Cell Dose on Engraftment After Scts: Personalized Estimates Based on Mathematical Modeling

ORIGINAL ARTICLE The impact of CD34 þ cell dose on engraftment after SCTs: personalized estimates based on mathematical modeling

T Stiehl1,ADHo2 and A Marciniak-Czochra1,3

It is known that the number of transplanted cells has a significant impact on the outcome after SCT. We identify issues that cannot be addressed by conventional analysis of clinical trials and ask whether it is possible to develop a refined analysis to conclude about the outcome of individual patients given clinical trial results. To accomplish this, we propose an interdisciplinary approach based on mathematical modeling. We devise and calibrate a mathematical model of short-term reconstitution and simulate treatment of large patient groups with random interindividual variation. Relating model simulations to clinical data allows quantifying the effect of transplant size on reconstitution time in the terms of patient populations and individual patients. The model confirms the existence of lower bounds on cell dose necessary for secure and efficient reconstitution but suggests that for some patient subpopulations higher thresholds might be appropriate. Simulations demonstrate that relative time gain because of increased cell dose is an ‘interpersonally stable’ parameter, in other words that slowly engrafting patients profit more from transplant enlargements than average cases. We propose a simple mathematical formula to approximate the effect of changes of transplant size on reconstitution time.

Bone Marrow Transplantation (2014) 49, 30–37; doi:10.1038/bmt.2013.138; published online 23 September 2013 Keywords: SCT; hematopoiesis; mathematical modeling

INTRODUCTION of benefit to individuals. It cannot be ruled out that some Hematopoietic SCT is a well-established clinical procedure.1 subpopulations benefit stronger from an intervention than Clinical trials have confirmed the impact of transplant size on averaged data suggest, whereas others may show worse, maybe fast and sustained engraftment.2 Accordingly, lower bounds on critical outcome, although average outcome improves. Figure 1 the number of transplanted cells have been defined to ensure safe demonstrates that subpopulations of trial groups may react treatment. Nevertheless, individual engraftment times differ differently to different treatment interventions even if the widely and delayed engraftment occurs.3–5 aggregate outcome for the different interventions does not differ The time before neutrophil reconstitution is clinically meaningful significantly. Only if aggregate data reflect individual responses, it for various reasons: (i) infections during neutropenia account for a is possible to directly apply trial results to individuals. Unlike considerable number of complications and deaths,6–9 especially in clinical trials, simulations allow to compare different treatments cord blood transplantations.10–13 (ii) Several studies propose an for the same individual. Using mathematical modeling, we focus association between rapid neutrophil recovery and long-term on the dependence of reconstitution time on transplanted cell engraftment14 or high marrow donor chimerism.15 (iii) In some dose. trials, transplant-related mortality or poor long-term outcome are Another methodology to compare the impact of different associated with delayed neutrophil engraftment.16–18 interventions is the case–control approach. This requires matching In almost every trial, there exist patients with recovery times of different patients with respect to traits possibly influencing the distant from average. The dose of transplanted cells has an impact outcome. However, in the considered case, such traits have not on the time to neutrophil reconstitution2,19 and is a tunable yet been established. parameter; therefore, it is important to know whether slowly In this manuscript, we address the question how aggregate data reconstituting patients might benefit from increased numbers of from clinical trials on reconstitution after SCT can be interpreted on transplanted cells. As such patients cannot be identified before the level of individuals and, based on this, whether outcome for transplantation, it is difficult to apply prospective clinical trials. slowly reconstituting patients could be improved by increasing the Therefore, it remains unknown how much these patients might transplanted cell numbers. We also ask how clinical recommenda- profit from increased numbers of transplanted cells. tions concerning the minimal number of transplanted cells apply As SCT can only be performed once at a given time for a given to individual patients. To take into account effects of cell source patient, direct comparison of effects of different modifications for and conditioning, we investigate the impact of higher transplant a given individual is not possible. In practice, this problem is doses on neutrophil engraftment separately for all common modes circumvented by the comparison of randomized study groups. of SCT, viz the autologous, allogeneic or cord blood stem cells, in This approach gives an idea of the average impact of different presence or absence of cytokine administration, and myeloablative modifications on clinical outcome, but fails to provide a measure vs reduced intensity conditioning.

