# Mathematical Modeling of MPNs Offers Understanding and Decision Support for Personalized Treatment

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## Abstract

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## 1. Introduction

^{11}cells per day [2]. Disturbances of this feedback system—e.g., malignant mutations escaping repair mechanisms in the HSCs—may be lethal. Competitive clones may cause myeloid neoplasms, including acute myeloid leukemia (AML) or Philadelphia negative myeloproliferative neoplasms (MPNs). The MPNs may further be divided into different subtypes: essential thrombocythemia (ET), polycythemia vera (PV), and primary myelofibrosis (PMF) [3]. In the biological continuum from early cancer stages (ET and PV) to the advanced myelofibrosis stage, these different subtypes may transform into each other, but also MPNs into AML [4,5,6]. The diagnoses are based on different diagnostic criteria, such as elevation in different cell counts (RBC, WBC, or PBC) or mutations in JAK2, CALR, or MPL. MPNs have an increasing but low incidence, with the annual incidence rates per 100,000 citizens being 1.6 for ET, 0.84 for PV, and 0.47 for PMF, respectively [7,8].

## 2. Results

## 3. Discussion

## 4. Materials and Methods

#### 4.1. Clinical Study Design

#### 4.2. Mathematical Study Design

#### 4.2.1. The Cancitis Model

#### 4.2.2. Mathematical Analysis Design

## 5. Conclusions

## Supplementary Materials

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**Top panel: JAK2V617F allele burden measurements for all the interferon-α2 (IFN)-treated myeloproliferative neoplasms (MPN) patients in the DALIAH trial normalized with their respective baseline value denoted JAK2

_{0}at the secondary axis (see Section 4: Materials and Methods). Median values fitted with exponential decay reveal that the JAK2V617F allele burden is halved every 25 months on a population level. Bottom panel: Boxplot showing the medians and percentiles of the JAK2V617F allele burden measurements for the IFN-treated MPN patients in the DALIAH trial normalized with their respective baseline values (see Section 4: Materials and Methods). Boxplot values are depicted for each visit in the clinic—i.e., at months 4, 8, 12, 18, 24, and 36, where all have the normalized value 1 at baseline. For each visit, the leftmost is for the cohort receiving Pegasys and of an age below 60, whereas the next (the second from left) is for the cohort receiving Pegasys and of an age 60 or above (both groups in green). The next two are for the cohorts receiving PegIntron of an age below 60 (the third from the left) and the cohort receiving PegIntron of age 60 or above (the rightmost) (both groups in red). Only patients with more than three observations are included. Below each boxplot, the number of patients is shown, whereas connected pairs of arrows and the numbers in black represent the p-value in a Welch’s unequal variances t-test for the equality of means.

**Figure 2.**Four typical patients: two good responders (

**top row**) and two poor responders (

**bottom row**) treated with IFN. Good and poor responders refer to a decrease or increase in allele burden, respectively, regardless of the changes in cell counts. Circles are clinical measurement, whereas full curves are the Cancitis model trajectories. The stipulated curves are sigmoidal increasing “population” master curves based on the data from patients off treatment (see [12]). Death rate of the malignant cells is used to calibrate the Cancitis model to patient-specific data for the JAK2V617F allele burdens. Measurements of leukocyte and thrombocyte counts are used for validation. Grey horizontal lines indicate the upper and lower limit for the normal cell count ranges, respectively. Below the JAK2V617F allele burden, figure panels of the patient-specific daily average IFN dose over time are shown. From the Cancitis model, it follows that malignant cells are suppressed and decreasing when the dose is in the green region, and when dose is in the red region the suppression is insufficient. The regions are separated by a patient-specific threshold value. For the JAK2V617F, leukocyte, and thrombocyte data as well as the model calibration for all patients, see Supplementary Material C.

