HSC Niche Dynamics in Regeneration, Pre-malignancy, and Cancer: Insights From Mathematical Modeling.

The hematopoietic stem cell (HSC) niche is a crucial driver of regeneration and malignancy. Its interaction with hematopoietic and malignant stem cells is highly complex and direct experimental observations are challenging. We here develop a mathematical model which helps relate processes in the niche to measurable changes of stem and non-stem cell counts. HSC attached to the niche are assumed to be quiescent. After detachment HSC become activated and divide or differentiate. To maintain their stemness, the progeny originating from division must reattach to the niche. We use mouse data from literature to parametrize the model. By combining mathematical analysis and computer simulations, we systematically investigate the impact of stem cell proliferation, differentiation, niche attachment, and detachment on clinically relevant scenarios. These include bone marrow transplantation, clonal competition, and eradication of malignant cells. According to our model, sampling of blood or bulk marrow provides only limited information about cellular interactions in the niche and the clonal composition of the stem cell population. Furthermore, we investigate how interference with processes in the stem cell niche could help to increase the effect of low-dose chemotherapy or to improve the homing of genetically engineered cells.

Toward an optimal contraception dosing strategy.

Anovulation refers to a menstrual cycle characterized by the absence of ovulation. Exogenous hormones such as synthetic progesterone and estrogen have been used to attain this state to achieve contraception. However, large doses are associated with adverse effects such as increased risk for thrombosis and myocardial infarction. This study utilizes optimal control theory on a modified menstrual cycle model to determine the minimum total exogenous estrogen/progesterone dose, and timing of administration to induce anovulation. The mathematical model correctly predicts the mean daily levels of pituitary hormones LH and FSH, and ovarian hormones E2, P4, and Inh throughout a normal menstrual cycle and reflects the reduction in these hormone levels caused by exogenous estrogen and/or progesterone. Results show that it is possible to reduce the total dose by 92% in estrogen monotherapy, 43% in progesterone monotherapy, and that it is most effective to deliver the estrogen contraceptive in the mid follicular phase. Finally, we show that by combining estrogen and progesterone the dose can be lowered even more. These results may give clinicians insights into optimal formulations and schedule of therapy that can suppress ovulation.

Mechanistic-mathematical modeling of intracranial pressure (ICP) profiles over a single heart cycle. The fundament of the ICP curve form.

The intracranial pressure (ICP) curve with its different peaks has been comprehensively studied, but the exact physiological mechanisms behind its morphology has not been revealed. If the pathophysiology behind deviations from the normal ICP curve form could be identified, it could be vital information to diagnose and treat each single patient. A mathematical model of the hydrodynamics in the intracranial cavity over single heart cycles was developed. A Windkessel model approach was generalized but the unsteady Bernoulli equation was utilized for blood flow and CSF flow. This is a modification of earlier models using the extended and simplified classical Windkessel analogies to a model that is based on mechanisms rooted in the laws of physics. The improved model was calibrated with patient data for cerebral arterial inflow, venous outflow, cerebrospinal fluid (CSF), and ICP over one heart cycle from 10 neuro-intensive care unit patients. A priori model parameter values were obtained by considering patient data and values taken from earlier studies. These values were used as an initial guess for an iterated constrained-ODE (ordinary differential equation) optimization problem with cerebral arterial inflow data as input into the system of ODEs. The optimization routine found patient-specific model parameter values that produced model ICP curves that showed excellent agreement with clinical measurements while model venous and CSF flow were within a physiologically acceptable range. The improved model and the automated optimization routine gave better model calibration results compared to previous studies. Moreover, patient-specific values of physiologically important parameters like intracranial compliance, arterial and venous elastance, and venous outflow resistance were determined. The model was used to simulate intracranial hydrodynamics and to explain the underlying mechanisms of the ICP curve morphology. Sensitivity analysis showed that the order of the three main peaks of the ICP curve was affected by a decrease in arterial elastance, a large increase in resistance to arteriovenous flow, an increase in venous elastance, or a decrease in resistance to CSF flow in the foramen magnum; and the frequency of oscillations were notably affected by intracranial elastance. In particular, certain pathological peak patterns were caused by these changes in physiological parameters. To the best of our knowledge, there are no other mechanism-based models associating the pathological peak patterns to variation of the physiological parameters.