1Interdisciplinary Center for Scientiﬁc Computing (IWR), University of Heidelberg, Heidelberg, Germany; 2Department of Hematology and Oncology, University-Hospital of Heidelberg, Heidelberg, Germany and 3BIOQUANT Center, University of Heidelberg, Heidelberg, Germany. Correspondence: T Stiehl, Interdisciplinary Center for Scientiﬁc Computing (IWR), University of Heidelberg, Im Neuenheimer Feld 294, Heidelberg D-60120, Germany. E-mail: [email protected] Received 18 April 2013; revised 5 July 2013; accepted 3 August 2013; published online 23 September 2013 Engraftment after SCT T Stiehl et al 31 30 30

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5 5 A B CD E A B C D E Figure 1. Aggregate data fails to describe response of individual patients. (a) The figure displays results of a hypothetical clinical intervention. We compare an intervention group of 1000 randomly chosen people to an independent control group of 1000 randomly chosen people. The end point, for example, time to recovery from a disease, is indicated on the vertical axis. We assume a normal distribution with mean 15 and s.d. 2 for the control group. The control group is displayed in E. The time of recovery that a patient needs without an intervention is referred to as the intrinsic time of recovery. Although aggregate data sets in A–D look practically identical and do not differ significantly (P ¼ 0.781 in Kruskal–Wallis test), the outcome at the level of individuals can be considerably different. In A, time of recovery of each individual patient is reduced by 10% because of the intervention. In this case, the change of average values corresponds to changes on the individual level. In B, patients with intrinsic long recovery times, above 19 days, benefit stronger, their recovery time is reduced by 20%. In C, the intervention is disadvantageous for 50% of patients with intrinsically long recovery times, above 19 days. Their recovery is delayed randomly between 0 and 50%, whereas all other patients benefit from a 10% reduction of their intrinsic recovery time. Although mean values improve, the intervention is in this case dangerous for the critical group of patients with long intrinsic recovery times. In D, the intervention leads to a 10% reduction of intrinsic recovery times between 13 and 17 days. Intrinsic recovery times of o13 days are delayed by 30% because of the intervention and intrinsic recovery times of 417 days are reduced by 40%. In this case, the intervention is beneficial for some patients and disadvantageous for others. The average over data suggests an improvement because of the intervention, although this is not the case for 415% of treated patients. The examples demonstrate that aggregate data are not suitable for drawing conclusions at the level of individuals. Although study outcome is identical in cases A–D, in cases B and D it would be helpful to develop a screening procedure that may distinguish between patients that benefit from the intervention and those who do not, whereas in case A, this is not necessary. Panel (b) depicts the outcome of each intervention applied to three different groups of 100 patients. In this case, statistical variability further confuses the outcome. Boxes show the 25th–75th percentile, whiskers denote 97.5 and 2.5 percentiles, values beyond the whiskers are depicted as circles, median values are indicated as horizontal lines.

