ARTICLES

Sci. Rep. Kanazawa Univ.
Vol. 61, pp. 25-38

Modeling immunotherapy and outcomesin acute myeloid leukemia
Yoshiaki NISHIYAMA1 and Nobuaki NISHIYAMA1,2,*
1Graduate School of Natural Science and Technology, Kanazawa University,
2Institute of Liberal Arts and Science, Kanazawa University,

Kanazawa, 920-1192, Japan(Received November 10, 2017 and accepted in revised form February 1, 2018)

Abstract Very recently, we proposed an ordinary differential equation model incorporatingpromotion of regulatory T cell (Tregs) expansion by leukemic cells, which describes co-evolutional
dynamics between leukemic and immune cells in progression of acute myeloid leukemia (AML).
To evaluate the ability of our model to predict effectiveness of immunotherapy for AML, we
performed Monte Carlo simulation of trajectories in phase plane and generated relapse free survival(RFS) curves, which could be compared with clinical data. The resulting RFS curves were in goodaccordance with clinical outcomes reported in immunotherapies of NK cells infusion with/without
Tregs depletion. In addition, our simulation results focusing on consecutive cycles of cell infusion
with/without cell depletion qualitatively accounts for the effectiveness of corresponding clinicalimmunotherapy. The present results suggest that our model may provide valuable information for
future design of immunotherapy in AML.
Keywords. acute myeloid leukemia; computational model; regulatory T cells; bistability;
relapse free survival curve

1 Introduction
Although the vast majority of patients with newly diagnosed acute myeloid leukemia (AML) achieve
cytological complete remission (CR) with induction chemotherapy, they have poor prognosis withan overall 5-year survival rate of approximately 27 % due to relapse, despite following consolidation
therapy. While cell survival leading to AML relapse is associated with clonal heterogeneity alreadyexisting at diagnosis [1], there is accumulating evidence that immunosuppressive AML
microenvironments developing through interaction of immune cells with leukemic cells contributeto disease progression and relapse.
AML antigen-specific cytotoxic T lymphocytes (CTLs) are detected in both peripheral blood andbone marrow of patients and have the capacity to kill leukemic cells. Conversely, over expressionof immunosuppressive molecules in leukemic cells leads to CTL inhibition, proliferation ofleukemic cells and leukemia progression through multiple mechanisms. Regulatory T cells (Tregs)
defined by transcription factor FoxP3 expression play a key role in such immunosuppressive
mechanisms. While Tregs physiologically play critical roles in the immune tolerance to suppress——————————————————————————————————————*Corresponding author E-mail: nnishiya@staff.kanazawa-u.ac.jp

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Modeling immunotherapy and outcomes in acute myeloid leukemia