Clonal haematopoiesis of indeterminate potential and impaired kidney function-A Danish general population study with 11 years follow-up.

The myeloproliferative neoplasms are associated with chronic kidney disease but whether clonal haematopoiesis of indeterminate potential (CHIP) is associated with impaired kidney function is unknown. In the Danish General Suburban Population Study (N = 19 958) from 2010 to 2013, 645 individuals were positive for JAK2V617F (N = 613) or CALR (N = 32) mutations. Mutation-positive individuals without haematological malignancy were defined as having CHIP (N = 629). We used multiple and inverse probability weighted (IPW)-adjusted linear regression analysis to estimate adjusted mean (95% confidence interval) differences in estimated glomerular filtration rate (eGFR; ml/min/1.73 m2 ) by mutation status, variant allele frequency (VAF%), blood cell counts, and neutrophil-to-lymphocyte ratio (NLR). We performed 11-year longitudinal follow-up of eGFR in all individuals. Compared to CHIP-negative individuals, the mean differences in eGFR were -5.6 (-10.3, -0.8, p = .02) for CALR, -11.9 (-21.4, -2.4, p = 0.01) for CALR type 2, and -10.1 (-18.1, -2.2, p = .01) for CALR with VAF ≥ 1%. The IPW-adjusted linear regression analyses showed similar results. NLR was negatively associated with eGFR. Individuals with CALR type 2 had a worse 11-year longitudinal follow-up on eGFR compared to CHIP-negative individuals (p = .004). In conclusion, individuals with CALR mutations, especially CALR type 2, had impaired kidney function compared to CHIP-negative individuals as measured by a lower eGFR at baseline and during 11-year follow-up.

Patient-specific parameter estimation: Coupling a heart model and experimental data.

This study develops a hemodynamic model involving the atrium, ventricle, veins, and arteries that can be calibrated to experimental results. It is a Windkessel model that incorporates an unsteady Bernoulli effect in the blood flow to the atrium. The model is represented by ordinary differential equations in terms of blood volumes in the compartments as state variables and it demonstrates the use of conductance instead of resistance to capture the effect of a non-leaking heart valve. The experimental results are blood volume data from 20 young (half of which are women) and 20 elderly (half of which are women) subjects during rest, inotropic stress (dobutamine), and chronotropic stress (glycopyrrolate). The model is calibrated to conform with data and physiological findings in 4 different levels. First, an optimization routine is devised to find model parameter values that give good fit between the model volume curves and blood volume data in the atrium and ventricle. Patient-specific information are used to get initial parameter values as a starting point of the optimization. Also, model pressure curves must show realistic behavior. Second, parametric bootstrapping is performed to establish the reliability of the optimal parameters. Third, statistical tests comparing mean optimal parameter values from young vs elderly subjects and women vs men are examined to support and present age and sex related differences in heart functions. Lastly, statistical tests comparing mean optimal parameter values from resting condition vs pharmacological stress are studied to verify and quantify the effects of dobutamine and glycopyrrolate to the cardiovascular system.

Mathematical modelling of the hematopoietic stem cell-niche system: Clonal dominance based on stem cell fitness.

Human blood cell production is maintained by hematopoietic stem cells (HSC) which give rise to all types of mature blood cells. Experimental observation of HSC in their physiologic bone-marrow microenvironment, the so-called stem cell niche, is challenging. Therefore, the details of HSC dynamics and the cellular interactions in the stem cell niche remain elusive. Mutations that lead to a competitive advantage are the cause of clinical challenges when treating HSC-derived malignancies such as acute myeloid leukemia or the myeloproliferative neoplasms (MPNs). To investigate the significance of the interaction between the HSC and the stem cell niche in these malignancies, we propose and analyse a mechanism-based mathematical model of HSC dynamics within the bone-marrow microenvironment. The model is based on the central hypothesis that HSC self-renewal depends on the niche. In the model, the interaction of HSC with specific niches located in the bone marrow are key to the indefinite HSC renewal necessary for long-term maintenance of blood cell production. We formulate a general model of n distinct clones that differ with respect to cell properties. We identify an attractive trapping region and compute and classify all steady states. A concept of HSC fitness naturally arises from the model analysis. HSC fitness is found to determine the asymptotic behaviour of the model, as the HSC clone with the highest fitness is related to the unique locally stable steady state. Based on biological assumptions about HSC, we propose two reduced models of different complexity. A thorough mathematical analysis reveals that both reduced models have the same asymptotic behaviour as the full model. We compare the simpler of the two models, a logistic equation of the disease burden, to clinical data of MPN-patients. The reduced model is found to agree well with data and suggests a simple interpretation and possible prediction of patient prognosis. The proposed mathematical model and the reduced forms have the potential to provide insights into the regulation of HSC dynamics and blood cell formation, and ultimately for future advances in treatment of hematologic malignancies.

