all having the same cell cycle
time (1 day) but varying in the probability of cell death. The growth
of 500 clones was simulated for each of ten probabilities of cell
death, ranging from 0.44 to 0.53. Clones with probability
of cell death above 0.50 all terminated before the 100th day
of growth. In clones with lower probabilities of cell death, there was some
clonal survival, but in all cases the majority of clones terminated before
the 100th day. When the probability of cell death per generation
was 0.44, 67.8% of the clones became extinct. The remaining clones
grew to a mean size of 156,921 cells. When the probability of
cell death was only one percent higher (0.45), the mean size
of the surviving clones was 25,023 cells. In all simulations
with small increments in the probability of cell death per generation,
there were large differences in survival rates and clonal growth.
Among 500 initial clones with a cell death probability less than
0.50, after 100 generations the surviving clones tend
to persist and behave in a near-deterministic manner. Thus it is reasonable
to speak of a cell doubling time. For example, with a cell death
probability of 0.49, starting with 500 cells, 22
clones survived to 100 generations, with a total of 2,288
cells; at 55 generations, the total number of cells was 965.
In other words, it required 55 generations to double its population
from 500 to nearly 1000 cells. In a Monte Carlo simulation,
the time of the first doubling (over 55 generations) is longer than
the time of the second doubling (less than 100 generations),
due to random extinction of small clones. Thus cell doubling time
is only an approximate concept in Monte Carlo simulations. The estimated
doubling time for each simulation group is shown in the rightmost column of
Table 3, as calculated from the equation
N = (N@0)× 2g/t, solved for t. N
is the cell population size at the 100th generation for a particular
cell death probability, N@0 is the number of cells at the 0th
generation, here 500, and g is the number of generations,
here 100. Solution is given by the expression
t = g/(log2N - (log2N@0)
Table 4 shows the growth of clones that differ by small
increments both in probability of cell death at each generation and
in cell generation time. The growth of 500 founder clones having
a generation time of 0.9 days and a probability of cell death of
0.45 was compared with the growth of 500 founder clones
having a generation time of 1.1 days and a probability of cell death
of 0.46. At 100 days, the clones having a shorter generation
time and lower probability of cell death had an average clonal size of
67,869 cells, compared to an average clonal size of 2,623
cells for the other group. Thus in a biclonal founder population that
expands into a lesion at 100 days of growth, the average lesion
would consist of approximately 7.0 x 104 cells, 96%
of which would derive from a single clone (i.e., the lesion would have
converged to near-monoclonality). Such a lesion would measure approximately
2.1 mm3.
9. DISCUSSION.
In a deterministic model of exponential cell growth, cells grow
continuously with a fixed cell cycle time and a zero probability of death
in any cell cycle. Under these conditions, minor differences in cell cycle
time produce major changes in the clonal composition of populations with
polyclonal origins. Experimentally, monoclonality is usually defined by
the presence of a single clone of cells occupying 95% of a population
(7). A proportion less than 100%
is necesssary because all tumor preparations are contaminated by
non-neoplastic stromal cells that would not be expected to belong
to a (clonal) neoplastic population. In addition, techniques that measure
clonality all have an inherent inaccuracies produced by the limitations
of measurement. After 60 days of deterministic growth,
a triclonal population of cells can easily achieve monoclonality with more
than 99% of cells derived from the fastest growing founder.
This model, however, does not accurately depict tumor cell growth,
as it does not account for cell death. In fact, when a single cell grows
exponentially for 60 days, it attains a cell mass of
260 cells. This number of cells, at
30,000 μ3 per cell
(6), would have a mass of 34,588
cubic meters! In fact, tumors grow slowly, often over many years,
and although tumors have high proliferative indices, this growth
is counterbalanced by cell death.
In this report, we assume that cells in a tumor all have a non-zero
probability of cell death, and that this probability of cell death is stable
and characteristic for a given clone. This assumption is based on
observations of a relatively constant growth fraction in tumors, although
the doubling times can vary greatly among various types of tumors
(8, 13,
14). A more general model, with two-event
carcinogenesis and a variable death probability, has been described
(9,
10). However, the stochastic form
of this model is mathematically intractable, and the deterministic form
is subject to asymptotic approximations. The present model requires
no approximations to obtain a solution, as is required for an analytic
mathematical solution. The only limitation in Monte Carlo methods
is the number of repetitions required to obtain a stable solution
(15).