So far such aspects were not approached using mathematical on a comparison to patient data. Having shown that model behavior is in modeling. The existing models of healthy hematopoiesis are agreement with clinical observations, we apply it to estimate individual either mostly phenomenological20–24 or solely based on treatment responses. regulation in the stem cell pool24–26 and do not describe regulation of the whole system of differentiating cells. The latter Clinical data is crucial for reconstitution after large perturbations and for Table 1 contains a listing of literature sources used to calibrate the model. quantitative analysis of post transplant dynamics. As various diseases are treated by PBSC transplantations (PBSCT), we focus Our reasoning is as follows. We devise a mathematical model on trial data including different diagnoses. We consider the following for neutrophil reconstitution after SCT of single patients. The scenarios used in current clinical practice: autologous PBSCT with and model is calibrated based on patient data and on measurements without post transplant cytokine administration,19,27 HLA-identical allogeneic PBSCT with28,29 and without30,31 post transplant cytokine found in literature. As reconstitution kinetics differ among 32,33 individuals, we investigate large groups of heterogeneous patients administration, haplo-identical PBSCT and umbilical cord blood transplantation.34 We also consider the impact of reduced conditioning to consider a wide spectrum of individual responses and to regimens.35 To compare simulations of leukocyte counts after autologous compare them with aggregate data. Estimation of individual PBSCT with patient data, we use single patient data of one arm (containing response based on aggregate data also requires the simulation patients treated with selected PBSCs) of the trial from.19 For this task, we of large patient groups that resemble the populations of clinical obtained original data of representative patients from Klaus et al.19 trials. We therefore apply the model to groups of patients with random interindividual differences and validate this approach Mathematical model based on data from clinical trials. On the basis of simulations of The model is a modification of the model developed by Marciniak–Czochra patient groups, we show that absolute reduction of reconstitution and colleagues.36–38 Unlike in the models of Marciniak–Czochra and times due to a fixed additional amount of transplanted cells colleagues,36–38 proliferation rate in the present model is cytokine differs strongly between individuals, whereas relative reduction is dependent only for primitive cells, as suggested by experiments in approximately conserved and equals the relative reduction of Thornley et al.39 Model structure is presented in Figure 2. Mathematical average reconstitution times determined in clinical trials. equations are found in Supplementary Methods (section 1) and in We provide a formula to approximate this effect and conclude Supplementary Figure 1. that patients prone to delayed engraftment benefit stronger We assume that mature blood cells are maintained by a population of hematopoietic stem cells and that there exists a finite number of from larger transplants than patients with average reconstitution 40 times. maturation stages. This structure is accepted in clinical practice. As leukopenia is responsible for most severe complications during aplasia, we only consider leukopoiesis. As neutrophils constitute the majority of peripheral WBC, the model is limited to granulopoiesis. The maturation MATERIALS AND METHODS stages considered include stem cells, different CFUs, different We first summarize clinical trial data used for this work. Then we formulate granulopoietic precursors and mature cells; they have been chosen our mathematical model and calibrate it based on a literature review and based on an extensive literature search (see Supplementary Methods,

& 2014 Macmillan Publishers Limited Bone Marrow Transplantation (2014) 30 – 37 Engraftment after SCT T Stiehl et al 32 Table 1. Overview of clinical trials used to calibrate and validate the model

Scenario Patient age Disease Conditioning Median Patient Reference CD34 þ cell count dose per kg

Autologous PBSC 44 (37–66) MM Melphalan (100 mg/m2 body 3.6 Â 106 118 19 without post transplant surface at days À 3 and À 2) cytokine administration 39 (11–65) Mostly AML, Heterogeneous 9.5 Â 106 215 27 ALL, MM, NHL Autologous PBSC with 48.5 (11–70) Mostly AML, Heterogeneous 8.8 Â 106 30 27 post transplant ALL, MM, NHL cytokine administration Allogeneic, HLA- 29.5 (9–51) AML, ALL, NHL, Heterogeneous 4.7 Â 106 18 30 identical PBSC without HL, MM, CML post transplant cytokine administration 38 (20–52) Mostly AML, Heterogeneous 12.3 Â 106 37 31 ALL NHL, HL Allogeneic, HLA- 38(22–55) CML, MM, Etoposide (1800 mg/m2) on day 7.73 Â 106 21 28 identical PBSC with AML, ALL, CLL, À 7, cyclophosphamide (60 mg/kg post transplant MDS, NHL per day) on days À 6 and À 5 and cytokine administration TBI (2 Gy twice daily) on days À 3 to À 1 34 (19–49) Mostly AML, Heterogeneous 6.7 Â 106 33 29 CML Haplo-identical PBSC 29 (2–63) AML, ALL 8 Gy TBI on day À 9 in a single 12.8 Â 106 255 32 without post transplant fraction, thiotepa (5 mg/kg daily) cytokine administration on days À 8 and À 7; fludarabine (40 mg/m2 daily) from days À 7to À 3 and rabbit antithymocyte globulin at 5 mg/kg daily from days À 5to À 2 Haplo-identical PBSC 8(o1–44) Mostly ALL, Heterogeneous 5.5 Â 106 74 33 with post transplant AML cytokine administration Placental blood o2: 20%, 2–5: 23%, Mostly ALL, Heterogeneous Different 562 34 transplantation with or 6–11: 24%, 12–17: AML groups without HLA 15%, X18: 18% mismatches Comparison of different Group 1: 34 (19–61) Group 1: Group 1: fludarabine (30–40 mg/m2 Group 1: Group 35 conditioning regimes Group 2: 49.5 (22–61) mostly CML per day i.v. from days À 9to À 6) 6.3 Â 106, 1: 18, before allogeneic PBSC Group 2: and BU (3.2 mg/kg single dose i.v. Group 2: Group transplantation without mostly MM per day for days À 5to À 2) 5.9 Â 106 2: 22 post transplant Group 2: fludarabine (30 mg/m2/ cytokine administration day i.v. for days À 6to À 2) and melphalan (70 mg/m2 per day i.v. for 2 days À 2to À 1) Abbreviations: MM ¼ multiple myeloma; (N)HL ¼ (non)hodgkin lymphoma.

