In conclusion, I am inclined to believe that all supposed very
late recurrences in the scar are not such in reality, for there is one
factor worthy of consideration. It is that scar tissue, with its epi-
thelial covering and deformed glandular tissue in its vicinity, is sub-
ject to diseases of its own, and that among them cancer is not un-
common. Why should it not occur, therefore, de novo, in the scar of
an old breast operation just as it occurs in the cicatrix of a healed
gastric ulcer, or in that of a torn cervix?
CLINICAL EXPERIENCE WITH THE LAW OF ACCEL-
ERATING RISK IN CANCER.
By E. WYLLYS ANDREWS, M.D.;
In a former paper ("The Law of Accelerating Risk," Annals 0}
Surgery^ December, 1905) I tried to prove that the law of mathe-
matics, the law of squares, applied to the speed of malignant
growth. This well-known law of squares applies to many phe-
nomenon in physics, to falling bodies, to momentum of masses, to
radiant energy, etc. It is a long step from physical processes to
vital ones, but in so simple a mechanical problem as the radiation
of cancer cells, which appear to be able to conquer their way cen-
trifugally into any and all tbsues, it ought not to be difficult to
formulate the ratio of extension, unless this is modified by certain
resistance or antagonism, such as the occurrence of immunity.
The growth of cancer in the animal body is unchecked and un-
remitting exactly as if it were upon dead soil. We seem to see no
recessions occurring from natural or acquired resistance. It is
true that age predisposes to the occurrence of tumors, but we do
not know that it influences their severity, when once acquired. In
fact, malignant growths in the young and strong, when they do
take place, are possibly more rapid and fatal than in the aged and
I would not deny the possibility of an immunizing therapy being
discovered from animal pathology, but the clinical fact remains
that, as we see cancer, it presents an unvarying front of crescent
power, which beats down all resistance, and conquers the tissues
of its victim, not in steady or arithmetical ratio, but in an accelerat-
ANDREWS: ACCELERATING RISK IN CANCER IQ?
ing or geometrical ratio of speed. In a late stage it covers more
ground than in an early stage. Let us consider what law of
growth exists, if any.
In most organs a malignant tumor finds room to spread cen-
trifugally in an enlarging circle, or, more properly, a sphere.
Leyden justly observes that it begins as a strictly local phenom-
enon, and its most striking feature is its imlimited proliferation.
^'Unlimited proliferation" can be taken almost literally. The
clinical fact is admitted, regardless of our theories for or against
Starting with the strictly local atrium or focus, which we all
admit, and ending with imlimited proliferation, we have a phe-
nomenon so closely like that of radiant energy, heat, light, sound,
that we are forced to admit an analogy in the law of progression.
Stated mathematically, the infection radiates in a sphere, with
the primary focus as a centre. Like all radiations, it follows the
law of squares. The superficial area, which is an index of the risk
of metastasis, increases as the square of the diameter of the infected
area. If a uniform growth in diameter takes place in a uniform
time, when multiplying time by 2 would increase risk 4 times; mul-
tiplying time by 3 would increase risk 9 times; multiplying time
by 4 would increase risk 16 times; multiplying time by 5 would
increase risk 25 times; multiplying time by 10 would increase risk
This soon brings us to infinite risk in finite time. In other
words, a comparatively short time suffices to make every case infi-
nitely dangerous or practically hopeless. This only restates theo-
retically what every surgeon knows to be mournful truth clinically.
What we lack to confirm this law clinically is means of locating
the exact time of origin of any case. Theoretically, it is the date
when the growth crossed the line between the microscopic and the
macroscopic period. Practically, it is the accidental time of dis-
covery of a neoplasm â€” early in accessible and exposed tissues,
later in more concealed parts; perhaps never discovered before
death in certain remote or unusual locations, as in the brain, pros-
tate, or skeletal deposits.
198 ANDREWS: ACCELERATING RISK IN CANCER
The Law not a Death Warrant. Discouraging as this law
is when stated in its first or positive form, we may derive much
comfort from converse proposition.