excessive responses in allergy or autoimmunity[2,3], Tregs have an increased frequency in patientswith AML[4] and suppress the effector T cells (Teffs) including natural killer (NK) cells and CTLs.
The expressions of PD-L1, a ligand for programmed death-1 (PD-1) receptor, indoleamine 2,3dioxygenase(IDO) and CD200, a type-1 transmembrane glycoprotein in leukemic cells promoteformation of Tregs[5-8]. An increased frequency of Tregs induced by such immunosuppressive
molecules results in CTLs suppression and immune evasion.
Allogeneic hematopoietic stem cell transplantation (alloHSCT) as post-remission therapy is still
a promising treatment option to prevent relapsing leukemia, in which donor T cells is expected toeliminate residual leukemia cells. While the curative efficacy of HSCT logically has led to theinfusion of manipulated T cells to have enhanced anti-leukemic cytotoxic ability, or the activationof endogeneous T cells by supportive cytokine therapy for patients without suitable donors, there
has been considerable interest in targeting Tregs mediated-suppression of anti-AML reactive T cells.
In a rodent model with advanced AML, the efficacy of adoptive CTL therapy was improved bypreceding depletion of endogeneous Tregs using IL-2 diphtheria toxin (IL-2DT) [9]. Tregs depletion
by IL-2DT improves CR rates and disease-free survival of patients with relapsed or refractory AML
receiving NK cells infusion[10]. A phase 1 study of Tregs-depleted donor lymphocyte infusion forpatients with relapsed AML showed promising results of improved outcomes[11].
Our aim is to construct a mechanistic mathematical model for leukemia dynamics under the
impact of developing immunosuppressive environment, which contributes to design protocols of
immunotherapy for leukemia. Very recently, we proposed an ordinary differential equation model todescribe the dynamics of three components in AML: leukemic blast cells(L), matured Tregs (Treg)
and matured effective T cells (Teff) including NK cells and CTLs, in which L promotes Treg
expansion[12]. Several mathematical modeling have focused on the interaction of immune cells withleukemic cells[13-15]. These models incorporated the leukemic cell expansion, the promotion ofcytotoxic immune cell expansion by leukemic cells (immunogenicity), the killing of leukemic cellsby cytotoxic immune cells, and offered explanations for leukemia dynamics observed with andwithout chemotherapy. In modeling of the impact of tyrosine kinase targeting on chronic
myelogenous leukemia (CML) dynamics in patients, immunosuppression was formulated by thedecrease of anti-leukemia T cell expansion rate with increasing leukemic cell concentration[16,17].
Recently, in modeling tumor responses and outcomes under immunotherapy combined withradiotherapy, targeting of PD-1, PD-L1 or cytotoxic T-lymphocyte associated protein 4 (CTLA-4)
as immunosuppressive mechanism in cancer progression was distinctly incorporated[18]. Ourmathematical model incorporates leukemic cell-dependent expansion of immunosuppressive Tregs,
which none of these models have considered as a potential target of cancer immunotherapy.
Some modeling interactions between cancer and immune cells allowed multiple steady states andfocused on the effectiveness of transitions between the basins of attraction by hypothetical radiation
therapy and/or chemotherapy [19-21]. While cell-cell interactions including immunosuppressive
mechanism in our model also give rise to two stable steady states corresponding to high and low
concentrations of leukemic cell (L), our preliminary result was that longer CR durations observedin AML could be interpreted as transient dynamics in which the system spends longer time in theneighborhood of basin boundary before returning to the steady state with high concentration of L[12]. In the present study, the distribution of CR durations simulated by our model is translated torelapse free survival (RFS) curve which could be compared with clinical outcomes in
immunotherapy of AML, resulting in the validation of the ability to predict the impact of
immunotherapy such as Tregs targeting and to design immunotherapy protocols for AML.

Y. NISHIYAMA and N. NISHIYAMA

27

2 Material and Methods
The temporal evolution of the model schematized in Fig.1 is governed by a set of 3 kinetic equations
as follows [12].
𝑑[𝐿]𝑑𝑡= 𝑎𝐿 (𝑑[𝑇𝑒𝑓𝑓 ]𝑑𝑡
𝑑[𝑇𝑟𝑒𝑔 ]
𝑑𝑡

𝑝

𝑝

𝑘1

𝑝

𝑘1 +[𝑇𝑒𝑓𝑓 ]= 𝑎 𝑇𝑒𝑓𝑓 () − 𝑑𝐿 [𝐿]
𝑝

𝑝

𝑘2

𝑝

𝑘2 +[𝑇𝑟𝑒𝑔 ]) − 𝑑𝑇𝑒𝑓𝑓 [𝑇𝑒𝑓𝑓 ]

(1)

