Want to Know the Day You Got Cancer and the Day It Metastasized?

There's an error bar but it's not very big, maybe +/- a week

I’m going to apply my reasoning to a real life case in just a second but there is some mathematics and biology background you may not be familiar with.

First the Biology:

This stuff is very complicated. There are nonsense mutations, mis-sense mutations, frame shift mutations (which throw off multiple codons, causing proteins to be composed of many incorrect amino acids, completely changing their shapes and functions) etc. I’m not going to lose everyone by getting into any of that. I’ve learned my lesson. Consequently, I’m going to speak in generalities with sentences like, “Cancer arises from mutations in DNA.” Yes, I know there is the rare cancer that starts from a single mutation and that genetics also plays a role, making some people more susceptible to cancer. You’ll see when we get into the calculations used to determine the day cancer started, that none of that is important. So please don’t call me out by saying, “You forgot the 8% of cancers that…”. I want to keep this part of the background material very simple because it’s not important. With that disclaimer, let’s begin.

Cancer starts as a single cell. Something goes wrong- mutation(s) in the DNA controlling the behavior and protein production in that cell- and it starts dividing rapidly; not just rapidly, but uncontrollably.

[Note: You’ll see in a bit, why physicists call what I’m going to do today, a “back of the envelope calculation” so I’ll use envelopes for all my sketches.]

Look at A. and B. below You’d expect spherical enlargement if all the cells in a mole, for example, are dividing at the same rate; a nice symmetrical sphere. A. is a good example.

Now let’s suppose a cell inside of A. becomes cancerous. That cell will give rise to a new line of rapidly and uncontrollably dividing cells. A little “bubble” will appear on the surface of the mole as depicted in B.

A cross section of B:

It displays what we call an “irregular border”. This means trouble and should always be investigated with a biopsy.’ Inside the cell, this is happening:

The time it takes to go from 2 to 4 or 4 to 8 or 32 to 64 is called the “doubling time” and is ~constant. This makes sense because each doubling of the group still comes down to a single cell dividing. As a non-cancerous mole grows normally it does so at a slow and controlled rate. When the mutations occur necessary for a cell to become cancer, that cell and its family line divide very rapidly and in an uncontrolled fashion and forms its own tumor within a tumor. This cancerous component is depicted by the dotted circle in B.

The mathematics:

When you double something 10 times, you end up with (roughly) 1000 times what you started with. Let’s start with 1 single cell:

1 (double it) 2 (double it) 4 (double it) 8, 16, 32, 64, 128, 256, 512, 1024 (For our purposes, 1024 = 1000. Yes, we can figure it out exactly and we would if there was a lawsuit involved but remember, this is a “back of the envelope” calculation..

So our measly little cell, only .01mm in diameter, that you couldn’t quite see with the naked eye, is now its own nascent sphere made up of 1000 cells. It’s a tiny tumor , quite a bit smaller than a period on your screen, one of these “.” It’s one tenth the distance between the mm hashmarks on a ruler.

How do I know that?

[Note: you’re going to have to take your time and completely understand the next section before we go any further. so please don’t glance over it or you will be lost for the rest of the presentation]

I know the diameter of our tumor is one tenth of a millimeter (=.1mm) because the volume of a sphere is 4/3 (pi) r-cubed.

We’re now talking about the volume of the tumor, not the volume of just one cell. But the formula is the same.

The volume of our little tumor (now made up of 1000 cells) went up a thousand times. Of course it did- it’s made up of 1000 cells now. It’s radius must have gone up ten times because according to the formula, volume is proportional to the radius, cubed. Since 10 cubed = 10 x 10 x 10 it’s radius had to go up 10 times. Since radius = diameter/2, its diameter also went up 10 times. Thus, the diameter went from .01 mm (the diameter of a single cell) to .1mm (.01 x 10 = .1). Forget about all the constants; the 4, the 3, the 2, the 8, even pi.

(Pi is weird. Just because it goes on forever, doesn’t mean it’s not a constant 3.1415926535… It’s what we call irrational, meaning it can’t be expressed as a fraction. It’s the ratio of the circumference of a circle to its diameter for any circle. It just goes on forever, but it’s a constant and can be ignored for our purposes.

[Fun facts: People- mostly kids- take sport in memorizing pi to lots of digits. I think I could memorize pi to 100 digits in half a day or so. It’s pretty easy. At place 762, a string of six 9s starts. Richard Feynman once declared that he’d like to memorize pi to 767 digits so he could recite “9, 9, 9, 9, 9, 9, and so on”. From that day forward, place 762 has been known as “the Feynman point”.

