Take-home Message

Understanding patient's perspective

(Fictional narrative by the doctor)

James Fleck, MD, PhD & João A de Andrade, MD

Anticancerweb 21 (02), 2019

As soon as I finished my work that day, I went home to study and practice the Tower of Hanoi using the websites suggested by Theophilus.

The Tower of Hanoi is a mathematical game consisting of three rods and multiple disks, which can slide into any rod. The puzzle begins with all the disks inserted into the same rod. The disk with the largest diameter goes into the bottom, and the other disks are added in order of diameter to form a cone-shaped stack.

The objective of the game is to transfer all the disks to either one of the other two rods, only one at a time and without ever placing a larger disk over a smaller one. The game becomes increasingly more complex as the number of disks increases. 

The French mathematician François Lucas developed a simple formula [2ⁿ-1] to define the number of movements needed to solve the puzzle, where n represented the number of disks. With an increasing “n”, the process becomes more complex, requiring more sophisticated algorithms.

The Tower of Hanoi is similar to the Rubik’s Cube, a top-selling puzzle game, showing faces of six different colors. However, we now know that the Rubik’s Cube has a finite complexity, whereas the Tower of Hanoi does not.

Using Lucas's formula, when the game starts with three disks, the calculation indicates that the fastest solution should occur with seven moves. Adding only one more disk (n = 4), the number of movements necessary to solve the puzzle goes up to fifteen (figure 1).  

                             

Theophilus had provided me a license to play an online version of the game. It was a website where I could add an unlimited number of disks and my sense of adventure took me as far as five disks! It took me 31 moves to solve it, following a complex and precise algorithm. I felt that I began to understand how Theophilus’ mind operated.

Despite its appearance of simplicity, the Tower of Hanoi requires a keen capacity for abstract thinking, anticipation of movements and a complex contextual view, which could be represented by a “recursive algorithm”, as shown in figure 2.

                                

A recursive algorithm is used to solve a problem, as it fragments a complex decision into a sequence of simpler tasks.

To understand the recursive algorithm, illustrated in Figure 2, it is necessary to assign a letter to each rod. Looking at the Tower of Hanoi and starting from the left side, the first rod would be represented by the letter “a”, the second by the letter “b” and the third by the letter “c”. The circles would represent the positions occupied by the disks on the rods. The lines that connect the circles indicate the movements.

The algorithm showed in figure 2 was constructed to illustrate the solution of the Tower of Hanoi with three disks. Using the simple formula of François Lucas [2ⁿ-1] the minimum number of moves to solve the game is seven, exactly corresponding to the number of lines found in any side of the larger triangle. The letters inside the circles indicative the relative positions occupied by the disk in the rods before and after each movement. The algorithm also illustrates the starting point of the game at the angles of the larger triangle. 

The Tower of Hanoi demonstrates how recursive algorithms might help in the decision-making process. It also gives us an insight into how artificial intelligence and machine learning technologies may break paradigms in cognitive psychology and big data analysis.

After having spent 48 hours obsessing over algorithms, I felt that I had completed my homework! I was looking forward to my “debriefing” with Theophilus and asked my secretary to schedule his next appointment at the end of one afternoon. I wanted us to have plenty of time to exchange ideas and discuss our experiences.

Theophilus arrived on time.

This time, he came by himself and was carrying a cardboard tube. As he entered my office and settled down, I began describing my experience in solving the Tower of Hanoi. I told him that I had progressed to five disks and how impressed I was by the potential value of the “recursive algorithm” as a teaching tool.

He seemed impressed by my performance!

He did not waste any time and proceeded to open the cardboard tube, removing a few sheets of paper that had been neatly rolled up, proudly displaying his work.

He said he liked the material, especially because the language was clear and precise. He felt that could now understand the reasoning behind the diagnostic process and treatment of cancer. He was very excited about the subject and actually built two flowcharts (figure 3), which he enthusiastically explained:

“I named Step 1 “clinical evaluation”. It shows how doctors generate diagnostic hypothesis based on patient’s history and physical exam. The diagnostic hypothesis will be further investigated using imaging, endoscopic techniques, and blood tests. Step 2 is called “morphological evaluation”, and includes invasive methods such as fine needle aspiration that are aimed at getting to a pathological diagnosis in tissue (i.e. whether cancer cells are present or not). At this point, physicians will integrate clinical findings with morphological data toward a more specific diagnosis. During step 3, the extension of the disease (staging) is defined. Based on tumor staging and the patient’s overall health, he or she will be considered for further investigation of comorbidities and whether the tumor can be surgically resected or not. Step 4 is the treatment plan. The physician recommendation should be fully explained and based on evidence from the medical literature. Moreover, the physician also needs to take into consideration the impact of the proposed strategies into one’s social life and family as part of the informed consent process.

 At this moment, he interrupted the explanation, looked at me and started to relate his previous experiences with the steps of the flowchart. He recalled the general practitioner asking for PSA blood test after hearing about his urinary symptoms (step 1). Based on a high PSA value, the attending physician sent him to a urologist, who would further collect material (biopsy) for morphological diagnoses (step 2). At this particular time, Theophilus blamed himself for interrupting the diagnostic flow. Immediately, he asked me to resume the clinical investigation. 

Theophilus also understood that other medical professionals could be involved in the decision-making process, especially when other diseases were present (comorbidities). If the tumor is deemed to be resectable, the comorbidities would need to be further evaluated to better define the risk of surgery.

Suddenly, Theophilus pressed the pen against the paper and followed an upward path to the left of his flowchart, stating that significant comorbidities could restart the cycle with new hypotheses and exams.

We made eye contact and Theophilus said: "Doctor, I recognize now that your work is not easy. It may have an unpredictable number of variables "

I took the opportunity and emphatically replied, "You got it! This is the most important distinction between an exact science and Medicine".

He clearly had come to respect the challenges of Medicine. He was very motivated and could envision some opportunities for machine learning and artificial intelligence in medical decision making.

He was very enthusiastic and pleased to know that doctors categorize knowledge according to different levels of evidence, which would facilitate an eventual interaction with artificial intelligence.

I was pleasantly surprised to see that Theophilus was also a very sensitive man. He recognized the importance of a nuanced and humane approach to each case, sustained by a solid doctor-patient relationship. Without this magical touch, a comprehensive view of patient’s needs cannot be achieved. The multidimensional and integrative nature of Medicine will never be replaced by a machine. Machines have no feeling, no emotions, no ability to coordinate multiple professionals with different personalities. They will not be able to fully understand the emotional dynamics between a patient and their loved ones and nor would they be able to address complex ethical issues.

We were finally in sync!

I have solved the Tower of Hanoi and he gained valuable insights into the medical decision-making process. 

*       Attention: The story 2 will be published sequentially from the PLOT 1 to the PLOT 6, however it will appear backwards. So, you will always see the most recent publication. Just browse in numbered pages located at the bottom of the homepage and start to read the story 2 from the beginning. 

To be continued in PLOT 3 (conflict): Knowledge translation

 

© Copyright 2019 Anticancerweb

 James Fleck, MD, PhD: Full Professor of Clinical Oncology at the Federal University of Rio Grande do Sul, RS, Brazil 2019

Joao A. de Andrade, MD: Professor of Medicine and Chief Medical Officer, Vanderbilt Lung Institute, Vanderbilt University Medical Center, Nashville, TN – USA 2019 (Associate Editor)