Probably the fastest growing human tumor is Burkitt's lymphoma,
a tumor endemic in African children. This tumor can double its size every
three days. Other tumors, such as breast cancers, may grow very slowly,
many with doubling times of about six months. The simulations shown in
Table 3 result in tumor doubling times similar to the range observed
in human tumors. When the tumor cell death probability is 0.49,
tumor doubling time is about one-and-a-half months. When the tumor cell
death probability is 0.44, the tumor doubling time is 6.4
days. It is not feasible to simulate growth when the cell death probability
drops below 0.44, as the sample sizes increase dramatically,
and iterative calculations for each cell require excessive computer time.
Probability rates lower than 0.43 would probably result in tumors
growing at rates unobserved in clinical experience.
Do the cell death probabilities chosen for our simulations correspond
to cell death rates observed in human tumors? It is recognized that tumors
grow at rates much slower than the potential doubling time (determined
by fraction of cycling cells and their average cell cycle time). This
disparity between the observed rate of tumor growth and the potential rate
of tumor growth is reconciled by a cell loss factor
(3, 13),
defined as the rate of cell loss divided by the rate of growth. In steady
state conditions, such as normal skin or normal gastric mucosa, the cell loss
factor is always 1.0 (cell loss rate equals cell growth rate)
(13). In human tumors, the cell loss
rates varies, between a low of 0.70 to a high of about 0.95
(13). Anything higher than 1.0
would produce no net growth. In the simulations shown in
Table 3, probabilities for cell death
that apply to a single cell can be converted to cell loss probabilities
for aggregate tumor populations. For instance, a cell death probability of
0.50 results in a rate of cell loss equal to the rate of cell growth,
hence a cell loss factor of 0.50/0.50 = 1.0. A cell death probability
of 0.43 implies that when the cell loss rate is 0.43,
the cell proliferation rate must be 0.57, producing a cell loss factor of
0.43/0.57 = 0.75. A cell loss factor of 0.75 is observed
for Burkitt's lymphoma, the fastest-growing human tumor. Consequently,
cell death probabilities between about 0.43 and 0.49
can account for the entire range of tumor doubling times as well as
for cell loss factors observable in human tumors.
We assume that cells and their descendants have a constant cell cycle
time and that this is about one day. This assumption is based on cell growth
rates of tumor cells growing logarithmically in culture, and may have little
bearing on the cell cycle times of cells in tumors. The one day cell cycle
time is used largely as a convenience, to avoid having fractional
time-variables in the simulation. However, many tumors have tumor cell cycle
times between 1 and 4 days
(13). The predicted sizes of lesions
after any given time should thus be considered as approximations.
In summary, it is shown that with only minor variations in cell cycle
time and probability of cell death per generation, cells can have large
differences in average clonal growth rate (
Table 4). This phenomenon might account for clonality occurring
in tumors that arise from polyclonal populations. Furthermore, clonality
can be attained while the lesion is still small
(<3 mm3).
10. REFERENCES.
1. Alexander P.
Do cancers arise from a single transformed cell,
or is monoclonality of tumours a late event in carcinogenesis?
Br J Cancer. 1985;51:453-457.
2. Berman JJ, Moore GW.
Why do most initiated cells fail to produce early (preneoplastic)
lesions? Prediction by Monte Carlo simulation of growth.
Lab Invest. 1990;62:9A.
3. Day RS.
Exploring large tumor model spaces: drawing sturdy conclusions.
In: Thompson JR, Brown BW, eds.
Cancer Modelling.
Marcel Dekker, New York. 1987;:365-386.
4. Diggle PJ, Gratton RJ.
Monte Carlo methods of inference for implicit statistical models.
J Royal Statist Soc B. 1984;46:193-227.
5. Davis RG.
FileMan: A User Manual.
Bethesda, MD: National Association of VA Physicians. 1987;:.
6. Elias H, Sherrick JC.
Morphology of the liver.
New York: Academic Press. 1969;:13.
7. Fialkow PJ.
Clonal origin of human tumors.
Ann Rev Med. 1979;135-143.
8. Laird AK.
Dynamics of growth in tumors and in normal organisms.
Natl Cancer Inst Monogr. 1969;30:15.