Data-driven analysis of the kinetics of the JAK2V617F allele burden and blood cell counts during hydroxyurea treatment of patients with polycythemia vera, essential thrombocythemia, and primary myelofibrosis.

BACKGROUND: Hydroxyurea (HU) treatment of patients with essential thrombocythemia (ET), polycythemia vera (PV), and primary myelofibrosis (PMF) (MPNs) normalizes elevated blood cell counts within weeks in the large majority of patients. Studies on the impact of HU upon the kinetics of the JAK2V617F allele burden, leukocyte, and platelet counts over time are scarce. PURPOSE: Using data-driven analysis as a novel tool to model the kinetics of the JAK2V617F allele burden and blood cell counts over time during treatment with HU. MATERIAL AND METHODS: Using serial measurements of JAK2V617F and correlation analysis of routine hematological values (the Hb-concentration, leukocyte count, platelet count, and lactic dehydrogenase), we present a detailed description and analysis of the kinetics of the JAK2V617F, leukocyte, and platelet counts and lactic dehydrogenase in 27 patients (PV = 18; ET = 7; PMF = 2), who were followed in the Danish randomized trial (DALIAH). To further analyze the JAK2V617F kinetics, we use a machine learning clustering algorithm to group the response patterns. RESULTS: Response patterns were highly heterogeneous, with clustering resulting in 3 groups and 3 outliers. In the large majority of patients, HU treatment was initially associated with a modest decline in the JAK2V617F allele burden in concert with a decline in leukocyte and platelet counts. However, HU did not induce a sustained and continuous decrease in the JAK2V617F allele burden. CONCLUSION: Using data-driven analysis of the JAK2V617F allele burden, leukocyte, and platelet kinetics during treatment with HU, we have shown that HU does not induce a sustained decrease in the JAK2V617F allele burden and neither induces sustained normalization of elevated cell counts in MPN patients. Our results may explain why MPN patients during treatment with HU still have a substantially increased risk of thrombosis.

Validation of a mathematical model for understanding intracranial pressure curve morphology.

The physiology underlying the intracranial pressure (ICP) curve morphology is not fully understood. Recent research has suggested that the morphology could be dependent on arterial cerebral inflow and the physiological and pathophysiological properties of the intracranial cavity. If understood, the ICP curve could provide information about the patient's cerebrovascular state important in individualizing treatment in neuro intensive care patients. A mathematical model based on known physiological properties of the intracranial compartment was created. Clinical measurements from ten neuro intensive care patients in whom intracranial arterial blood inflow, venous blood outflow and cerebrospinal fluid flow over the foramen magnum had been measured with phase contrast MRI, concomitant with ICP measurements were used to validate the model. In nine patients the mathematical model was able to create an ICP curve mimicking the measured by using arterial intracranial inflow and adjusting physiological parameters of the model. The venous outflow and cerebrospinal fluid (CSF) flow over the foramen magnum predicted by the model were within physiologically reasonable limits and in most cases followed the MRI measured values in close adjunct. The presented model could produce an ICP curve in close resemblance of the in vivo measured curves. This strengthens the hypothesis that the ICP curve is shaped by the arterial intracranial inflow and the physiological properties of the intracranial cavity.

Bridging blood cancers and inflammation: The reduced Cancitis model.