The Risk of Recurrence Diminishes in the Ratio of the
Square Root of the Time after Incidence. The law, thus
stated, admonishes us that an early golden period is always given
us for saving the life of the cancer victim, and imperatively de-
mands us to take action during the brief and precious stage. We
should look almost reverentially on the opportunity which then
It is this curable stage only which is of strategic importance in
surgery. Just what are its limits? Looking at the life history of
any malignant case, we may consider it as composed of three
periods: (i) The microscopic period; (2) the macroscopic period,
before metastases; (3) period after metastases or carcinosis period.
Of the first or microscopic period we know nothing except by
For the carcinosis period we have little to oflfer therapeutically,
save the hope that the jc-rays, or some remedy yet unknown, may
come as a sort of deus ex machina to the rescue.
Of the second stage, that of tumor building without metastases,
we think we have abundant clinical evidence. Radical surgery
should be mainly limited to this stage. By the law I have attempted
to prove, I have obtained a working formula which, when applied
clinically, will determine for us not, perhaps, the exact time limits
within which it is safe to operate, but, at any rate, certain limits
beyond which it is useless to operate for radical extirpation.
Clinical Test of the Law. On the chart, two extreme cases,
one extraordinarily rapid and the other unusually slow, both of
which illustrate its accuracy, can be represented by the line,
0, p, q, etc.
Case I. â€” Miss M., aged forty-seven years, robust and well in
appearance, had, in November, 1894, a small movable nodule,
size one-half inch, in right breast. Known duration, three weeks.
I gave a bad prognosis, but allowed a delay of one week for obser-
vation. Patient, however, waited six weeks, and consulted me in
ANDREWS: ACCELERATING RISK IN CANCER 199
January, with the tumor increased sixfold, and ahready some
glands in axilla. I estimate the growth at fully 100 per cent,
weekly, and it proved to be the most rapidly malignant carcinoma
of the mamma I ever saw.
Plotting the curve of this case on the basis of a doubling each
week, we have the extraordinary result of a practically hopeless
prognosis in five weeks, and apparently fatal result imminent in a
few months. This actually happened. I removed first one breast
and axillary contents, and the opposite one a few weeks later,
patient dying in May, six months after the first invasion, with large
metastatic masses in liver, both lungs, and pleurae.
The risk curve in carcinoma, i, 2, 3, etc., time elapsed. 10, 20, 30, etc , per
cent, of risk. O, P, Q, "risk cure."
Case II (the slowest I can remember). â€” Mrs. R. K., patient of
Dr. C. P. Paldwell. Had slow-growing carcinoma of left breast.
I estimated the time required for doubling at six months, basing
this on history. This rate, plotted with the abscissa representing
six-months' intervals, gives a danger limit very slowly accelerated,
and a fatal result years distant. Exactly this did occur. The
breast and glands were removed by me, and patient had no recur-
rence for three years. I considered her cured.
Very slow re-development in the old breast scar and axilla then
appeared, and patient eventually died of the cancer eight years
after the first appearance.
200 ANDREWS: ACCELERATING RISK IN CANCER
I have tested this graphic method in a large number of cases by
the past history, and a few by way of prophecy, and have every
faith in its accuracy. By it we can exclude, with fair accuracy, all
those cases which ought not to be operated upon. When the risk
curve plotted by my law has risen to the upper half of the card,
say to 90 or 100 per cent., it is useless to do other than palliative
operations. There is no class of cases likely to discredit surgery
more than those tumor operations so often done, in which rapid
recurrence takes place, and in which a subsequent review of the
whole case shows patient's family and physician alike that the oper-
ation really never had a chance of succeeding. A careful applica-
tion of this law will put us at a middle stage of any case almost in
the position of one who has seen its whole course. I am certain
that the first stages of any growth furnish the data for all the later
stages, whether it be very slow or very rapid. Although each case
has its own rate of progression, that rate, once determined, will
accelerate uniformly, according to the law of squares.
I shall be very much interested to learn if these conclusions are
not confirmed by the experience of other operators.
ACCELERATING RISK IN CANCER 20I
DISCUSSION ON CANCER SYMPOSIUM.