section 1.21). Cell dynamics are determined by proliferation, differentiation Simulations show that the number of transplanted hematopoietic and death. Each of the progeny cells arising from division either remains in stem cells and long-term culture-initiating cells (LTC-ICs) does not the same maturation stage as the parent cell, which is referred to as self- inﬂuence short-term reconstitution (Supplementary Figure 2). This is in renewal, or progresses to the subsequent more mature stage, which is line with telomere studies42 and demonstrates independence of short- referred to as differentiation. We assume that the proliferation of all cell term reconstitution of primitive cell parameters. types is regulated by cytokines, such as G-CSF and that the fraction of self- 36,41 renewal depends on cytokine levels. Simulation of large patient groups For simulation of large patient groups, we generate random perturbation of cell parameters; see Supplementary Methods (section 3). Comparison Simulations, parameter choice and validation of the model with data is shown in Figure 4 and Supplementary Figure 3. We use the following data to calibrate the model: composition of To study the impact of transplanted cell dose on individual engraftment, peripheral CD34 þ grafts, mitotic activity of immature cells, half-life we consider absolute and relative gain of reconstitution time. Absolute of mature cells, steady state cell counts and change of proliferation activity gain describes by how many days the reconstitution is reduced if the under cytokine stimulation. Unknown parameters were estimated to satisfy transplanted cell dose is increased. Relative gain expresses the gain in clinical observations; see Supplementary Methods (section 2) and percent. Both indices can be calculated using averaged data from clinical Supplementary Tables 1–3. trials. We use this averaged absolute and relative time gains as candidate We conclude that our model can be applied to simulate clinical data, as predictors for individual time gains. To compare both modes of prediction, (i) simulated steady state population sizes, generation times and we simulate clinical trials and compare for each virtual patient the granulocyte half-life are in good agreement with data from literature; ‘effective’ (simulated) gain with the gain predicted by average absolute see Supplementary Tables 4 and 5. (ii) All individual patterns of leukocyte or relative changes obtained from clinical trials. For details see reconstitution observed in clinical data can be reproduced; see Figure 3. Supplementary Methods (section 4).

Bone Marrow Transplantation (2014) 30 – 37 & 2014 Macmillan Publishers Limited Engraftment after SCT T Stiehl et al 33 Feedback s, sˆ fixed additional amount of cells decreases for average patients with increasing transplant size. On the individual level, this result Differentiation 1-a 1-a is reflected by the approximation formula (1). Increasing cell dose 1 7 6 6 from 10 to 2 Â10 cells leads to a reduction of reconsti- 6 log10ð2Â10 ÞÀ8:4 tution time by 1 À 6 Â 100% 12% ffi 2 days, State 1: log10ð10 ÞÀ8:4 HSC State 2: State 7: whereas increasing cell dose by the same amount from LTC-1C State 8: myelocyte a 3 106 to 4 106 cells leads to a reduction only by d1 Self- 7 neutrophils/ Â Â 6 rene- d2 leukocytes log10ð4Â10 ÞÀ8:4 Death d 1 À 6 Â 100% 6% ffi 1 day. wal a 7 log10ð3Â10 ÞÀ8:4 1 d8