[𝐿]𝑝

= 𝑎 𝑇𝑟𝑒𝑔 ( 𝑘 𝑝 +[𝐿]𝑝 ) − 𝑑𝑇𝑟𝑒𝑔 [𝑇𝑟𝑒𝑔 ]3

We consider the populations of leukemic blast cells (L), mature regulatory T cells (Treg), andmature effective T cells (Teff), including CTLs and NK cells. We assume that the dynamics of eachcell population (L, Treg, Teff) are due to constant influx and first order decay by apoptosis, in whichconstant influx rates are denoted by aL, aTreg, aTeff, and decay rate constants are denoted by dL, dTreg,
dTeff. Three intercellular interactions were modeled as Hill functions with threshold constants (k1, k2,k3) specifying the strength of intercellular interactions and the Hill coefficient p [12].
We assume that the concentrations of drugs are constant and the decay rate of each cell population(L, Treg, Teff) is proportional only to the cell population ([L], [Treg], [Teff]) during hypotheticalchemotherapy. The rate constants of decay due to apoptosis and drugs are accordingly combined
together as dL, dTreg, dTeff during the chemotherapy. Teffs infusion and Tregs depletion as hypotheticalimmunotherapy were modeled by instantaneous increases and decreases in [Teff] and [Treg],
respectively.
Some parameters (aTreg, aTeff, dTreg, dTeff) in Eq. (1) were estimated using Bayesian inference via aMarkov chain Monte Carlo (MCMC) technique (SAS v.9.4 (SAS Institute, Cary, NC)) with clinicaldata [22] of lymphocytes recovery after induction chemotherapy [12]. While keeping the parameters
aTreg, aTeff, dTreg and dTeff to estimated values by the MCMC method, we searched a wide range of theparameter space of aL, dL, k1 and found parameter ranges characterized by the existence of one or
two stable steady states separated by an unstable fixed point [12]. The values of k2, k3 and p were
fixed to be those in parameter ranges of bistability. However, we cannot exclude the existence ofdifferent dynamics, such as a limit cycle. The values of model parameters in the present study arelisted in Table 1.
Steady states of the model were determined as the intersection of three nullclines (d[L]/dt = 0,d[Teff]/dt = 0 and d[Treg]/dt = 0), which were numerically solved using the nleqslv R-package [23].
The ordinary differential equations in Eq.(1) were numerically solved by ode23 using second andthird order Runge-Kutta-Fehlberg formulas with automatic step-size from MATLAB (Ver. 7.13; The
Mathworks, Inc.).

3 Results
Very recently, we showed that our proposed model offers bistable steady states (denoted as SShi andSSlo) with low and high concentration of leukemic blast cell (L), which could be respectively
interpreted as long-term CR and relapsed disease state [12]. The locations of two stable steady statesin three dimensional space defined by the concentrations of L, Teff and Treg are [L]=100000/μL,[Teff] =0.00031/μL, [Treg]=4955/μL for SShi and [L]=40/μL, [Teff]=283/μL, [Treg]=8/μL for SSlo.
We assume that [L] is approximately to be a constant [L]ss during complete remission (CR) after28

Modeling immunotherapy and outcomes in acute myeloid leukemia

intensive induction chemotherapy. While < 5% as the percentage of leukemic blast cells present
within the total of nucleated cells in bone marrow is given as a clinical criteria for CR in AML, there
is no definitive criteria of peripheral circulating blasts count during CR. According to the clinicalobservation that 0% to 5% peripheral blast cells during CR had no effects on relapse free survival(RFS) time[24], we could set 500/μL as [L]ss during CR with 5% peripheral blast cells and 10000/μL
as normal counts of peripheral nucleated cells. Together, we had the definition of CR duration as thetime interval with less than 500/μL of [L]. In addition, our interpretation of SSlo as long-term CR
was rationalized by the definition of CR duration as [L]=40/μL of SSlo is less than the threshold[L]= 500/μL. SShi of [L]=100000/μL is also consistent with cell counts of peripheral leukemic blast
in relapsed patients with AML[25].

Figure 1. Mechanistic model for crosstalk among leukemic cells and immune cells in AML. The
processes of cell-cell interaction are numbered as follows: 1. Leukemic blast cells targeted by effector
T cells, 2. Effector T cell suppression mediated by Treg, and 3. Treg formation promoted by leukemic
blast cells (L).