9. Moolgavkar SH, Knudson AG jr.
Mutation and cancer: A model for human carcinogenesis.
J Natl Cancer Inst. 1981;66:1037-1052.
10. Mookgavkar SH, Luebeck G.
Two-event model for carcinogenesis:
biological, mathematical, and statistical considerations.
Risk Anal. 1990;10:323-341.
11. Moore GW, Berman JJ.
Cell growth simulations predicting polyclonal origins
for "monoclonal" tumors.
Lab Invest. 1990;62:69A.
PubMed Entry
Full Text:
http://www.netautopsy.org/monoclon.htm
Public-domain open-source code:
http://www.netautopsy.org/monoclon.htm#table1
Last tested: February 26, 2010.
12. Nowell PC.
Clonal evolution of tumor cell subpopulations.
Science. 1976;194:23-28.
13. Schiffer LM.
Cellular proliferation in tumor and in normal tissues.
In: Perez CA, Brady LW, eds.
Principles and Practice of Radiation Oncology.
Philadelphia: JB Lippincott. Philadelphia. 1987;:56-66.
14. Steel GG.
Cytokinetics of Neoplasia.
In: Holland JF, Frei E, eds. Cancer Medicine.
Philadelphia: Lea and Febiger. 1982;:177-189.
15. Thompson JR, Atkinson EN, Brown BW. (1987)
SIMEST: An algorithm for simulation-based estimation of parameters
characterizing a stochastic process.
In: Thompson JR, Brown BW, eds. Cancer Modelling.
New York: Marcel Dekker. 1987;:387-415.
16. Wainscoat JS, Fey MF.
Assessment of Clonality in Human Tumors: A Review.
Cancer Research. 1990;50:1355-1360.
17. Woodruff MFA, Ansell JD, Forbes GM,
Gordon JC, Burton DI, Micklem HS.
Clonal interaction in tumours.
Nature. 1972;299:822-824.
TABLE 1.
American National Standard MUMPS source program for calculating
a single cell growth simulation. Program was executed 500 times apiece
at each cell death probability and each generation time shown
in subsequent tables and figures.
1 CLONGRTH ; MONTE CARLO CLONAL GROWTH MODEL;
2 ENTRY S FRSZ=1,DTHR=45,EOUT=100,CLSZ=FRSZ,NXCL=0 ;
3 W !,"FOUNDER CLONE: ",FRSZ," CELLS"," DEATH RATE: ",DTHR,"%",!!
4 NXCL W $J(CLSZ,7) S NXCL=NXCL+1 W:((NXCL#10)=0) ! ;
5 S DBSZ=CLSZ*2,CLSZ=0 G:(NXCL>EOUT) EOUT ;
6 F FCL=1:1:DBSZ S RND=$R(100)+1 S:(RND>DTHR) CLSZ=CLSZ+1 ;
7 G:CLSZ NXCL W !,"EXTINCTION" G EXIT ;
8 EOUT W !,"OUTPUT TERMINATED" ;
10 EXIT W !!,"EXECUTION COMPLETE" ;
TABLE 1a.
COMMENT: In the nearly 20 years since this paper was published,
several cost-free, internet-ready computer languages have been introduced,
most importantly, Perl, Python, and Ruby. I have rewritten the Monte Carlo
Clonal Growth program in Perl, as follows. The minimum requirements for
a useful programming language for amateurs are:
1. Free, downloadable from the internet.
2. Easy to learn.
3. Large user base, so it won't disappear soon.
4. Works on different operating systems (Microsoft, Apple, Unix, etc.).
5. Reasonably standard core commands, available in all versions.
6. Expansible to large-sized problems, if needed.
You can download a free single-user license from ActiveState Perl
download. Look for the current, exact internet address on
google.com.
To verify that your download has created a usable version of Perl
on your computer, you should write a small program, filename
hellowrl.pl, on Microsoft® Notepad®, or some other
plain text processor. The file contents are:
#!/usr/bin/perl
print "Content-type: text/html\n\n";
print "Hello, World.";
exit;
Run the program as follows:
perl hellowrl.pl
The program prints Hello, World. and stops.
Perl program to sum the integers from 1 to 10.
The pound-symbol, #, means that everything on that line past
the pound-symbol is ignored by the Perl processor. This is the place
for comments from the programmer to the user.