Relative gain of reconstitution time is conserved among individuals Cytokines To estimate how increased transplant sizes improve outcome of extremely slowly reconstituting patients, we repeated the simulations for different groups of patients: group 1, o20 days for (+) +––3 Â 106 cells per kg; group 2, 20–30 days; and group 3 430 days. Simulation results show that relative time gain is similar for patients with average and with short reconstitution times; see Proliferation Self-renewal Death Supplementary Figure 4. This implies that the absolute time gain is larger for slowly reconstituting patients. Non mature cells Mature cells

Figure 2. Structure of the mathematical model. (a) Proliferation and Transplant enlargement above the clinically established threshold differentiation of cells in different stages of granulopoiesis. In self- might have impact on recovery times of slowly reconstituting renewal, at least one of the two daughter cells stays in the same patients stage as the mother cell; in differentiation, cells move to the next downstream compartment. (b) Cell behavior is regulated by The relative reduction of the reconstitution time because of X cytokine feedback (for example, G-CSF). Shortage of mature cells additional CD34 þ cells is calculated using the formula (1), with causes cytokine levels to increase. Cytokines enhance proliferation C ¼À8.4±0.71. For the subpopulation of patients with reconsti- and self-renewal of immature cell populations, and these lead to tution times between 20 and 30 days, we obtain C ¼À8.1±1.1. faster production of mature cells that normalizes cytokine levels. Above, we calculated the impact of adding 106 CD34 þ cells to a Cytokines also increase the half-life of mature cells in the blood transplant of 3 Â 106 cells, which was 6%. In case of average stream. The effect of cytokines on each maturation stage is chosen patients with reconstitution times between 15 and 20 days, this in accordance to literature. leads to reduction by B1 day. In case of a slowly reconstituting patient with reconstitution time of 30 days, this leads to 6 log10ð4Â10 ÞÀ8:1 a reduction by 1 À 6 Â 100% 8% ffi 2:4 days, Approximation formula for the relative change of reconstitution log10ð3Â10 ÞÀ8:1 time depending on cell dose that is, the gain is more than twofold. If we increase dose from 6 7 Linear regression leads to formula (1) 2 Â 10 to 1.5 Â 10 CD34 þ cells per kg of body weight, we obtain an estimated reduction of reconstitution time of 7 log10ðx þ XÞþC log10ð1:5Â10 ÞÀ8:1 Relativegain ¼ 1 À Â 100% ð1Þ 1 À 6 Â 100% 47% for this group. log10ð2Â10 ÞÀ8:1 log10ðxÞþC estimating the relative gain of reconstitution time because of X cells per kg of body weight added to a transplant of x cells per kg of body weight. Relative change of neutrophil reconstitution time from clinical C is a constant depending on the measure of cell dose; see Supplementary trials reflects individual patient’s response Methods (section 5). It is an important question how data from clinical trials can be optimally used to estimate treatment response of individual patients. We use the in silico approach to tackle this question. Clinical trials RESULTS usually record average reconstitution times for different ranges of Transplant enlargement above the clinically established threshold transplant size. We compare two algorithms of estimating reduction has little impact on recovery of average patients of individual hematopoietic reconstitution using these data: (1) The proposed model is in agreement with clinical data (Figures 3–4) absolute reduction of reconstitution time of an individual due to an and other data from literature (Supplementary Tables 4–5). Our additional fixed amount of cells is estimated by absolute reduction of in silico approach allows to investigate individual benefits from average reconstitution time of a large group of patients and (2) additionally transplanted cells. We simulate the impact of a fixed relative reduction of reconstitution time of an individual is estimated amount of cells added to transplants of different sizes. Figure 5 by the relative reduction of average reconstitution time of a large summarizes relative and absolute reduction of reconstitution time group of patients. Differences between simulated and estimated for 2000 virtual patients after autologous transplantation without changes are shown in Supplementary Figure 5. The s.d. of the post transplant cytokine administration. For other modes of difference between predicted and effective values, which is a transplantations similar results are obtained. measure of the number of predictions that strongly deviate from Clinical trials suggest the existence of a minimal stem cell dose effective values, is up to 2.5 times larger if predictions are based on necessary for fast reconstitution2 and conclude that, above this absolute differences. This implies that it is more appropriate to use minimal dose, additionally transplanted cells have little effect.2 therelativechangeofaveragereconstitution times to estimate the Simulation results justify this reasoning, as: (i) above the threshold individual benefit. We now consider the subpopulation that needs of about 2 Â 106 cells per kg of body weight, interindividual 20 days or more to engraft after transplantation of 3 Â 106 CD34 þ heterogeneity of reconstitution times decreases. The interquartile per kg of body weight. We want to estimate how reconstitution time range is 4 days for a hypothetical transplant of 0.5 Â 106 and decreases if we increase cell dose from 3 Â 106 per kg to 107 per kg. o1 day for 2 Â 106 cells per kg (Figure 5). (ii) The benefit from a Estimation based on average absolute difference obtained from