A novel mechanism-based model - the Cancitis model - describing the interaction of blood cancer and the inflammatory system is proposed, analyzed and validated. The immune response is divided into two components, one where the elimination rate of malignant stem cells is independent of the level of the blood cancer and one where the elimination rate depends on the level of the blood cancer. A dimensional analysis shows that the full 6-dimensional system of nonlinear ordinary differential equations may be reduced to a 2-dimensional system - the reduced Cancitis model - using Fenichel theory. The original 18 parameters appear in the reduced model in 8 groups of parameters. The reduced model is analyzed. Especially the steady states and their dependence on the exogenous inflammatory stimuli are analyzed. A semi-analytic investigation reveals the stability properties of the steady states. Finally, positivity of the system and the existence of an attracting trapping region in the positive octahedron guaranteeing global existence and uniqueness of solutions are proved. The possible topologies of the dynamical system are completely determined as having a Janus structure, where two qualitatively different topologies appear for different sets of parameters. To classify this Janus structure we propose a novel concept in blood cancer - a reproduction ratio R. It determines the topological structure depending on whether it is larger or smaller than a threshold value. Furthermore, it follows that inflammation, affected by the exogenous inflammatory stimulation, may determine the onset and development of blood cancers. The body may manage initial blood cancer as long as the self-renewal rate is not too high, but fails to manage it if an inflammation appears. Thus, inflammation may trigger and drive blood cancers. Finally, the mathematical analysis suggests novel treatment strategies and it is used to discuss the in silico effect of existing treatment, e.g. interferon-α or T-cell therapy, and the impact of malignant cells becoming resistant.

Parameter subset selection techniques for problems in mathematical biology.

Patient-specific models for diagnostics and treatment planning require reliable parameter estimation and model predictions. Mathematical models of physiological systems are often formulated as systems of nonlinear ordinary differential equations with many parameters and few options for measuring all state variables. Consequently, it can be difficult to determine which parameters can reliably be estimated from available data. This investigation highlights pitfalls associated with practical parameter identifiability and subset selection. The latter refer to the process associated with selecting a subset of parameters that can be identified uniquely by parameter estimation protocols. The methods will be demonstrated using five examples of increasing complexity, as well as with patient-specific model predicting arterial blood pressure. This study demonstrates that methods based on local sensitivities are preferable in terms of computational cost and model fit when good initial parameter values are available, but that global methods should be considered when initial parameter value is not known or poorly understood. For global sensitivity analysis, Morris screening provides results in terms of parameter sensitivity ranking at a much lower computational cost.

Cardiovascular dynamics during head-up tilt assessed via pulsatile and non-pulsatile models.

This study develops non-pulsatile and pulsatile models for the prediction of blood flow and pressure during head-up tilt. This test is used to diagnose potential pathologies within the autonomic control system, which acts to keep the cardiovascular system at homeostasis. We show that mathematical modeling can be used to predict changes in cardiac contractility, vascular resistance, and arterial compliance, quantities that cannot be measured but are useful to assess the system's state. These quantities are predicted as time-varying parameters modeled using piecewise linear splines. Having models with various levels of complexity formulated with a common set of parameters, allows us to combine long-term non-pulsatile simulations with pulsatile simulations on a shorter time-scale. We illustrate results for a representative subject tilted head-up from a supine position to a [Formula: see text] angle. The tilt is maintained for 5 min before the subject is tilted back down. Results show that if volume data is available for all vascular compartments three parameters can be identified, cardiovascular resistance, vascular compliance, and ventricular contractility, whereas if model predictions are made against arterial pressure and cardiac output data alone, only two parameters can be estimated either resistance and contractility or resistance and compliance.

Increased Intracranial Pressure Attenuates the Pulsating Component of Cerebral Venous Outflow.