Table 1: Parameter values used in the simulation

Symbolcell influx
aL
aTeff
aTreg
cell decay
dL
dTeff
dTreg
cell interaction
k1
k2
k3
hill coefficient
p

Value

0.1 - 1000 μL-1day-1
56.53 μL-1day-1
198.2 μL-1day-1
0.0001 - 1.0 day-1
0.2 day-1
0.04 day-1
1 - 1000 μL-1
160 μL-1
200 μL-1
1 - 10

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29

Fig.2 shows time-courses of concentrations of L, Teff and Treg in the case of hypotheticalchemotherapy applied to the stable steady state (SShi) with high L load. With the definition of CR
duration, it is found in Fig.2 that the system returns to the original steady state (SShi) with transient
increase of Teff concentration during CR. CR duration depends on the arrived location in the phaseplane of [L], [Teff] and [Treg] by hypothetical chemotherapies[12]. It also depends on the arrived
location whether the system is forced to go to SSlo or return to SShi[12].

Figure 2. Time courses of [L], [Teff] and [Treg] after chemotherapy applied for the system staying
at SShi. Solid lines are for [L] (blue) and [Treg] (red) and dots are for [Teff]. Parameter values are
aL=1000, aTeff=56.53, aTreg=198.2, dL=0.01, dTeff=0.2, dTreg=0.04, k1=40, k2=160, k3=200, p=4. The
chemotherapy was applied with enhanced cell decay rate constants (dL =1.0, dTeff =0.68, dTreg =5.0)
during 30 days. The system goes towards the original SShi after the chemotherapy with transient
increase of [Teff].

We performed Monte Carlo simulation of the trajectories from the stable steady state (SShi) withhigh L load after hypothetical chemotherapy applied with random sampling from normal
distributions of three rate constants of cell decay (dL, dTeff, dTreg). The distributions of resulting CR
durations were translated into relapse free survival (RFS) curves as shown in Fig.3. Fig.3 shows
one example of RFS curves in the cases of instantaneous Teffs infusion with/without preceding
Tregs depletion. This result suggests that infusion of Teffs such as NK cells and CTLs accompanying
with conventional chemotherapy is effective for outcome improvement. The assumption of normal
distributions for the rate constants was originated from patient-to-patient variability of sensitivity
for chemotherapy. The effectiveness of Teffs infusion with/without preceding Tregs depletion was
confirmed with normal distributions for dL, dTeff, dTreg with a wide range of standard deviations. In
Fig.3, it is found that the three curves converge to steady ratios of RFS, which correspond to theratios of the trajectories from SShi to SSlo without relapse, compared with the trajectories returning
to the original steady state SShi. We repeated 10 times of generating RFS curves corresponding to30

Modeling immunotherapy and outcomes in acute myeloid leukemia

Figure 3. Relapse free survival (RFS) curves in the cases of Teffs infusion with/without Tregs depletionand no treatment after chemotherapy. The relapse was defined as the event that the system overrides thethreshold of [L] towards SShi from CR states, and the duration of CR as a time interval from thetermination of chemotherapy to the crossing of the threshold. The threshold was set to be [L]=500/μL.
500 trajectories from SShi by applying chemotherapy during 30 days were calculated with dL, dTeff, dTregof the values selected randomly from normal distributions of N(1.0,0.33), N(0.75,0.25), N(5.0,1.67),
respectively. Instantaneous Teffs infusion or Tregs depletion was applied after 0.0001 days from time
point of chemotherapy termination. The instantaneous Tregs depletion was followed by instantaneous
Teffs infusion with a time interval of 0.0002 days. Increment of [Teff] by instantaneous infusion was set
to be 200/μL and decrement of [Treg] by instantaneous depletion was set to be 100/μL. Parameter values
are aL=1000, aTeff=56.53, aTreg=198.2, dL=0.01, dTeff=0.2, dTreg=0.04, k1=40, k2=160, k3=200, p=4. The
number of the trajectories without occurring relapse was plotted against the CR duration of the last
trajectory with relapse.