& 2014 Macmillan Publishers Limited Bone Marrow Transplantation (2014) 30 – 37 Engraftment after SCT T Stiehl et al 34

20 Patient 1 Patient 9 Patient 17 Patient 2 Patient 10 Patient 18 15 Patient 3 Patient 11 Patient 19 cells/l blood] 9 Patient 4 Patient 12 Patient 20 10 Patient 5 Patient 13 Patient 21 Patient 6 Patient 14 Patient 21 5 Patient 7 Patient 15 0 Patient 8 Patient 16

Leucocytes [10 Leucocytes –10 0 10 20 30 40 50 Time [days post-transplant]

25 12 12 Simulation (parameterset 1) Simulation (parameterset 2) Simulation (parameterset 3) 20 10 10 8 8 15 cells/l blood] cells/l blood] cells/l blood] 9 9 6 9 6 10 4 4 5 2 2 0 0 0 Leucocytes [10 Leucocytes Leucocytes [10 Leucocytes –10 0 10 20 30 40 50 –10 0 10 20 30 40 50 [10 Leucocytes –10 0 10 20 30 40 50 Time [days post-transplant] Time [days post-transplant] Time [days post-transplant]

20 20 20 Leucocyte recovery to 1×108/l Leucocyte recovery to 1×108/l Leucocyte recovery to 1×108/l Leucocyte recovery to 5×108/l Leucocyte recovery to 5×108/l Leucocyte recovery to 5×108/l Leucocyte recovery to 1×109/l Leucocyte recovery to 1×109/l Leucocyte recovery to 1×109/l 15 15 15

10 10 10 Time [days] of recovery Time [days] of recovery Time [days] of recovery 5 5 5 106 107 106 107 106 107 CD34(+) cells/kg CD34(+) cells/kg CD34(+) cells/kg Figure 3. Comparison of simulations to single patient data (a) All individual patterns of leukocyte reconstitution observed in clinical data can be reproduced using different model parameters (see Supplementary Tables 3–5). Pattern 1 (left): slow monotonous increase of the number of mature cells, pattern 2 (right): fast increase of the number of mature cells during the ﬁrst period and nearly constant levels of mature cells during the second period and pattern 3 (middle): other patients, including those with oscillating levels of mature cells. Individual patient data were provided from the authors of the trial by Klaus et al.19 Graft size was set to 3.6 Â 106 CD34 þ cells per kg body weight in agreement with clinical data; see Supplementary Table 2. (b–d) Dependence of reconstitution time on logarithmic transplant size for different representative parameter sets. (b) Parameter set 1, (c) parameter set 2, (d) parameter set 3 (see Supplementary Tables 3–5).