BACKGROUND: The underlying physiology of the intracranial pressure (ICP) curve morphology is still poorly understood. If this physiology is explained it could be possible to extract clinically relevant information from the ICP curve. The venous outflow from the cranial cavity is pulsatile, and in theory the pulsatile component of venous outflow from the cranial cavity should be attenuated with increasing ICP. In this study, we explored the relationship between ICP and the pulsatility of the venous outflow from the intracranial cavity. METHODS: Thirty-seven neuro-intensive care patients that had been examined with phase-contrast magnetic resonance imaging regarding cerebral blood flow (CBF) through the internal carotid and vertebral arteries and venous flow in the internal jugular veins were retrospectively included. The pulsatility of the jugular flow was determined by calculating the venous pulsatile index. The results were correlated to clinical data registered in the patient data monitoring system, including ICP and cerebral perfusion pressure (CPP). RESULTS: CBF was 996 ± 298 ml/min, and the flow in the internal jugular veins equaled 67 ± 17% of the CBF, with a range of 22-97%. The venous pulsatile index correlated negatively to ICP (R = - 0.47 p = 0.003). The lowest flow in the internal jugular veins over the cardiac cycle (Fmin) was not correlated to ICP. Temperature, end-tidal CO2, MAP, and CPP were not correlated to venous pulsatility. CONCLUSION: An increase in ICP correlates to a lower pulsatility of the venous outflow from the cranial cavity. A lower pulsatility could be due to increased pressure requirements to compress intracranial veins with increasing ICP.

ICP curve morphology and intracranial flow-volume changes: a simultaneous ICP and cine phase contrast MRI study in humans.

BACKGROUND: The intracranial pressure (ICP) curve with its different peaks has been extensively studied, but the exact physiological mechanisms behind its morphology are still not fully understood. Both intracranial volume change (ΔICV) and transmission of the arterial blood pressure have been proposed to shape the ICP curve. This study tested the hypothesis that the ICP curve correlates to intracranial volume changes. METHODS: Cine phase contrast magnetic resonance imaging (MRI) examinations were performed in neuro-intensive care patients with simultaneous ICP monitoring. The MRI was set to examine cerebral arterial inflow and venous cerebral outflow as well as flow of cerebrospinal fluid over the foramen magnum. The difference in total flow into and out from the cranial cavity (Flowtot) over time provides the ΔICV. The ICP curve was compared to the Flowtot and the ΔICV. Correlations were calculated through linear and logarithmic regression. Student's t test was used to test the null hypothesis between paired samples. RESULTS: Excluding the initial ICP wave, P1, the mean R 2 for the correlation between the ΔICV and the ICP was 0.75 for the exponential expression, which had a higher correlation than the linear (p = 0.005). The first ICP peaks correlated to the initial peaks of Flowtot with a mean R 2 = 0.88. CONCLUSION: The first part, or the P1, of the ICP curve seems to be created by the first rapid net inflow seen in Flowtot while the rest of the ICP curve seem to correlate to the ΔICV.

Modeling the differentiation of A- and C-type baroreceptor firing patterns.

The baroreceptor neurons serve as the primary transducers of blood pressure for the autonomic nervous system and are thus critical in enabling the body to respond effectively to changes in blood pressure. These neurons can be separated into two types (A and C) based on the myelination of their axons and their distinct firing patterns elicited in response to specific pressure stimuli. This study has developed a comprehensive model of the afferent baroreceptor discharge built on physiological knowledge of arterial wall mechanics, firing rate responses to controlled pressure stimuli, and ion channel dynamics within the baroreceptor neurons. With this model, we were able to predict firing rates observed in previously published experiments in both A- and C-type neurons. These results were obtained by adjusting model parameters determining the maximal ion-channel conductances. The observed variation in the model parameters are hypothesized to correspond to physiological differences between A- and C-type neurons. In agreement with published experimental observations, our simulations suggest that a twofold lower potassium conductance in C-type neurons is responsible for the observed sustained basal firing, where as a tenfold higher mechanosensitive conductance is responsible for the greater firing rate observed in A-type neurons. A better understanding of the difference between the two neuron types can potentially be used to gain more insight about pathophysiology and treatment of diseases related to baroreflex function, e.g. in patients with autonomic failure, a syndrome that is difficult to diagnose in terms of its pathophysiology.

Integrated Inflammatory Stress (ITIS) Model.

