Optimal Interval for Detection of Molecular Relapse after Stop of TKI in Ph+ ALL Calculating By MRD Kinetics
Authors: Miyamura Koichi , Nishiwaki Satoshi 
Published: October 2019

Abstract
In the era of new-generation tyrosine kinase inhibitors (TKIs), prognosis of Ph+ leukemia (CML/ALL) has dramatically improved. Furthermore the number of CML patients who have stopped TKI is increasing. Usually TKI is stopped in patients who have sustained a deep molecular response. The MRD monitoring interval and threshold of restarting TKI is mostly established in CML. In Ph+ALL patients, prophylactic/maintenance administrations of TKI are used during post hematopoietic stem cell transplantation (HSCT) as well as post chemotherapy. Unlike CML, currently there are no standard methods of detection BCR-ABL in Ph+ALL and no established selection of patients who can stop TKI. In addition, after TKI stopped, there is no consensus about how often to monitor to detect molecular relapse and threshold of restart for TKI. In the current study, we tried to determine the optimal frequency of MRD monitor after the cessation of TKI in Ph+ALL using a mathematical model.
In this model, we determined several agreed items. Mimicking CML, we defined BCR-ABL/ABL ratio of 0.1% as"MR3" and undetectable levels of BCR-ABL transcript as "MR5". We estimate that patients with MR3 and MR5 have 109 and 107 Ph+ cells in the body, respectively. In this perspective, we defined "MR3" and "MR5" as "optimal intervention threshold" and "detection threshold". From the literatures, we determined that growth rate of leukemia is distributed between 1%/day and 100%/day (doubling time of leukemic cells is 1 day). Also, we assumed that single cell have a relapse potency and the growth rate is constant during observation in each patient. The number of Ph+ cells in a MR5 patient is distributed between 1 cell and 1 x 107 (MR5). "Success" is defined as if molecular relapse is detected between MR3 and MR5 and "Failure" is defined as if detected more than MR3.
Table shows the interval from single leukemia cell to MR5 leukemia burden (1 x 107 cells) and the interval from MR5 to MR3 (X100) according to growth rate. Figure is a graph of Table. We calculated using most extreme cases. In the highest growing speed (100%/day), if the number of Ph+ cells is just below detection level (MR5) , it will take 6.6 days to reach MR3 (optimal intervention threshold). Also, if the number of Ph+ cells is only 1 cell, it will take 23.3 days to reach MR5. The other ultimate condition is that the number of leukemia cells is only one in the body and has the slowest growth rate (1%/day). In this case it will take 1620 days (4.4 years) to reach MR5. It was reported that the growth rate of Ph+ cells in the blastic phase of CML is approximately 8% (doubling time 9 days) (Branford. Blood. 2012;119:4264). Applying this value to our model, it will take 209 days to reach MR5 (detection threshold) from single Ph+ cell. If the number of leukemia cells is just below the detection level (MR5), it will take 60 days to reach MR3 (optimal intervention threshold). In this patient a 2 months interval can detect MRD before it reaches to MR3 (Success). If 1 Ph+ cell remains when TKI is stopped, it will reach the MRD detection level (MR5) in 269 days. If Ph+ cells does not appear until this time, this patient is supposed to be cured in this model.
In the clinical setting, growth rate is unknown. Thus in the beginning, a highest growth rate of 100% is applied. (Figure) Monitoring should be performed every 6.6 days for avoiding MRD is detected over MR3 (Failure). If Ph+ cells does not appear until 23.3 days after stop of TKI, which indicate growth rate of 100% is neglected. Because MRD does not increase from MR5 to MR3 during 23.3 days, the growth rate is less than 21.8% from the Table and Graph. At this point, interval MRD monitoring can be prolonged from 6.6 to 23.3 days until 82 days after stop of TKI. Similarly, if Ph+ cells does not appear at 82 days, growth rate is calculated less than 5.8% and interval can be prolonged from 23.3 to 82 days until 290 days. Again if Ph+ cells does not appear, now growth rate is estimated less than 1.6%.
Taken together, soon after stop of TKI, frequent monitoring of MRD is needed. The interval can be prolonged with the passage of time. After allogeneic HSCT, the growth rate of leukemia may be down regulated to some extent according to the GVL effect. At the detection of MRD, interventions such as TKI, donor lymphocyte infusion or chemotherapy are started as soon as possible. Thus the tight monitoring according to the mathematical model is important. The current strategy may be applied to other leukemia in which MRD monitoring by PCR is established.
Figure. Figure.

Disclosures
No relevant conflicts of interest to declare.