**Figure 3.**A typical good responder is shown with a high baseline value (50% JAK2V617F allele burden). Black and grey stars are clinical measurements, whereas the full curves are model predictions. The dotted curve is a sigmoidal increasing “population” master curve corresponding to unperturbed disease growth. Grey data points are used to calibrate the Cancitis model for personalized prediction, and the black data points are the clinical measurements used for validation. Generally, three data points for calibrating the model provide good predictions, but increasing the number of data points increases the accuracy of the predictions. A curve generated by a pharmacokinetic model displays the daily average IFN dose in µg in black in the bottom panel (see Supplementary Material A). The red dose–response region indicates the dosing value of poor individual response, and the green dose–response region indicates the dosing value of good individual response, hence the separation between the two represents the effect threshold for the particular patient shown. A catalogue of all model predictions based on the various numbers of visits to the clinic for each patient can be found in Supplementary Material B.

**Figure 4.**An inverse Kaplan–Meier plot is shown illustrating the fraction of patients obtaining a partial molecular response (50% reduction relative to baseline) during the 60 months of measurement. The full black curve shows data and the grey dashed curve shows model prediction using all data points for calibration. The dotted blue curve shows the model prediction, where for each step only the preceding data points were used. The dashed purple curve shows the predictions of the first three data points using these for calibration.

**Figure 5.**The “confusion matrix” of model trajectories showing whether the Cancitis model correctly classifies the patient as having a partial molecular response (left). The true positives increase as more data are obtained while the true negatives decrease. The sensitivity, specificity, and accuracy of the Cancitis model are illustrated in the right panel.

**Figure 6.**Boxplots of the absolute difference between the personalized JAK2V617F allele burden data and model predictions over time—i.e., at month 4, 8, 12, 18, 24, 36, 48, and 60 after baseline.

**Figure 7.**From the Cancitis model, it can be computed whether the specific patient dose–responses suffice to force the patient towards a healthy or a diseased state (i.e., the cancer is about to be eradicated or the cancer escapes with ensuing disease progression). Each patient prediction in the study is represented by one column. The blue part of the columns depicts if the patient received an average daily dose of 5 µg IFN, the green depicts if the patient received 10 µg IFN per day on average, and the red depicts if the patient received 15 µg IFN per day on average. If the top of the columns are above the black dashed line, corresponding to 1.8-fold increase in the malignant stem cell death rate, the patient is said to respond well to the treatment—i.e., the allele burden steadily declines and so do the leukocyte and thrombocyte counts. For an average daily dose of 15 µg, the model predicts that there are 3 non-responders (not visible) at the left most part of the figure, followed by 6 poor responders. The remaining 54 are good responders. A similar interpretation can be made for an average daily dose of, e.g., 5 or 10 mg IFN. A stratification of the figure into patients receiving Pegasys and PegIntron, respectively, resembles the merged figure but with lower number of patients.

**Figure 8.**Different hypothetical modelling treatment scenarios: treatment discontinuation and prolonged treatment, respectively. Pausing the treatment after month 8 predicts a relapse of the cancer, and the pre-treatment JAK2V617F value is reached after 1.6 years (pink dashed curve). In contrast, prolonged treatment suppresses the cancer in the model (black solid curve) even with a lower dose (blue dashed curve). The model average daily IFN dose in µg is indicated in the lower panel, with line colors corresponding to those in the upper panel. Patient-specific model prediction for all patients exposed to hypothetical treatment discontinuation and prolongation, respectively, are depicted in Supplementary Material D.

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**MDPI and ACS Style**

Ottesen, J.T.; Pedersen, R.K.; Dam, M.J.B.; Knudsen, T.A.; Skov, V.; Kjær, L.; Andersen, M.
Mathematical Modeling of MPNs Offers Understanding and Decision Support for Personalized Treatment. *Cancers* **2020**, *12*, 2119.
https://doi.org/10.3390/cancers12082119

**AMA Style**

Ottesen JT, Pedersen RK, Dam MJB, Knudsen TA, Skov V, Kjær L, Andersen M.
Mathematical Modeling of MPNs Offers Understanding and Decision Support for Personalized Treatment. *Cancers*. 2020; 12(8):2119.
https://doi.org/10.3390/cancers12082119

**Chicago/Turabian Style**

Ottesen, Johnny T., Rasmus K. Pedersen, Marc J. B. Dam, Trine A. Knudsen, Vibe Skov, Lasse Kjær, and Morten Andersen.
2020. "Mathematical Modeling of MPNs Offers Understanding and Decision Support for Personalized Treatment" *Cancers* 12, no. 8: 2119.
https://doi.org/10.3390/cancers12082119