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Toniutto et al. Hepatoma Res 2020;6:50 I http://dx.doi.org/10.20517/2394-5079.2020.40 Page 15 of 21

were likely related to the high heterogeneity of the immunosuppressive drugs added to sirolimus and to
having left the LT centers completely free to manage therapy with steroids.

Studies performed with the other mTOR inhibitor, everolimus [158] , suggested that patients treated with this
inhibitor had significantly lower HCC recurrence rates when compared to those treated with sirolimus
or with CNI. However, it is important to note that everolimus-treated recipients had a shorter follow-up
period and were more frequently transplanted for HCC within the Milan criteria. Overall, based on the
available data from retrospective studies, meta-analyses, and post-hoc assessments of randomized trials, it
seems advisable to consider mTOR inhibition-based immunosuppression after transplantation for HCC,
particularly in patients who exceed the Milan criteria; however, prospective data are required to verify this
claim.

If immunosuppression load appears to serve a determinant role in cancer recurrence [159,160] , it seems
justified to explore immunosuppressive protocols aimed at weaning exposure to immunosuppressive
drugs. The liver is a solid organ that - more than other organs - is suitable for tolerating transplantation
with total withdrawal of immunosuppression without developing rejection. This phenomenon is known as
operational tolerance [161] . A large European prospective study on immunosuppressive treatment withdrawal,
which enrolled 102 adult LT recipients, showed that 40% of them reached the status of operational tolerance
for at least 1 year [162] . The clinical predictors for achieving operational tolerance were a minimal time of
3 years from LT to immunosuppression weaning, the absence of autoimmune liver disease, and recipient
age > 60 years [163] . Regarding the impact of operational tolerance on HCC recurrence, 17 patients
transplanted for HCC were enrolled in a protocol of immunosuppression weaning in Italy [163] . The results
demonstrated that no HCC recurrence was detected in those patients achieving operational tolerance,
while one patient who presented only transient tolerance experienced HCC recurrence after 3 years from
LT and died within 4 years. Despite these promising results, the identification criteria for precisely selecting
patients who may develop operational tolerance remain lacking. Furthermore, if the purpose of utilizing
the development of operational tolerance is to reduce the risk of HCC recurrence, it would be essential to
obtain the suspension of immunosuppression within the first 2 to 3 years after LT, since this is the time
interval during which the recurrence of HCC is more likely [117] .

CONCLUSION
LT remains an effective treatment in patients with unresectable HCC within the Milan criteria or in those
who can be downstaged to being within the Milan criteria; however, HCC recurs despite careful selection
of recipients. The growing demand for LT for HCC is expected, and the probable modest increase in the
availability of organs to allocate for this indication - in the face of a clear decrease in transplantation for
hepatitis C virus-related liver disease - makes the intention to expand the Milan criteria justifiable. The
key question will now be: how can we balance the expansion of the Milan criteria with the risk of an
exponential increase in HCC recurrence after LT? From a mathematical perspective, squaring the circle
is a geometry problem that consists of constructing a square with the same compass and ruler with the
same area as a circle. The study of the relationship between circumference and diameter of the rim has
accompanied the history of humanity since the invention of the wheel. In 212 B.C., Archimedes was the
first to attempt a calculation based on geometry through the method of exhaustion, which consisted of
attempting to trap the circumference between a registered and a circumscribed polygon. Using 96-sided
polygons, he calculated the value of π at 3.14163. Trapping that number in a finite series of digits is a feat
that almost all mathematicians do, and when the mathematician Johan Lambert showed that it is irrational
in 1761, he took the real challenge to calculate the highest number of decimal places to make it as precise
as possible. Lambert’s proof marks a turning point since it shows, that our number cannot be trapped in the
relationship between two numbers in practice (one in the numerator and one in the denominator); thus, it
cannot be “rationalized”.