Another aside about Feynman…

Feynman was a showman and would have figured out a way to recite all 767 digits publicly. The show would have raised a lot of money for charity.

Feynman delighted in things like that. At Los Alamos, where he was part of the Oppenheimer team developing the atom bomb, he used to break into the safes of the other physicists and leave silly notes, showing he was there, uninvited. He famously told General Lesley Groves, another MIT alumnus whose job it was to hire the person who would lead the Manhattan Project a job that could fairly be considered the most important of the 20th century, “ just because the public calls them ‘safes’ doesn’t mean they’re safe.

Feynman used to like to think about physics (among other things) while looking at the naked girls at a strip club in Pasadena where he was on the faculty at Caltech after getting his degrees from MIT and Princeton. At this point, he had been awarded a Nobel Prize in Physics for Quantum Electrodynamics (QED) (but could just as easily have received three by then). He was known by everyone at the place; the girls, the regulars, management and the owner. He felt so comfortable there, he used to go behind the counter and pour himself an orange juice- he never drank alcohol- and grab some doilies to do calculations on. Sagging breasts were Newton’s apple to Feynman.

When the county tried to close it down on account of the downside of public nudity, he was the bar’s only regular customer willing to come forward and testify publicly in court in defense of the place. Feynman’s testimony focused on how the place “provided an important public outlet for various misfits and n’ere-do-wells including thieves, hoodlums, hustlers, petty criminals and one physics professor”.

Once, Professor Feynman was invited to Brasil for a stint as a visiting professor. Since he knew he would be doing a lot of lecturing and explaining difficult concepts to the students there, he spent the whole summer taking Spanish lessons only to learn the day he arrived, that they speak Portuguese in Brasil.

Now let’s let each of our 1000 cells go through 10 more doublings. How many cells will we have then? Well, the same thing will happen. If you double something 10 times, you will have 1000 times as much. So, after we let our 1000 cells each double 10 times, we will have one thousand thousands or a million cells. What will be the diameter of our little tumor at this point?

1mm

and after all those million cells go through 10 more doublings? We’ll have a billion cells and a tumor diameter of

10 mm = 1cm (remember, 2.54 cm’s make an inch.

Our tumor is now one billion cells strong and about the size of a Red Hot, my favorite candy.

The guitar pick is there to show the relative size of the tumor, if you’re not familiar with Red Hots. This is about the size when a tumor can be detected by a CT scan. (This will be important when we apply this to a real-life case.)

Let’s send our tumor through 10 doublings one more time. We now have:

One trillion cells.

The diameter is 10 cm ( = 4 1/2 inches, larger than a softball). It’s hard to believe that the time it takes to go from a spec to something much smaller than a period is the same time it takes to go from a Red Hot to a sphere that’s bigger than a softball, but it’s true. They both take the doubling time, times ten.

Imagine a big ball like that in your brain, your pancreas or your heart. It’s actually bigger than a grown man’s heart. It’s big and people usually die for a number of reasons when their primary tumor gets this big.

A single sentence can sum up all that we’ve learned so far: TEN DOUBLING TIMES WILL MAKE THE DIAMETER GO UP TEN TIMES.

Is everything 100% understood at this point by everybody? This is what I would ask a class of students sitting in front of me and we wouldn’t go on until everyone was on board.

It’s time to apply this to a real-life case of someone you are all familiar with, Steve Jobs.

I do so with the utmost respect to his family;

I think it’s time for a timeline: Note: The timeline is not drawn to scale.

SJ is born] Get’s CA] CA spreads] CA dx’d] 1st Surgery] 2nd Surg] Liver Trans] SJ dies

2/24/55 ? ? 10/2003 7/31/2004 3/2009 2/2011

0 ? ? 48 49 54 56

0 .01 mm 1 cm op report op report autopsy

0 1 1 Billion

Since Steve’s surgeons never released his operative reports (and wouldn’t be expected to), we don’t know the exact size of the tumors removed at surgery. This was not a problem for me when I used to do this calculation for my patients or for other surgeons who asked me to do it for them. So I’ll make a few assumptions so we can get some answers for when Steve got his cancer and when it spread (the question marks, above).