#!/usr/bin/perl
print "Content-type: text/html\n\n";
print "\n Hello, World. \n Sum from 1 to 10."; # \n starts a new line.
$i=0; # initialize counter, $i=0
$sum=0; # initialize sum, $sum=0
while($i<10){ # perform while-loop while counter, $i<10
$i++; # increment counter by one, $i++
$sum=$sum+$i; # increment sum by $i, $sum=$sum+$i
}; # end of while-loop
print "\n Sum = $sum."; # print Sum
exit; # exit program
Run the program, as before:
perl hellowrl.pl
The result is: 1+2+3+4+5+6+7+8+9+10=55.
Random death of Simulated Cancer Cells.
Create twenty clones, named $clone[1], $clone[2],...,
$clone[20], starting with a single cell in each clone.
Run the cloning program for 12 cycles (i.e., 12 cell divisions).
Most clones become extinct. Even at fairly low death probabilities,
you need thousands of starter clones to guarantee the survival
of only a few clones. In this model, surviving cancer clones
can be regarded as very rare.
#!/usr/bin/perl
print "Content-type: text/html\n\n";
$deathprby=0.5; #Set Death Probability, $deathprby .
print "\n Random Cancer Clones. \n Death Probability=$deathprby";
$maxndiv=12; #Maximum number of divisions.
$nclones=20; #Initial Number of Cancer Clones.
$i=0; #Initial Size of Cancer Clones, $clone[$i] = 1.
print "\n Division 0:";
while($i<$nclones){
$i++;
$clone[$i]=1;
print " 1,";
};
$h=0;
while($h<$maxndiv){
$h++;
print "\n Division $h:";
$i=0; #Calculate Random Survival Probability for Daughter Cells.
while($i<$nclones){
$i++;
$clonei=$clone[$i];
$j=0;
$nwclone=0;
if($clonei>0){
while($j<$clonei){
$j++;
$r1=rand;
$d1=$r1*(1-$deathprby);
if($d1>0.5){$nwclone++;};
$r2=rand;
$d2=$r2*(1-$deathprby);
if($d2>0.5){$nwclone++;};
};
};
$clone[$i]=$nwclone;
print " $nwclone,";
};
};
exit;
Run the program:
perl hellowrl.pl
TABLE 2.
Monte Carlo simulation of polyclonal cell populations with a constant
0.47 probability of cell death, and 500 initial clones
for each cell cycle time.
Cell cycle # Clones at Clone sizes
time 100 days at 100 days
Mean S.D.
1.1 DAYS 84 792 749
1 DAY 88 1569 1755
0.9 DAYS 79 2053 2398
TABLE 3.
Monte Carlo simulation of 500 founder clones apiece, with constant
1 day cycle time and different probabilities of cell death.
Cell doubling time estimated by the equation
N = (N@0)× 2g/t, solved for t.
Probability Percent surv- Clone Size at 100 Days Estimated
of cell death ing clones at Total Mean St. Dev. N No. Doubling
per cycle 100 days Time, days
0.44 32.2% 2.53x107 156,921 174,568 161 6.39
0.45 25.4% 3.18x106 25,023 24,087 127 7.90
0.46 21.8% 6.25x107 5,733 7,167 109 9.70
0.47 14.4% 1.04x107 1,445 1,843 72 12.95
0.48 8.6% 1.34x104 311 411 43 21.00
0.49 4.4% 2.29x103 104 121 22 45.22
0.50 0.2% 415 42 47 10 ∞
0.51 0% 0 0 ∞
0.52 0% 0 0 ∞
0.53 0% 0 0 ∞
TABLE 4.
Monte Carlo simulation of 500 founder clones apiece, that differ in
growth rate by 10% and in probability of cell death by 0.01.
POPULATION AT 100 GENERATIONS
Surviving Clone Size Average %
Clones at 100 days Population
Mean S.D.
0.45 probability of death
generation time 0.9 28% 67,869 79,423 96%
0.46 probability of death
generation time 1.1 26% 2,623 2,893 4%
FIGURE LEGENDS.
Figure 1. Single Monte Carlo experiment, first forty cell cycles,
using the computer source code in Table 1. Cell death probability is
0.45. Cell cycle number (number of generations) versus clone size
(number of cells). A complete simulation consists of assembling the results
of 500 individual experiments.