aggregate data underestimates time gain by 7 days (s.d. 11 days), The combination of mathematical modeling and clinical trial data whereas estimation based on the average relative time gain derived leads to new quantitative and qualitative insights into medical from aggregate data underestimates the gain by only 2 (s.d. 6.4 days) treatment procedures. The proposed model implies that relative days. This demonstrates that the average relative time gain is a change in reconstitution time because of enlargement of transplant better measure of individual time gain and is accurately conserved (i.e., increase in CD34 þ cell dose) is an interpersonally stable between different patient subpopulations, whereas the use of parameter decreasing with increasing transplant size. This parameter average absolute time gains may underestimate benefits for slowly can be estimated from clinical trial data. The finding implies that the engrafting patients. absolute time gain because of additionally transplanted cells is In summary, relative change in reconstitution time is a better larger in slowly reconstituting patients who, accordingly, could profit measure of benefit as it is conserved over different patients and from higher counts of transplanted cells in clinical practice. We can be estimated by average relative change of aggregate data. propose a simple formula that allows estimating this effect for cell Individual relative change is approximately equal to the relative doses up to about 5 Â 107 CD34 þ cells per kg of body weight. change of averaged values from large patient groups. Our study confirms, at the individual patient level, the existence of a lower bound on cell dose for successful transplantation, which is 2–3 Â 106 cells per kg in clinical practice2,43 and has been DISCUSSION derived from clinical trials. Our results support the finding that for We developed and validated a mathematical model of short-term average patients transplant sizes above this threshold have little neutrophil reconstitution after different kinds of SCTs. This impact,2,43 but they underline that this may not be the case for approach allows quantifying effects that are not estimable via slowly reconstituting patients. conventional statistical analysis of clinical trials and that cannot be The absolute reconstitution time may differ strongly among concluded from aggregate data. The in silico approach offers the individuals. The model suggests that these variations stem from possibility of directly comparing different interventions for the interindividual differences in parameters of hematopoiesis. Thus, a same virtual patient. precise prediction of absolute reconstitution time is not possible.

Bone Marrow Transplantation (2014) 30 – 37 & 2014 Macmillan Publishers Limited Engraftment after SCT T Stiehl et al 35

Autologous Allogeneic without GCSF Allogen with GCSF 1.0 1.0 1.0

0.8 0.8 0.8

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Simulations (CD34+/kg) 0.4 Simulations (CD34+/kg) 0.4 0.4 Simulations (CD34+/kg) 6.7 Mio (n =2000) 9 Mio (n =2000) 7.7 Mio (n =2000) 9 Mio + GCSF (n =2000) 4.7 Mio (n =2000) Data (CD34+/kg) 0.2 Data (CD34+/kg) 0.2 12.3 Mio (n =2000) 0.2 6.7 Mio (n =33) 9.5 Mio (n =215) Data (CD34+/kg) 7.7 Mio (n =21) 8.8 Mio + GCSF(n =30) 4.7 Mio (n =18) 12.3 Mio (n =37)

Fraction of engrafted patients of engrafted Fraction 0.0 patients of engrafted Fraction 0.0 patients of engrafted Fraction 0.0 0510 15 20 25 30 35 0510 15 20 25 30 35 0 5 10 15 20 25 30 35 Time [days] Time [days] Time [days]

Haplo-identical UCB RIC 1.0 1.0 1.0

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Simulations (NC/kg) 0.6 Simulations (CD34+/kg) 0.6 20 Mio (n =2000) 0.6 2 Mio+GCSF (n =2000) 30 Mio (n =2000) 5.5 Mio+GCSF (n =2000) 85 Mio (n =2000) 0.4 6.3 Mio+GCSF (n =2000) 0.4 260 Mio (n =2000) 0.4 Simulations (CD34+/kg) 12 Mio (n =2000) Data (NC/kg) Data (CD34+/kg) 7–24 Mio (n =162) 6 Mio, ablative (n =2000) 0.2 < 4 Mio+GCSF (n =65) 0.2 25–49 Mio (n =198) 0.2 6 Mio, RIC (n =2000) > 4 Mio+GCSF (n =68) 50–99 Mio (n =121) Data (CD34+/kg) 5.5 Mio+GCSF (n =74) >100 Mio (n =65) 6.3 Mio, ablative (n =18) 12.8 Mio (n =175) 5.8 Mio RIC (n =12) Fraction of engrafted patients of engrafted Fraction patients of engrafted Fraction 0.0 0.0 patients of engrafted Fraction 0.0 0 10 2030 40 0 20 40 60 80 100 0 10 20 30 40 Time [days] Time [days] Time [days] Figure 4. Calibration of the model to different clinical scenarios: (a) autologous PBSC with and without post transplant cytokine administration; patient data taken from Lowenthal et al.27 (b) Allogeneic HLA-identical PBSC without post transplant cytokine administration; patient data taken from trials by Vigorito et al.30 and Bensinger et al.31 (c) Allogeneic HLA-identical PBSC with post transplant cytokine administration; patient data taken from different trials.28–29 (d) Allogeneic HLA-haplo-identical PBSC with and without post transplant cytokine administration; patient data taken from trials by Aversa et al.32 and Kato et al.33 Model has been scaled to the fraction of patients alive and engrafted after 40 days. (e) Transplantation of umbilical cord blood; patient data taken from Rubinstein et al.34 Model has been scaled to the fraction of patients alive and engrafted after 100 days. (f) Allogeneic PBSC after reduced intensity conditioning; data taken from Chunduri et al.35

