A mathematical model for optimizing the indications of liver transplantation in patients with hepatocellular carcinoma

Abstract

BackgroundThe criteria for organ sharing has developed a system that prioritizes liver transplantation (LT) for patients with hepatocellular carcinoma (HCC) who have the highest risk of wait-list mortality. In some countries this model allows patients only within the Milan Criteria (MC, defined by the presence of a single nodule up to 5 cm, up to three nodules none larger than 3 cm, with no evidence of extrahepatic spread or macrovascular invasion) to be evaluated for liver transplantation. This police implies that some patients with HCC slightly more advanced than those allowed by the current strict selection criteria will be excluded, even though LT for these patients might be associated with acceptable long-term outcomes.MethodsWe propose a mathematical approach to study the consequences of relaxing the MC for patients with HCC that do not comply with the current rules for inclusion in the transplantation candidate list. We consider overall 5-years survival rates compatible with the ones reported in the literature. We calculate the best strategy that would minimize the total mortality of the affected population, that is, the total number of people in both groups of HCC patients that die after 5 years of the implementation of the strategy, either by post-transplantation death or by death due to the basic HCC. We illustrate the above analysis with a simulation of a theoretical population of 1,500 HCC patients with tumor size exponentially. The parameter λ obtained from the literature was equal to 0.3. As the total number of patients in these real samples was 327 patients, this implied in an average size of 3.3 cm and a 95% confidence interval of [2.9; 3.7]. The total number of available livers to be grafted was assumed to be 500.ResultsWith 1500 patients in the waiting list and 500 grafts available we simulated the total number of deaths in both transplanted and non-transplanted HCC patients after 5 years as a function of the tumor size of transplanted patients. The total number of deaths drops down monotonically with tumor size, reaching a minimum at size equals to 7 cm, increasing from thereafter. With tumor size equals to 10 cm the total mortality is equal to the 5 cm threshold of the Milan criteria.ConclusionWe concluded that it is possible to include patients with tumor size up to 10 cm without increasing the total mortality of this population.

The Optimum Level of Meld to Minimize the Mortality on Liver Transplantation Waiting List, and Liver Transplanted Patient in São Paulo State, Brazil

“…This paper applied a model originally designed to optimize liver transplantation in liver tumors patients 3 . The model provides a mathematical framework upon which an optimal strategy for organ allocation can be planned considering the MELD scores of patients in the LTWL.…”

“…At our hospital, the recipients with a MELD score of 20–29 received organs fulfilling at least one extended donor criterion significantly more frequently. For the present study, we applied the model originally designed to optimize liver transplantation in patients with liver tumors 3 . It provides a mathematical framework upon which an optimal strategy for organ allocation can be designed considering the MELD scores of patients in the LTWL.…”

“…Numerous studies have investigated, with varying results, the prognostic value of the MELD score for early and late posttransplant survival [1][2][3][4] .…”

“…Walter de Biase SILVA-NETO 1 , Claudemiro QUIRESE 1 , Eduardo Guimarães Horneaux de MOURA 2 , Fabricio Ferreira COELHO 3 , Paulo HERMAN 3 ABSTRACT -Background: The treatment of choice for patients with schistosomiasis with previous episode of varices is bleeding esophagogastric devascularization and splenectomy (EGDS) in association with postoperative endoscopic therapy. However, studies have shown varices recurrence especially after long-term follow-up.…”

Impact of HCV antiviral therapy on the Liver Transplantation Waiting-List assessed by mathematical models

“…In addition, as the duration of infection increases, the proportion of new patients with cirrhosis will double by 2020 in an untreated patient population. In previous papers our group[14][15][16][17][18][19], proposed a series of mathematical models dealing with distinct aspects of liver transplantation. Some of the models were simple like the present one and some more complex.…”