Mathematical modeling allows us to better understand myeloproliferative neoplasms (MPN), a group of blood cancers, emergence and development. We test different mathematical models on an initial cohort to determine the emergence and evolution times before diagnosis of JAK2V617F+ classical MPN (Polycythemia Vera (PV) and Essential Thrombocythemia (ET)). We consider the time before diagnosis as the sum of two independent periods: the time (from embryonic development) for the JAK2V617F mutation to occur, not disappear and enter proliferation, and a second time corresponding to the expansion of the clonal population until diagnosis. We prove that the rate of active mutation occurrence increases exponentially with age following the Gompertz model rather than being constant. We find that the first tumorous cell takes an average time of $63.1 \pm 13$ years to appear and start proliferation. On the other hand, the expansion time is constant: $8.8$ years once the mutation has emerged. These results are validated in an external cohort. Using this model, we analyze JAK2V617F ET versus PV, and obtain that the time of active mutation occurrence for PV takes approximately $1.5$ years more than for ET to develop, while the expansion time was similar. In conclusion, our age-dependent approach for the emergence and development of MPN demonstrates that the emergence of a JAKV617F mutation should be linked to an aging mechanism, and indicates a $8-9$ years period of time to develop a full MPN.

翻译：数学模型有助于我们更好地理解骨髓增殖性肿瘤（MPN）——一类血液癌症——的发生与发展。我们在一个初始队列上测试了不同的数学模型，以确定JAK2V617F+经典MPN（真性红细胞增多症（PV）和原发性血小板增多症（ET））在诊断前的发生与演变时间。我们将诊断前的时间视为两个独立阶段的总和：一是JAK2V617F突变发生、未消失并进入增殖所需的时间（从胚胎发育开始计算），二是对应于克隆群体扩增直至诊断的时间。我们证明，活性突变的发生率随着年龄增长呈指数增加，遵循Gompertz模型，而非恒定不变。我们发现，第一个肿瘤细胞出现并开始增殖平均需要 $63.1 \pm 13$ 年。另一方面，一旦突变发生，其扩增时间是恒定的：为 $8.8$ 年。这些结果在一个外部队列中得到了验证。利用该模型，我们分析了JAK2V617F ET与PV，发现PV的活性突变发生时间比ET长约 $1.5$ 年，而两者的扩增时间相似。总之，我们这种基于年龄的MPN发生与发展研究方法表明，JAKV617F突变的发生应与衰老机制相关联，并指出发展成完全MPN需要 $8-9$ 年的时间。