those shown in Fig.3. The resulting RFS ratios at 700 days after the termination of chemotherapy
were 35.6±2.2%, 54.8±2.7% and 54.8±2.6% for no treatment, Teffs infusion, and Teffs infusion
with preceding Tregs depletion, respectively. Fig.4 shows the impacts of hypothetical chemotherapy
only and Teffs infusion with preceding Tregs depletion after chemotherapy with random samplingfrom normal distributions of three cell decay rates. The incoming trajectories from SShi are divided
into those converging to SShi and to SSlo. More trajectories converging to SSlo in the case of Teffs
infusion with preceding Tregs depletion are observed, which are compared with the case of
chemotherapy only and are consistent with higher ratios of RFS in the cases of Teffs infusion
with/without preceding Tregs depletion, as shown in Fig.3. In our modeling, the effect of treatmentsof chemotherapy combined with/without Teffs infusion with/without preceding Tregs depletion
depends on whether the system overrides the basin boundary and is forced to enter the basin of

Y. NISHIYAMA and N. NISHIYAMA

Figure 4. 10 trajectories from SShi (out of figure) by applying chemotherapy only (upper figure) andchemotherapy followed by instantaneous Teffs infusion with preceding Tregs depletion (lower figure).
10 trajectories from SShi by applying chemotherapy during 30 days were calculated with dL, dTeff, dTregof the values selected randomly from normal distributions of N(1.0,0.33), N(0.75,0.25), N(5.0,1.67),
respectively. Instantaneous Tregs depletion was applied after 0.0001 days from time point ofchemotherapy termination. The instantaneous Tregs depletion was followed by instantaneous Teffs
infusion with time interval of 0.0002 days. Increment of [Teff] by instantaneous infusion was set to be
200/μL and decrement of [Treg] by instantaneous depletion was set to be 5/μL. Parameter values are
aL=1000, aTeff=56.53, aTreg=198.2, dL=0.01, dTeff=0.2, dTreg=0.04, k1=40, k2=160, k3=200, p=4.

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Modeling immunotherapy and outcomes in acute myeloid leukemia

attraction of SSlo from one of SShi. The basin boundary is shown in Fig.5, in which one trajectoryfrom SShi intersects the basin boundary and converges to SSlo, while another trajectory stays in thebasin of attraction of SShi and returns to SShi. The existence of the basin boundary suggests that
infusion of higher number of Teff cells could be associated with treatment efficiency. While theimpact of infused cell number may be crucial for treatments of cell transplantation, some works has
been devoted to clarify the role of multiple cell infusions, which could avoid graft-versus-hostdisease (GVHD) with reduced number of infused cells [26]. As our modeling directs to future designof protocols of combined immunotherapy with chemotherapy in AML, the effectiveness ofconsecutive cycles of instantaneous Teffs infusion with/without preceding Tregs depletion as
hypothetical immunotherapies was examined. Fig.6 shows time schedule of induction chemotherapy
followed by consecutive cycles of instantaneous Teffs infusion with preceding Tregs depletion. The
first Tregs depletion was applied with a time interval (duration 0) after induction chemotherapy.
Time intervals between Tregs depletion and Teffs infusion were set to be constant (duration 1). Timeintervals between two Teffs infusions in the case of Teffs infusion without Tregs depletion weredouble time of duration 1. Fig.7 shows one example of RFS curves for 5 cycles of Teffs infusion
without Treg depletion and Teffs infusion with preceding Tregs depletion, compared with the caseof no treatments. Fig.8 shows dependence of relapse free survival (RFS) rate on the number ofconsecutive cycles of instantaneous Teffs infusion with/without preceding Tregs depletion,compared with the case of no treatment. We repeated 10 times of generating RFS curves
corresponding to those shown in Fig.7. The resulting RFS ratios at 700 days after the termination ofchemotherapy were 36.5±2.7%, 54.1±1.8% and 56.7±2.1% respectively for no treatment, 5 cyclesof Teffs infusion, and 5 cycles of Teffs infusion with preceding Tregs depletion, as shown in Fig.8.
It should be noted that increment of [Teff] by each instantaneous infusion was set to be 40/μL anddecrement of [Treg] by each instantaneous depletion was set to be 20/μL in Fig.7 and 8, comparedwith increment of [Teff] (200/μL) and decrement of [Treg](100/μL) in the case of Fig.3. Fig.9 shows
examples in the cases of 3 cycles and 5 cycles of Teffs infusion with preceding Tregs depletion,suggesting effectiveness of more cycles of the treatment. These results shown in Fig.7, 8 and 9
suggest the effectiveness of consecutive cycles of immunotherapy with less doses of Teffs infusion
and Tregs depletion.