Figure 2. Deterministic model (i.e., zero cell death
probability) showing monoclonal convergence of a triclonal tumor
at sixty days, with cell cycle times of 0.9 days (solid),
1 day (checkered), and 1.1 days (crosshatched).
11. ADDITIONAL READINGS.
1. Coxeter HSM, Greitzer SL.
Geometry Revisited.
New Mathematical Library.
Washington, DC: Math Assn America. 1967;:.
ISBN: 0883856190, 207 pages.
2. Honsberger R.
Episodes in Nineteenth and Twentieth Century Euclidean Geometry.
New Mathematical Library.
Washington DC: Math Assn America. 1996. Second printing. 2005
;:.
ISBN: 0883856395, 174 pages.
3. Coxeter HSM.
Introduction to Geometry.
New York: John Wiley & Sons, Inc. 1961;:.
Library Congress Catalogue # 72-93903.
SBN: 471-18283.
4. Moore GW, Berman JJ.
Cell growth simulations predicting polyclonal origins
for 'monoclonal' tumors.
Cancer Lett. 1991 Nov;60(2):113-119.
PMID: 1933835.
PubMed Entry
Full Text:
http://www.netautopsy.org/monoclon.htm
Public-domain open-source code:
http://www.netautopsy.org/monoclon.htm#table1
Last tested: February 26, 2010.
5. Berman JJ, Moore GW.
Spontaneous regression of residual tumour burden:
prediction by Monte Carlo simulation.
Anal Cell Pathol. 1992 Sep;4(5):359-368.
PMID: 1445794.
PubMed Entry
Full Text:
http://www.netautopsy.org/sponregr.htm
Last tested: February 26, 2010.
6. Berman JJ, Moore GW.
The role of cell death in the growth of preneoplastic lesions:
a Monte Carlo simulation model.
Cell Prolif. 1992 Nov;25(6):549-557.
PMID: 1457604.
PubMed Entry
Full Text:
http://www.netautopsy.org/celdeath.htm
Last tested: February 26, 2010.
8. Moore GW, Berman JJ.
Anatomic Pathology Data Mining.
In: Cios KJ, ed. Medical Data Mining and Knowledge Discovery.
2001. XVIII, 502 pp. 98 figs., 98 tabs. Hardcover.
ISBN: 3-7908-1340-0.
Copyright Springer-Verlag: Berlin/Heidelberg 1999.
Full Text:
http://www.netautopsy.org/apdmchap.htm
Last tested: February 26, 2010.
9. Berman JJ.
Tumor classification: molecular analysis meets Aristotle.
BMC Cancer. 2004 Mar 17;4:10.
PMID: 15113444
PubMed Entry
Aristotle (384-322 BCE), Greek philosopher.
This article is among the all-time most-viewed articles in BMC Cancer,
and, as of September 2008, has been downloaded about 15,000 times
from BiomedCentral.
Last tested: February 26, 2010.
10. Berman JJ.
Tumor taxonomy for the developmental lineage classification of neoplasms.
BMC Cancer. 2004 Nov 30;4(1):88.
PMID: 15571625.
PubMed Entry
Last tested: February 26, 2010.
11. Berman JJ.
Doublet method for very fast autocoding.
BMC Med Inform Decis Mak. 2004 Sep 15;4:16.
PMID: 15369595
PubMed Entry
Last tested: February 26, 2010.
12. Berman JJ.
Modern classification of neoplasms: reconciling differences
between morphologic and molecular approaches.
BMC Cancer 2005, 5:100.
PMID: 16092965
PubMed Entry
Last tested: February 26, 2010.
13. Berman JJ.
Biomedical Informatics.
Boston, Toronto, London, Singapore:
Jones & Bartlett Publishers; 1 edition (October 18, 2006)
ISBN-10: 0763741353, 459 pages.
ISBN-13: 978-0763741358, 459 pages.
http://www.jbpub.com/catalog/9780763741358/
http://www.julesberman.info/
Last tested: February 26, 2010.
14. Berman JJ.
Perl Pogramming for Medicine and Biology.
Boston, Toronto, London, Singapore:
Jones & Bartlett Publishers; 1 edition (April 6, 2007)
ISBN-10: 076374333X, 407 pages.