1. The tumor was probably ~1cm in diameter when it was seen on CT Scan in October of 2003 when Steve was 48. If it had been bigger, it would probably would have been detected in a scan Steve had 5 years previously. Mets to the liver were not noted in the CT report of 10/2003 so they were too small to be seen at that time, but were easily seen at the 1st operation nine months later on 7/31/2004. Their size would have been noted in the op report which we do not have access to. The liver mets look like a cobblestone street with bumps (tumors) all over the surface of the liver that, in the absence of pathology, has a smooth surface. The last thing the surgeon wants to feel is bumps all over the surface of the liver because this means the cancer cells have spread away from the primary tumor. Let’s assume the mets were 5 mm in diameter when they opened up the abdomen in 2004. So the mets were “behind” the primary tumor by 1/2 the diameter plus 9 months. Since the surgeons would not have cut up the liver at that first operation, they could have gotten another diameter reading at the second operation or the day they did the liver transplant. They would be able to calculate the doubling time precisely, based on those two diameter readings and the time elapsed between them. Doing this for the primary, assuming Steve’s case was average and his death would have occurred when his primary reached 10 cm, I get a doubling time of 8.8 months.

Here’s how I did it:

Steve died 7 years and 4 months = 88 months after he was diagnosed. During that time Steve’s tumor went from 1 cm to 10 cm in diameter. 10 doubling times elapsed during that time as we already learned. So 88 months is 10 doubling times. That means Steve’s tumor had a doubling time of 8.8 months. Since it takes 30 doublings to go from 1 cell to 1 billion cells ( 1 cell to 1000 = 10 doublings + 1000 to 1,000,000 = 10 more doublings +1,000,000 to 1,000,000,000 = 10 more doublings = 30 doublings total, Steve’s tumor was composed of only 1 cell 30 doublings before it was composed of 1 billion cells = 1 cm. This means 30 x 8.8 months prior to 10/2003 is the day Steve got cancer. 30 x 8.8 = 264 months = 22 years (because there are 12 months in a year). Steve’s cancer started in October of 1981, when he was 26 years and 7 months old.

Using my assumptions for the size of the mets on his liver- again, we would know the sizes exactly if we could see the op reports- we calculate that Steve’s cancer spread to his liver when he was 4 doublings older (if the radius doubles, the volume goes up 8 times which is three doublings (1 to 2, 2 to 4, 4 to 8)) plus 9 months = one doubling ( = 35.2 months = 2 years 11 months older = when Steve was 29 years and 6 months old when his pancreatic tumor metastasized to his liver.

How I did it:

2 times the radius = 8 times the volume = three doublings plus one to account for the 9 months that went by = 4 doublings = 4 x 8.8 = 35.2 months = 2 years and 11 months.

Steve lived a very long time after he got cancer; almost 30 years. Perhaps more impressive is the fact that he lived more than 26 years after the cancer spread to his liver. Steve did have a cancer of the cells in the Islets of Langerhans which grow much slower than those that arise from the exocrine cells of the pancreas. Islet cells produce insulin, an endocrine hormone. Exocrine cells produce enzymes that help you digest proteins, primarily.

Had Steve been unlucky and had his tumor arise in the exocrine portion of the pancreas, he would not have lived as long since these tumors have a much shorter doubling time. With this type, patients usually have about 6 months to live after their diagnosis.

Would it have mattered if Steve had had his first surgery as soon as possible after he was diagnosed? No the cancer had studded his peritoneal cavity by then.

Steve Croft and Walter Isaacson called Steve “stupid” for not going ahead with his surgery as soon as he was diagnosed. They think if he had gotten his surgery when he was diagnosed, it might have saved his life. They are 100% wrong. It wouldn’t have made any difference. The cancer had spread all over his abdomen many years earlier. People can look like idiots when they try to play doctor. Just ask Tony Blair, Andrew Cuomo, Barack Obama and others whose actions in this regard resulted in the deaths of thousands of people from the Covid vaccines. Now we have Croft and Isaacson to add to the list. People like them made Steve feel very bad about himself over the last several years of his life for waiting the nine months. I wish he would have called me. I would have explained this to him and added that the very healthy foods he ate probably prolonged his life, not shortened it. The truth would have made him feel good about himself and the decisions he made throughout his life about his diet. It was considered extreme by many and it was; extremely healthy, that is. Steve eschewed the sugary, oily and processed foods that so many of us have fallen into the habit of eating, in favor of fruits and vegetables, mostly. Please see the video below.