Figure 5. The basin boundary denoted by a dotted plane and two trajectories from SShi (out of figure).
Parameter values are aL=1000, aTeff=56.53, aTreg=198.2, dL=0.01, dTeff=0.2, dTreg=0.04, k1=40, k2=160,
k3=200, p=4. Two trajectories from SShi by applying chemotherapy during (a) 10 days and (b) 30 days
were calculated with the values of (a) dL=1.0, dTeff=0.75, dTreg=5.0 and (b) dL=1.0, dTeff=0.6, dTreg=5.0.

Y. NISHIYAMA and N. NISHIYAMA

Figure 6. Time schedule of induction chemotherapy followed by consecutive cycles of instantaneous
Teffs infusion with preceding Tregs depletion. The first Tregs depletion was applied with a time interval(duration 0) after induction chemotherapy. Time intervals between Tregs depletion and Teffs infusion
were set to be constant (duration 1). Arrows denote time points of instantaneous Teffs infusion andclosed circles denote time points of instantaneous Tregs depletion.

Figure 7. Relapse free survival (RFS) curves in the cases of 5 consecutive cycles of Teff cells infusion
with/without Treg cells depletion and no treatment after chemotherapy. The threshold for relapse was
set to be [L]=500/μL. 500 trajectories from SShi by applying chemotherapy during 30 days were
calculated with dL, dTeff, dTreg of the values selected randomly from normal distributions of N(1.0,0.33),
N(0.75,0.25), N(5.0,1.67), respectively. Instantaneous Teffs infusion or Tregs depletion was applied
after 0.0001 days from time points of chemotherapy termination. The instantaneous Tregs depletion was
followed by instantaneous Teffs infusion with time interval of 0.0002 days. Increment of [Teff] by each
instantaneous infusion was set to be 40/μL and decrement of [Treg] by each instantaneous depletion was
set to be 20/μL. Parameter values are aL=1000, aTeff=56.53, aTreg=198.2, dL=0.01, dTeff=0.2, dTreg=0.04,
k1=40, k2=160, k3=200, p=4. The number of the trajectories without occurring relapse was plotted against
the CR duration of the last trajectory with relapse.

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Modeling immunotherapy and outcomes in acute myeloid leukemia

Figure 8. Dependence of relapse free survival (RFS) rate on the number of consecutive cycles of
instantaneous Teffs infusion or instantaneous Tregs depletion followed by instantaneous Teffs infusion.
The RFS rates after 700 days from the time point of chemotherapy termination are indicated. The RFS
rates were based on RFS curves which were estimated from 500 trajectories. Standard deviations in the
figure were estimated from 10 RES curves. 500 trajectories from SShigh by applying chemotherapy
during 30 days were calculated with dL, dTeff, dTreg of the values selected randomly from normal
distributions of N(1.0,0.33), N(0.75,0.25), N(5.0,1.67), respectively. Instantaneous Teffs infusion or
Tregs depletion was applied after 0.0001 days from the time point of chemotherapy termination. The
instantaneous Tregs depletion was followed by instantaneous Teffs infusion with time interval of 0.0002
days. Increment of [Teff] by each instantaneous infusion was set to be 40/μL and decrement of [Treg]
by each instantaneous depletion was set to be 20/μL. Parameter values are aL=1000, aTeff=56.53,
aTreg=198.2, dL=0.01, dTeff=0.2, dTreg=0.04, k1=40, k2=160, k3=200, p=4.