ISBN-13: 978-0763743338, 407 pages.
http://www.jbpub.com/catalog/9780763743338/
http://www.julesberman.info/
Last tested: February 26, 2010.
15. Berman JJ.
Ruby Programming for Medicine and Biology.
Boston, Toronto, London, Singapore:
Jones & Bartlett Pub; 1 edition (September 13, 2007)
ISBN-10: 0763750905, 378 pages.
ISBN-13: 978-0763750909, 378 pages.
http://www.jbpub.com/catalog/9780763750909/
http://www.julesberman.info/
Last tested: February 26, 2010.
16. Berman JJ.
Neoplasms: Principles of Development and Diversity.
Boston, Toronto, London, Singapore:
Jones & Bartlett Publishers. 2008 Oct 1.
ISBN: 9780763755706, 464 pages.
http://www.jbpub.com/catalog/9780763755706/
Last tested: February 26, 2010.
17. Berman JJ.
Perl: The Programming Language.
Boston, Toronto, London, Singapore:
Jones & Bartlett Publishers. 2009;:.
ISBN: 9780763757588, 52 pages.
http://www.jbpub.com/catalog/9780763757588/
http://www.julesberman.info/
Last tested: February 26, 2010.
18. Berman JJ.
Ruby: The Programming Language.
Boston, Toronto, London, Singapore:
Jones & Bartlett Publishers. 2009;:.
ISBN: 9780763757571, 46 pages.
http://www.jbpub.com/catalog/9780763757571/
Last tested: February 26, 2010.
19. Berman JJ, with Moore GW.
Precancer: The Beginning and the End of Cancer.
Boston, Toronto, London, Singapore: Jones and Bartlett. 2009 Aug 11;:.
ISBN 9780763777845, 200 pages.
http://www.jbpub.com/catalog/9780763777845/
Last tested: February 26, 2010.
20. Berman JJ.
Developmental Lineage Classification and Taxonomy of Neoplasms.
http://www.julesberman.info/devclass.htm
Last tested: February 26, 2010.
21. Berman JJ.
Resource page.
http://www.julesberman.info/resource.htm
Last tested: February 26, 2010.
22. Berman JJ, Moore GW.
Implementing an RDF schema for pathology images.
http://www.julesberman.info/spec2img.htm
Last tested: February 26, 2010.
23. Berman JJ.
Chronology of Earth.
http://www.julesberman.info/chronos.htm
Last tested: February 26, 2010.
24. Berman JJ.
Web site:
http://www.julesberman.info/
Last tested: February 26, 2010.
25. Berman JJ.
Blog site:
http://julesberman.blogspot.com/
Last tested: February 26, 2010.
26. Hanahan D, Weinberg RA.
The hallmarks of cancer.
Cell 2000;100:57-70.
27. Kansal AR, Torquato S, Harsh GR IV, Chiocca EA, Deisboeck TS.
Simulated brain tumor growth dynamics
using a three-dimensional cellular automaton.
J Theor Biol. 2000 Apr 21;203(4):367-382.
PMID: 10736214.
PubMed Entry
Last tested: February 26, 2010.
28. Kansal AR, Torquato S, Chiocca EA, Deisboeck TS.
Emergence of a subpopulation in a computational model of tumor growth.
J Theor Biol. 2000 Dec 7;207(3):431-441.
PMID: 11082311
PubMed Entry
Last tested: February 26, 2010.
29. Kansal AR, Torquato S.
Globally and locally minimal weight spanning tree networks.
Physica A. 2001;301:601-619.
30. Kansal AR, Trimmer J.
Application of predictive biosimulation within pharmaceutical clinical
development: examples of significance for translational medicine
and clinical trial design.
Syst Biol (Stevenage). 2005 Dec;152(4):214-220.
PMID: 16986263
PubMed Entry
Last tested: February 26, 2010.
31. Kansal AR.
Modeling approaches to type 2 diabetes.
Diabetes Technol Ther. 2004 Feb;6(1):39-47. Review.
PMID: 15000768.
PubMed Entry
Last tested: February 26, 2010.
32. Kansal AR, Torquato S, Stillinger FH.
Diversity of order and densities in jammed hard-particle packings.
Phys Rev E Stat Nonlin Soft Matter Phys.
2002 Oct;66(4 Pt 1):041109. Epub 2002 Oct 24.
PMID: 12443179.