Professor Kuster, of Maxburg.
First I regret that I did not find an opportunity to obtain reports of
all my patients operated on for cancer of the breast, in number about
650 persons, so I cannot therefore present any statistics. I prefer to
speak only of two points which seemed to me particularly remarkable
in the excellent papers read.
The one point is the classification of the cases of cancer of the breast.
We have heard spoken of adenocarcinoma, scirrhus, medullary carci-
noma, and other forms. But if we consider anatomically the mammary
cancer we may only discover two forms, differing by the maternal ground
from which they emerge. The one form contains fine alveoles in the
form of small rents, filled by small epithelia in one or two rows. These
epithelia are so similar to the epithelia of the finest milk ducts of the
mammary glands that there is no doubt this is the maternal ground.
On the other side, we see great irregular alveoles stopped up with
large epithelia. The form resembles so completely the enlarged acini
that we may conceive them as emerged on the ground of the acinous
tissue of the gland. Therefore, we call the first form the tubular, the
second the acinous form of the mammary cancer. Now there is no doubt
that there are certain differences in the course of the two forms, supposed
that they remain unchanged, but, unhappily, we see great changes as
soon as the tumor becomes large. Then we find on the one side a tubular
and on the other an acinous cancer in all transitions, so that it seems
quite impossible to say which has been the maternal ground on which the
tumor first emerges.
The second point remarkable in the statistics presented is the length
of time in which a patient may be considered surely healed. Richard
V. Volkmann first stated the time of three years, but later it was extended
to five years. We know now that even this seems not sufficient, and
surely every surgeon of great experience has seen similar cases to those
reported. I saw a case operated upon in 1872, without opening of the
axilla, return with a cancerous gland on the neck after seventeen years;
it could not be completely extirpated. These cases seem to be of great
importance in the question of the causation of cancer. If we see a cancer
return after seventeen years, as I did, we may suppose a new cancer has
taken place without connection with the first. This is not possible to
suppose if we find a cancerous gland after so long a time; and as it is
impossible to suppose that the cancerous epithelia endure so long a time
without regressive metamorphosis, one must say that there is a good
proof of the parasitical nature of the cancer.
Dr. James E. Moore, of Minneapolis.
In the matter of recurrence, we have all censured ourselves when
we have had local recurrences. I have some photographs here that
have led me to believe that possibly we have censured ourselves unjustly
in thinking we have not performed a complete operation, when it really
was as complete as might have been. These photographs are of a patient
operated upon first in August, 1904. A complete operation was done,
both muscles removed with a wide area of skin, and the axilla cleared
out as well. She was seemingly perfectly well for two years. In August,
1906, two years exactly, she came back to me and had areas of recurrence.
The little nodules in the skin were quite a distance from the original
disease. In other words, they occurred in portions of the skin which
were originally away over under the woman's arm and down on her
abdomen. At her urgent request I made a wide removal of the skin,
removing these nodules completely, and again dissected the skin
on her side and down below the thorax, bringing the edges together
and getting primary union. She returned from California in April,
1907, seven months after this last operation, and again has nodules of
recurrence, not at the line of suture, but quite a distance away in skin
that had been originally almost around on her back, and one spot down
on her abdomen.
Now is it not possible that my original operation was as radical as I
could make it, and the foci which have caused these recurrences were
in the mediastinum? What led me to think this is that this woman is
rapidly failing from mediastinal growth. Is it not possible that these
mediastinal foci were there all the while and that these nodules in the
skin are secondary to them and not to foci left in the skin? The second
recurrence occurred immediately over the same space that had the first
I wish to say just a word about an idea brought out by Dr. Vander
Veer. I entered the profession as quite a young man and with surgical
aspirations; I did my first breast operation over thirty years ago while
a country physician in western Pennsylvania. After repeating the
operation a few times my recurrences were so uniform that I became
totally discouraged and did not operate; and even in later years, when
I removed to a city and became more actively engaged in surgery, I
did not encourage operation until after the appearance of Dr. Halsted's
report. Since that time I have grown more and more optimistic, and,
in spite of the disappointing results in many cases, have we not greater
reason for optimism than for pessimism in this matter? Have we not
made wonderful strides in the past, and can we not hope for more in
ACCELERATING RISK IN CANCER 203
Dr. John B. Roberts, of Philadelphia.