During the last decade, there has been an increasing interest in the coupling between the acute inflammatory response and the Hypothalamic-Pituitary-Adrenal (HPA) axis. The inflammatory response is activated acutely by pathogen- or damage-related molecular patterns, whereas the HPA axis maintains a long-term level of the stress hormone cortisol which is also anti-inflammatory. A new integrated model of the interaction between these two subsystems of the inflammatory system is proposed and coined the integrated inflammatory stress (ITIS) model. The coupling mechanisms describing the interactions between the subsystems in the ITIS model are formulated based on biological reasoning and its ability to describe clinical data. The ITIS model is calibrated and validated by simulating various scenarios related to endotoxin (LPS) exposure. The model is capable of reproducing human data of tumor necrosis factor alpha, adrenocorticotropic hormone (ACTH) and cortisol and suggests that repeated LPS injections lead to a deficient response. The ITIS model predicts that the most extensive response to an LPS injection in ACTH and cortisol concentrations is observed in the early hours of the day. A constant activation results in elevated levels of the variables in the model while a prolonged change of the oscillations in ACTH and cortisol concentrations is the most pronounced result of different LPS doses predicted by the model.

Absorption and initial metabolism of 75Se-l-selenomethionine: a kinetic model based on dynamic scintigraphic data.

Selenomethionine (SeMet) is an important organic nutritional source of Se, but the uptake and metabolism of SeMet are poorly characterised in humans. Dynamic gamma camera images of the abdominal region were acquired from eight healthy young men after the ingestion of radioactive 75Se-l-SeMet (75Se-SeMet). Scanning started simultaneously to the ingestion of 75Se-SeMet and lasted 120 min. We generated time-activity curves from two-dimensional regions of interest in the stomach, small intestine and liver. During scanning, blood samples were collected at 10-min intervals to generate plasma time-activity curves. A four-compartment model, augmented with a delay between the liver and plasma, was fitted to individual participants' data. The mean rate constant for 75Se-SeMet transport was 2·63 h-1 from the stomach to the small intestine, 13·2 h-1 from the small intestine to the liver, 0·261 h-1 from the liver to the plasma and 0·267 h-1 from the stomach to the plasma. The delay in the liver was 0·714 h. Gamma camera imaging provides data for use in compartmental modelling of 75Se-SeMet absorption and metabolism in humans. In clinical settings, the obtained rate constants and the delay in the liver may be useful variables for quantifying reduced intestinal absorption capacity or liver function.

Modeling the afferent dynamics of the baroreflex control system.

In this study we develop a modeling framework for predicting baroreceptor firing rate as a function of blood pressure. We test models within this framework both quantitatively and qualitatively using data from rats. The models describe three components: arterial wall deformation, stimulation of mechanoreceptors located in the BR nerve-endings, and modulation of the action potential frequency. The three sub-systems are modeled individually following well-established biological principles. The first submodel, predicting arterial wall deformation, uses blood pressure as an input and outputs circumferential strain. The mechanoreceptor stimulation model, uses circumferential strain as an input, predicting receptor deformation as an output. Finally, the neural model takes receptor deformation as an input predicting the BR firing rate as an output. Our results show that nonlinear dependence of firing rate on pressure can be accounted for by taking into account the nonlinear elastic properties of the artery wall. This was observed when testing the models using multiple experiments with a single set of parameters. We find that to model the response to a square pressure stimulus, giving rise to post-excitatory depression, it is necessary to include an integrate-and-fire model, which allows the firing rate to cease when the stimulus falls below a given threshold. We show that our modeling framework in combination with sensitivity analysis and parameter estimation can be used to test and compare models. Finally, we demonstrate that our preferred model can exhibit all known dynamics and that it is advantageous to combine qualitative and quantitative analysis methods.

Mathematical modelling of stem and progenitor cell dynamics during ruxolitinib treatment of patients with myeloproliferative neoplasms.