PubMed Entry
Last tested: February 26, 2010.
33. Deisboeck TS, Berens ME, Kansal AR, Torquato S,
Stemmer-Rachamimov AO, Chiocca EA.
Pattern of self-organization in tumour systems:
complex growth dynamics in a novel brain tumour spheroid model.
Cell Prolif. 2001 Apr;34(2):115-134.
PMID: 11348426
PubMed Entry
Last tested: February 26, 2010.
34. Kansal AR, Torquato S, Harsh IV GR, Chiocca EA, Deisboeck TS.
Cellular automaton of idealized brain tumor growth dynamics.
Biosystems. 2000 Feb;55(1-3):119-127.
PMID: 10745115
PubMed Entry
Last tested: February 26, 2010.
35. Schmitz JE, et al.
A cellular automaton model of brain tumor treatment and resistance.
J Theor Medicine. 2002(4):223-239.
36. Gevertz JL, Torquato S.
Modeling the effects of vasculature evolution
on early brain tumor growth.
J Theor Biol. 2006;243:517-531.
37. Holash J, et al.
Vessel cooption, regression, and growth
in tumors mediated by angiopoietins and VEGF.
Science 1999;284: 1994-1998.
38. Helmlinger G, et al.
Solid stress inhibits the growth of multicellular tumor spheroids.
Nature Biotech. 1997;15:778-783.
39. Gevertz JL, Gillies G, Torquato, S.
Simulating tumor growth in confined heterogeneous environments.
Submitted to Physical Biology. 2008;:. submitted.
40. Fialkow PJ.
Clonal origin of human tumors.
Ann Rev Med. 1979;30:135-143.
41. Gevertz JL, Torquato S.
Growing heterogeneous tumors in silico.
Submitted.
42. Kitano H.
Cancer as a robust system: implications for anticancer therapy.
Nat Rev Cancer. 2004 Mar;4(3):227-235. Review.
PMID: 14993904.
PubMed Entry
Last tested: February 26, 2010.
43. Kitano H, Oda K, Kimura T, Matsuoka Y,
Csete M, Doyle J, Muramatsu M.
Metabolic syndrome and robustness tradeoffs.
Diabetes. 2004 Dec;53 Suppl 3:S6-S15. Review.
PMID: 15561923.
PubMed Entry
Last tested: February 26, 2010.
44. Kitano H.
Biological robustness.
Nat Rev Genet. 2004 Nov;5(11):826-37. Review.
PMID: 15520792.
PubMed Entry
Last tested: February 26, 2010.
45. Kyoda K, Baba K, Onami S, Kitano H.
DBRF-MEGN method: an algorithm for deducing minimum equivalent
gene networks from large-scale gene expression profiles
of gene deletion mutants.
Bioinformatics. 2004 Nov 1;20(16):2662-75. Epub 2004 May 27.
PMID: 15166016.
PubMed Entry
Last tested: February 26, 2010.
46. Kitano H.
Cancer robustness: tumour tactics.
Nature. 2003 Nov 13;426(6963):125.
PMID: 14614483.
PubMed Entry
Last tested: February 26, 2010.
47. Gevertz JL, Gillies GT, Torquato S.
Simulating tumor growth in confined heterogeneous environments.
Phys Biol. 2008 Sep 29;5(3):36010.
PMID: 18824788.
PubMed Entry
Last tested: February 26, 2010.
48. Gevertz JL, Torquato S.
A novel three-phase model of brain tissue microstructure.
PLoS Comput Biol. 2008 Aug 15;4(8):e1000152.
PMID: 18704170.
PubMed Entry
Last tested: February 26, 2010.
49. Gevertz JL, Torquato S.
Modeling the effects of vasculature evolution on early brain tumor
growth.
J Theor Biol. 2006 Dec 21;243(4):517-531. Epub 2006 Jul 15.
PMID: 16938311.
PubMed Entry
Last tested: February 26, 2010.
50. Conway JH, Torquato S.
Packing, tiling, and covering with tetrahedra.
Proc Natl Acad Sci U S A. 2006 Jul 11;103(28):10612-10617.
Epub 2006 Jul 3.
51. Deisboeck TS, Berens ME, Kansal AR, Torquato S,
Stemmer-Rachamimov AO, Chiocca EA.