I would ask the Fellows in discussing this question to also express
their opinions on the propriety of the actual amputation of the arm in
cancer of the breast which has involved the axilla, either in the primary
or secondary operation. This suggestion has been made a number of
times by me, in the Annals of Surgery^ January, 1898, p. iii, and other
writers. We see by these papers that the acti\ity of the operator is
sometimes stopped at a point not quite as far distant from the primary
lesion as it should be. In cases where the inMtration of nodes extends
high up around the vessels, cannot we do better by actual sacrifice of the
arm to reach the higher regions of the armpit ? Dr. Vander Veer reported
successful excision of one or two inches of the axillary artery. I myself
have excised the subclavian vein and portions of the subclavian with
satisfactory results. It seems to me the more radical step of brachial
amputation should be included in this discussion.
Dr. C. B. G. de Nancr^de, of Ann Arbor, Mich.
There are a sufficient number of cases on record such as I shall relate
to justify my mentioning one case if not more in my own experience.
I made a clinical diagnosis of sarcoma of the breast, and to my great
surprise I received word from Professor Warthin, who examined the
specimen microscopically, that it was an epitheliomatous neoplasm,
not a connective-tissue one. Shortly after that one of my assistants,
examining this same breast, submitted to Dr. Warthin some sections
which he unhesitatingly pronounced to be sarcoma. When he was
told it came frOm the breast he had asserted was carcinomatous
he could not believe it, but felt sure that some mistake in labelling
the tumors must have occurred. That breast was examined over and
over again and presented the most typical forms of both carcinoma
Dr. Dennis mentioned a case, where after a carcinomatous breast had
been removed, if I am not mistaken, sarcoma appeared in the other
breast. I believe that probably the original growth that was removed
and pronounced carcinomatous was also sarcomatous.
There is another thing I wish to mention. In quite a number of cases
in which I have removed the breast for carcinoma I have also found
the breast to have been tuberculous as well.
I would therefore recommend a little more widespread microscopic
examination of breasts than we are in the habit of giving them. Portions
of the tumor from different, widely separated localities should be exam-
ined, and I believe they will explain some of our otherwise inexplicable
Dr. Alexander H. Ferguson, of Chicago.
In taking up the point mentioned by Dr. Roberts regarding very
extensive operations even at the sacrifice of the upper extremity, let me
sound a note of warning. Amputation of the upper extremity does
not facilitate the removal of the deep lymphatics of the neck. If these
lymphatics are extensively involved there is no sense in removing the
upper extremity with the idea that such an amputation will aid in obtain-
ing a permanent cure. I removed the upper extremity in one case,
a recurrence one and one-half years after operation. The recurrence
involved one and one-half inches of the axillary vein and the musculo-
cutaneous and internal cutaneous nerves, causing partial paralysis
of the arm with extensive edema. Here was a case where I thought
amputation to be the only thing. I could find no extension along the
lymphatics at the root of the neck, I removed the upper extremity
and, I think, all the recurrences in that region. On the tenth day,
while my patient was eating breakfast and sitting at the table, she com-
menced to have bad symptoms and died within fifteen minutes.
That is my only experience with amputation of the upper extremity.
I have gone into the neck a number of times, probably seven or eight.
Every patient died inside of two years. I have removed ribs, costal
cartilages, and sternum, and even a portion of lung. One of the cases,
where I removed the ribs extensively, was a carcinoma in a male. He
died inside of a year after operation. I have had three such operations
on males. Two died inside of a year, the other is still living, having been
operated on about fourteen years ago. I removed about one-third of
the sternum, a portion of the lung and pleura in two cases. These
patients recovered from the operation, but I do not believe that the
operation did any good whatever. We used the :)c-rays afterward;
both patients died inside of nine months.