Introduction: The Philadelphia chromosome-negative myeloproliferative neoplasms are a group of slowly progressing haematological malignancies primarily characterised by an overproduction of myeloid blood cells. Patients are treated with various drugs, including the JAK1/2 inhibitor ruxolitinib. Mathematical modelling can help propose and test hypotheses of how the treatment works. Materials and methods: We present an extension of the Cancitis model, which describes the development of myeloproliferative neoplasms and their interactions with inflammation, that explicitly models progenitor cells and can account for treatment with ruxolitinib through effects on the malignant stem cell response to cytokine signalling and the death rate of malignant progenitor cells. The model has been fitted to individual patients' data for the JAK2 V617F variant allele frequency from the COMFORT-II and RESPONSE studies for patients who had substantial reductions (20 percentage points or 90% of the baseline value) in their JAK2 V617F variant allele frequency (n = 24 in total). Results: The model fits very well to the patient data with an average root mean square error of 0.0249 (2.49%) when allowing ruxolitinib treatment to affect both malignant stem and progenitor cells. This average root mean square error is much lower than if allowing ruxolitinib treatment to affect only malignant stem or only malignant progenitor cells (average root mean square errors of 0.138 (13.8%) and 0.0874 (8.74%), respectively). Discussion: Systematic simulation studies and fitting of the model to the patient data suggest that an initial reduction of the malignant cell burden followed by a monotonic increase can be recapitulated by the model assuming that ruxolitinib affects only the death rate of malignant progenitor cells. For patients exhibiting a long-term reduction of the malignant cells, the model predicts that ruxolitinib also affects stem cell parameters, such as the malignant stem cells' response to cytokine signalling.

Neutrophil-to-lymphocyte ratio and all-cause mortality with and without myeloproliferative neoplasms-a Danish longitudinal study.

The neutrophil-to-lymphocyte ratio(NLR) is increased in chronic inflammation and myeloproliferative neoplasms (MPN). We hypothesize that NLR is associated with all-cause mortality and mortality by comorbidity burden in the general population and individuals with MPN. We included 835,430 individuals from The Danish General Suburban Population Study, general practitioners, and outpatient clinics. We investigated NLR on mortality stratified by prevalent and incident MPN, essential thrombocythemia (ET), polycythemia vera (PV), myelofibrosis (MF), comorbidity burden (CCI-score), and the Triple-A risk score using hazard ratio (HR) and 95% confidence interval (95%CI). NLR 1-1.9 was the reference level. During a median follow-up of 11.2 years, 197,802 deaths were recorded. All-cause mortality increased for a stepwise increasing NLR with a HR (95%CI) for NLR ≥ 6 of 2.06(2.03-2.09) for the whole population and 2.93(2.44-3.50) in prevalent MPN. ET, PV, and MF had a HR (95%CI) for NLR ≥ 2 of 2.14(1.71-2.69), 2.19(1.89-2.54), and 2.31(1.91-2.80). Results were similar for incident MPN. Mortality was higher for stepwise increasing NLR and CCI-score(pinteraction < 2×10-16), with a HR for NLR ≥ 6 of 2.23(2.17-2.29), 4.10(4.01-4.20), and 7.69(7.50-7.89), for CCI-score 0, 1-2, or ≥3. The Triple-A risk score demonstrated alignment with NLR. Increasing NLR and comorbidity burden were associated with lower survival in individuals without MPN but were even worse in prevalent and incident MPN, ET, PV, and MF.

A practical approach to parameter estimation applied to model predicting heart rate regulation.

Mathematical models have long been used for prediction of dynamics in biological systems. Recently, several efforts have been made to render these models patient specific. One way to do so is to employ techniques to estimate parameters that enable model based prediction of observed quantities. Knowledge of variation in parameters within and between groups of subjects have potential to provide insight into biological function. Often it is not possible to estimate all parameters in a given model, in particular if the model is complex and the data is sparse. However, it may be possible to estimate a subset of model parameters reducing the complexity of the problem. In this study, we compare three methods that allow identification of parameter subsets that can be estimated given a model and a set of data. These methods will be used to estimate patient specific parameters in a model predicting baroreceptor feedback regulation of heart rate during head-up tilt. The three methods include: structured analysis of the correlation matrix, analysis via singular value decomposition followed by QR factorization, and identification of the subspace closest to the one spanned by eigenvectors of the model Hessian. Results showed that all three methods facilitate identification of a parameter subset. The "best" subset was obtained using the structured correlation method, though this method was also the most computationally intensive. Subsets obtained using the other two methods were easier to compute, but analysis revealed that the final subsets contained correlated parameters. In conclusion, to avoid lengthy computations, these three methods may be combined for efficient identification of parameter subsets.