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5.10 5 5.10 Relative time gain due to Relative time gain Absolute time gain due to Absolute time gain 0 0 5.105 1.10 6 5.106 1.10 7 5.105 1.10 6 5.106 1.10 7 CD34(+) cells per kg body weight CD34(+) cells per kg body weight Figure 5. Reduction of reconstitution time because of enlargement of transplant: simulations and calculations. Boxes show the 25th–75th percentile, whiskers denote the 2.5th percentile and the 97.5th percentile, median values are indicated as horizontal lines and average values are indicated as circles. Simulations refer to autologous PBSCT without post transplant cytokine administration. Results for other transplantation scenarios are similar. (a) Absolute reduction of reconstitution time because of 5 Â 105 CD34 þ cells per kg of body weight added to the transplant size is indicated on the horizontal axis. (b) Relative reduction of reconstitution time because of 5 Â 105 CD34 þ cells per kg of body weight added to the transplant size is indicated on the horizontal axis. The results for other types of transplantations look similar. Simulations for slowly reconstituting patients are depicted in Supplementary Figure 4.

The results presented hold across different types of SCTs and when interpreting trial results, it should be taken into account that conditioning regimens. not absolute but relative changes of reconstitution time because We use model parameters with a biological interpretation; of different cell doses are similar for all patients. (ii) Patients at risk however, some of the values are not known accurately. For this for delayed reconstitution might profit remarkably from enlarged reason, we chose random sets of model parameters to simulate large transplants. This raises the question as to whether more careful patient groups. Further research could include explicit incorporation patient triage and risk-adjusted lower bounds of transplant size of immunological mechanisms and the impact of the microenviron- could be helpful in clinical practice. This has to be a subject of ment as soon as data on these subjects are available. further research. Up to now, several risk factors for delayed The finding that relative change in reconstitution time is nearly engraftment have been identified, including HHV6 infection,44 conserved between patients is new and cannot be concluded gene polymorphisms,45 splenomegaly46,47 and others.3,44–53 The from clinical data. Clinically relevant results of this work are (i) current results underline that further investigation of this topic

& 2014 Macmillan Publishers Limited Bone Marrow Transplantation (2014) 30 – 37 Engraftment after SCT T Stiehl et al 36 and individual adaptation of lower cell bounds may improve the transplantation from unrelated donors using pretransplant in vivo T-cell depletion outcome after SCTs. with anti-thymocyte globulin. Br J Haematol 2001; 113: 1060–1071. 19 Klaus J, Herrmann D, Breitkreutz I, Hegenbart U, Mazitschek U, Egerer G et al. Effect of CD34 cell dose on hematopoietic reconstitution and outcome in 508 CONFLICT OF INTEREST patients with multiple myeloma undergoing autologous peripheral blood stem The authors declare no conflict of intrest. cell transplantation. Eur J Haematol 2007; 78: 21–28. 20 Engel C, Scholz M, Loeffler M. A computational model of human granulopoiesis to simulate the hematotoxic effects of multicycle polychemotherapy. Blood 2004; ACKNOWLEDGEMENTS 104: 2323–2331. 21 Scholz M, Engel C, Loeffler M. 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