Pattern of self-organization in tumour systems: complex growth dynamics
in a novel brain tumour spheroid model.
Cell Prolif. 2001 Apr;34(2):115-134.
PMID: 11348426.
PubMed Entry
Last tested: February 26, 2010.
52. Moore GW, Berman JJ.
Cell growth simulations predicting polyclonal origins
for 'monoclonal' tumors.
Cancer Lett. 1991 Nov;60(2):113-119.
PMID: 1933835.
PubMed Entry
http://www.netautopsy.org/monoclon.htm Full text, including
public-domain open-source code.
Last tested: February 26, 2010.
53. Berman JJ, Moore GW.
Spontaneous regression of residual tumour burden:
prediction by Monte Carlo simulation.
Anal Cell Pathol. 1992 Sep;4(5):359-368.
PMID: 1445794.
PubMed Entry
Full Text:
http://www.netautopsy.org/sponregr.htm
Last tested: February 26, 2010.
54. Berman JJ, Moore GW.
The role of cell death in the growth of preneoplastic lesions:
a Monte Carlo simulation model.
Cell Prolif. 1992 Nov;25(6):549-557.
PMID: 1457604.
PubMed Entry
Full Text:
http://www.netautopsy.org/celdeath.htm
Last tested: February 26, 2010.
55. Berman JJ, with Moore GW.
Precancer: The Beginning and the End of Cancer.
Boston, Toronto, London, Singapore: Jones and Bartlett. 2009 Aug 11;:.
ISBN 9780763777845, 200 pages.
http://www.jbpub.com/catalog/9780763777845/
Last tested: February 26, 2010.
56. Berman JJ.
Tumor classification: molecular analysis meets Aristotle.
BMC Cancer. 2004 Mar 17;4:10.
PMID: 15113444
PubMed Entry
Aristotle
(Αριστοτελης,
384-322 BCE), Greek philosopher, teacher of Alexander the Great.
This article is among the all-time most-viewed articles in BMC Cancer,
and, as of September 2008, has been downloaded about 15,000 times
from BiomedCentral.
Last tested: February 26, 2010.
57. Berman JJ.
Developmental Lineage Classification and Taxonomy of Neoplasms.
http://www.julesberman.info/devclass.htm
Last tested: February 26, 2010.
58. Berman JJ.
Biomedical Informatics (Paperback)
Publisher: Jones & Bartlett Publishers; 1 edition (October 18, 2006)
ISBN-10: 0763741353, 459 pages.
ISBN-13: 978-0763741358, 459 pages.
http://www.jbpub.com/catalog/9780763741358/
Last tested: February 26, 2010.
59. Berman JJ.
Perl Programming for Medicine and Biology
(Series in Biomedical Informatics).
Publisher: Jones & Bartlett Publishers; 1 edition (April 6, 2007)
ISBN-10: 076374333X, 407 pages.
ISBN-13: 978-0763743338, 407 pages.
http://www.jbpub.com/catalog/9780763743338/
Last tested: February 26, 2010.
60. Berman JJ.
Perl: The Programming Language.
Publisher: Jones & Bartlett Publishers. 2009;:.
ISBN: 9780763757588, 52 pages.
http://www.jbpub.com/catalog/9780763757588/
Last tested: February 26, 2010.
61. Berman JJ.
Ruby Programming for Medicine and Biology (Jones and Bartlett Series
in Biomedical Informatics).
Publisher: Jones & Bartlett Pub; 1 edition (September 13, 2007)
ISBN-10: 0763750905, 378 pages.
ISBN-13: 978-0763750909, 378 pages.
http://www.jbpub.com/catalog/9780763750909/
Last tested: February 26, 2010.
62. Berman JJ.
Ruby: The Programming Language.
Publisher: Jones & Bartlett Publishers. 2009;:.
ISBN: 9780763757571, 46 pages.
http://www.jbpub.com/catalog/9780763757571/
Last tested: February 26, 2010.
63. Berman JJ.
Neoplasms: Principles of Development and Diversity.
Publisher: Jones & Bartlett Publishers. 2008 Oct 1.
ISBN: 9780763755706, 464 pages.
http://www.jbpub.com/catalog/9780763755706/
Last tested: February 26, 2010.
Last updated: 2/26/2010, by G. William Moore, MD, PhD.