Y. NISHIYAMA and N. NISHIYAMA

Figure 9. The trajectories from SShi (not shown in figure) after chemotherapy followed by consecutive
cycles of instantaneous Teffs infusion with preceding Tregs depletion: (upper figure) 3 cycles, (lower
figure) 5 cycles. Parameter values are aL=1000, aTeff=56.53, aTreg=198.2, dL=0.01, dTeff=0.2, dTreg=0.04,
k1=40, k2=160, k3=200, p=4. Chemotherapy during 30 days were applied with dL=1.0, dTeff=0.69,
dTreg=5.0. First instantaneous Tregs depletion was applied after 0.0001 days from the time point ofchemotherapy termination. The instantaneous Tregs depletions were followed by instantaneous Teff
infusions with the time interval of 0.0002 days. Increment of [Teff] by each instantaneous infusion was
set to be 40/μL and decrement of [Treg] by each instantaneous depletion was set to be 20/μL.

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Modeling immunotherapy and outcomes in acute myeloid leukemia

4 Discussion
Our model proposed recently was capable of explaining variable CR durations as clinical finding[12].
Especially, long-term CR duration was suggested to associate with transient dynamics in theneighborhood of basin boundary [12]. In the present study, we translated the distributions ofsimulated CR durations into RFS curves which could be compared with clinical data. Curti et al.[27]suggested the effectiveness of allogeneic NK cell infusion as post CR consolidation treatment for
elderly AML patients and identified higher number of infused NK cells as a favorable prognostic
factor. They reported improved outcomes for patients in CR receiving NK cells infusion(n=16, RFS
ratio=0.56 with a median follow-up of 22.5 months), compared with non-NK cells-treatedcontrol(n=15, RFS ratio=0.25). Bachanova et al. focused on the impact of preceding Tregs depletion
followed by NK cells infusion, with the hypothesis that Tregs may suppress the effectiveness of antileukemic NK cell infusion[10]. Patients with refractory AML received Tregs depletion with IL-2
diphtheria toxin (IL2DT), which could selectively deplete IL-2 receptor expressing cells, including
Tregs. They reported that RFS ratio is 33% (n=42) at 6 month after NK cells infusion with adding
IL2DT, compared with 5% for patients (n=15) receiving only NK cells infusion[10]. With ourpresent model, RFS curves were produced numerically by assuming that cell decay rate constantsof L, Teff and Treg characterizing hypothetical chemotherapy are random variables with normal
distributions. Despite such simplifications, the model was qualitatively capable to explain theeffectiveness of a single infusion of NK cells compared with only chemotherapy, as shown in Fig.3.
In general, consecutive cycles of cell infusion with minimal cell number have been used in
immunotherapy, as a single infusion of high number of Teff cells is often associated with higher
incidence of GVHD. Dazzi et al. examined the effectiveness of consecutive cycles of donor
lymphocyte infusion with lower cell number for relapsed patients with chronic myeloid
leukemia[26]. They suggested that the occurrence of GVHD in patients is significantly inhibitedwith consecutive cycles of cell infusion, compared with that in the case of a single administration ofcomparable total cell number, while the difference of remission achievement between the two groups
is not significant. In general, the protocols of NK cells infusion for AML are in line with this study,
in which a single infusion of NK cells is followed by consecutive cycles of IL2 administration forinfused NK cell activation[10,27]. Although there are no clinical studies which could directly
evaluate our results of the impact of consecutive cycles of instantaneous Teffs infusion with/without
preceding Tregs depletion as shown in Fig.8, the effectiveness of consecutive activation ofendogenous T cells and NK cells for AML [28-30] supports the ability of our modeling to predict
the outcomes. Brune et al. [28] reported that consecutive administration of IL2 and histamine
dihydrochloride (HDC) for patients with AML in CR significantly improved RFS, compared withpatients with no treatment, which is comparable with our results shown in Fig.8.

5 Conclusion
Our model might be proposed to be a candidate to contribute to make determination of optimal
dosing and scheduling of immune cell modulation for AML, while the location of the boundary ofbasins inherent in our model remain to be identified for each individual patient.

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