From my own limited experience with these very extensive operations
of removal of ribs, sternum, etc., to eradicate the disease when deeply
seated, I believe it is better not to operate at all. It is my belief that
these patients will probably live longer and with more comfort if not
operated on than when they undergo such extensive operations.
Dr. Thomas W. Huntington, of San Francisco.
I have been interested in the discussion in reference to extensive opera-
tions in these cases and want to call attention to the work of Dr. Rixford,
of San Francisco. In three of Dr. Rixf ord's cases he has gone completely
into the thorax, has removed a very considerable portion of the pleura
and all tissue that seemed to be involved. These cases are still living,
and have been practically mthout suflfering since operation. The
intention of the operator should be for the prolongation of the life and
ACCELERATING RISK IN CANCER 205
the comfort of the patient. I do not think that we should hold out that
our patient will be permanently cured. This is not expected.
I wish to allude briefly to the matter taken up by Dr. Roberts. In
one case of recurrence taking place six years after operation in a patient
aged sixty-nine years, I found the axillary vessels involved in a large
cancerous mass. Intrascapular thoracic amputation was performed.
This old lady is living in Brookl3m, very comfortably, at the end of
nine months, and there is no evidence of a recurrence.
It seems to me that such operations as this are not only justifiable
but are to be urgently advocated.
Dr. William B. Coley, of New York.
I have observed 65 cases of recurrent cancer of the breast and wish to
give you a summary of them according to the time of recurrence: 10,
or 15 per cent., recurred after the three-year period; 4, or 6 per cent.,
after fourteen years; the longest was seventeen years; i, sixteen years;
I, fifteen years; i, fourteen years; i, seven years. One other inter-
esting case recurred one and one-half years after the primary operation,
was operated upon a second time and remained well for five and one-half
years and had a second recurrence two years afterward; 30 cases, or
nearly 50 per cent., recurred within the first six months, 8 cases within
one to two years, 6 cases within two to three years.
Regarding the question of sarcoma and carcinoma in the same indi-
vidual I reported, at the meeting of the Association a year ago, one case in
which the carcinoma of the breast had been removed two years pre-
viously by another operator. I operated upon a recurring tumor, a
large typical carcinoma. About two months later there was a tumor
which developed in the submaxillary region which proved to be a
typical round-cell sarcoma. It recurred promptly after removal and
killed the patient in a few months.
I had another case of large sarcoma of the abdominal wall operated
upon first by Dr. Tuttle and Dr. McBumey. At the end of ten years
there was typical carcinoma of the breast^ which I removed, but which
recurred within a year and finally caused death.
I have one other case of sarcoma and carcinoma in the same individual,
and I believe, in view of the recent investigations of Ehrlich, in which
he succeeded in producing carcinoma and sarcoma in the same strain
of mouse tumors after twelve generations, a tumor which was originally
carcinoma, showing carcinoma and sarcoma in the same tumor, and
later on showed pure sarcoma only. This goes toward confirming
Mr. Ballance's opinion, that the infectious cause of malignant tumors
may be the same organism, which under different conditions produce
connective-tissue and epithelial tumors.
With regard to removing the entire upper extremity I have had no
experience. A few years ago a patient of mine was advised by another
surgeon to submit to this. The operation was performed against my
advice and the woman died on the operating table. I think there is
another side of the question which has not been touched upon. That
is, the effect these extensive operations have upon other patients suf-
fering from the early stages of cancer. If they see the results in the
case of removal of the entire extremity, the patients usually dying shortly
after the operation, then those with small malignant tumors are pre-
judiced against all operative measures, and I think in the long run we
do far more harm than good.
Dr. William L. Rodman, of Philadelphia.
In the first place a word as to Volkmann's law. Everyone admits,
as a matter of course, that three years are not sufficient to enable one
to declare a patient immune from recurrence, but Dr. Coley has just
stated that only 15 per cent, of such cases recur after three years. So,
after all, it seems to me that the Volkmann law is a good working rule,
for if you extend the limit, to what period ^'ill you extend it? Ten
years are not sufficient, probably fifteen are not sufficient, and it would
seem also that at least a few of these supposed cases of late recurrences