- Email: [email protected]
Computational models of blood disorders
DDMOD-423; No of Pages 3
Drug Discovery Today: Disease Models
DRUG DISCOVERY
TODAY
DISEASE
MODELS
Vol. xxx, No. xx 2016
Editors-in-Chief Jan Tornell – AstraZeneca, Sweden Andrew McCulloch – University of California, SanDiego, USA
Editorial
EDITORIAL
Computational models of blood disorders George Em Karniadakis Division of Applied Mathematics, Brown University, Providence, RI 02912, USA. Email: ([email protected])
Computational models for modeling blood flow in health and disease have been advanced greatly in the last ten years. Not too long ago, the state-of-the-art was based on idealized two-dimensional arterial bifurcations with the blood treated as homogeneous simple fluid but today three-dimensional patient-specific simulation studies of blood flow are performed routinely in many bioengineering labs around the world. Moreover, there is plethora of mathematical models and computational approaches in carrying out such simulations at various levels of fidelity from atomistic, to mesoscopic, to continuum. Continuum models are based on solutions of partial differential equations, for example the incompressible Navier– Stokes equations, often coupled to other advection–diffusion-reaction equations or simplified systems of ordinary differential equations that may represent complex reaction dynamics. On the other hand, atomistic level descriptions and more specifically coarse-grained versions of the molecular dynamics have emerged as powerful alternatives, especially when the discrete nature of the blood has to be considered explicitly in diseases such as malaria, sickle cell anemia, diabetes, HIV, etc. Such particle based computational methods rely on Newton’s law to describe the plasma (solvent) but they are also employed to construct virtual analogs of white cells, red blood cells, and platelets. They can also be used to construct multi-scale models of cancer cells, for example, in simulation studies of metastasis where the circulating tumor cells may have to be modeled explicitly (having different biomechanical properties) along with the red blood cells that dominate the blood composition; see a recent study in Fig. 1. In the emerging paradigm of multi-scale modeling, it may be necessary to combine the efficiency of the continuum models with the higher fidelity of the atomistic or mesoscopic models leading to hybrid type computations that can tackle 1740-6757/$ ß 2016 Elsevier Ltd. All rights reserved.
spatial and temporal scales, which may be several orders of magnitude apart. There is currently a lot of fundamental mathematical developments in this area but no single effective hybrid method has emerged yet that can be used readily by the biomedical modelers without deep knowledge of the underlying mathematics. We expect, however, that in the next few years both the mathematical and computational issues will be resolved and that robust software will be available that can be used effectively in multi-scale simulations.
George Em Karniadakis is the Charles Pitts Robinson and John Palmer Barstow Professor of Applied Mathematics at Brown University. His current research focuses on stochastic multi-scale modeling of biological systems and soft matter. He received his Ph.D. from MIT and his postdoctoral training at Stanford University. He has been a visiting faculty at Caltech, MIT, and Peking University. He has written three books and over 300 research papers. He is a Fellow of the Society for Industrial and Applied Mathematics (SIAM), Fellow of the American Physical Society (APS), Fellow of the American Society of Mechanical Engineers (ASME) and Associate Fellow of the American Institute of Aeronautics and Astronautics (AIAA). He received the CFD award (2007) and the J Tinsley Oden Medal (2013) by the US Association in Computational Mechanics, and more recently the Ralf E Kleinman award (2015) by SIAM for many outstanding contributions to Applied Mathematics in a broad range of areas, including computational fluid dynamics, spectral methods and stochastic modeling. In 2015, he received the Microcirculation Society (MCS) Wiederhielm Award for the most highly cited original article in Microcirculation over the previous five year period for the paper, ‘Blood Flow and Cell-Free Layer in Microvessels.’
http://dx.doi.org/10.1016/j.ddmod.2016.01.001
Please cite this article in press as: Drug Discov Today: Dis Model (2016), http://dx.doi.org/10.1016/j.ddmod.2016.01.001
e1
DDMOD-423; No of Pages 3 Drug Discovery Today: Disease Models | Editorial
Vol. xxx, No. xx 2016
Drug Discovery Today: Disease Models
Figure 1. Red blood cells (red) and circulating tumor cells (green) traveling through a microfluidic cell sorting device as simulated by uDeviceX, a GPUaccelerated parallel solver developed by a joint team of researchers from Brown University, ETH Zurich, University of Lugano. These results were obtained based on the Dissipative Particle Dynamics (DPD) method on the Titan supercomputer at Oak Ridge Leadership Computing facility. The solvent (plasma), the red blood cells, as well as the cancel cells are all represented by DPD. The image is rendered using ray tracing by Yu-Hang Tang of Brown University.
In this special issue, we have included three papers focusing on different aspects of blood diseases. The first paper by Clapp and Levy reviews mathematical models for leukemia and lymphoma, which affect over one million people in the United States according to the Leukemia and Lymphoma Society. The paper first discusses hematopoiesis, which is often modeled as system of discrete maturity stages starting with hematopoietic stem cells and ending with mature blood cells. Despite its complexity, simple ordinary differential equation (ODE) models have already provided useful insight into the process. Moreover, delay ODEs (DDEs) can be employed to capture events such as cell divisions. Stochasticity may also be important, especially for small cell populations in order to capture the emerging dynamics. The second part of the paper examines the utility of mathematical models for treatment, specifically how to improve and optimize the way various therapies are administered. To this end, parametric sensitivity analysis and numerical simulation can determine the dependence of a treatment outcome on a specific model. The final part of the paper reviews how mathematical models can be used to evaluate drug resistance, what combinations of drugs may be the most effective, and also how to quantify the probability of treatment failure. The second paper by Kunz et al. presents a review of flow, structure and biochemistry models of the tumor microenvironment. The focus is on melanoma metastasis, where the biochemical and dynamic interactions between e2
polymorphonuclear neutrophils (PMNs) and tumor cells (TCs) are of interest; PMNs comprise 50–70% of all circulating leukocytes. PMN-mediated tumor cell adhesion to the endothelium under shear flow conditions is a critical step in metastasis. The paper presents first cell-scale fluid dynamics methods, followed by a discussion on geometric and structural dynamics modeling of cells in blood flow. Then, the authors review the adhesive dynamics method applied to adherent leukocytes that participate in TC capture. Adhesion kinetics are modeled as probabilistic interactions between receptor and ligand molecules with the adhesion molecules modeled as springs. The specific biochemistry of adhesion kinetics models of relevance to PMN-TC and PMN-EC (endothelium cell) bonding are then presented. Finally, they briefly touch on scale-bridging approaches that have appeared for molecular-to-cell and cell-to-cell-population interactions. The authors also present a new method for predicting adhesion efficiency at the cell-population-scale using a statistical technique. They pose the important modeling question on when to model at the cell-resolving level and what modeling fidelity to employ at the cell-population level. Simplified models where the expensive fluid dynamics is taken into account only implicitly allow for systematic parametric studies on adhesion biochemistry, cell deformation and margination, without excessive computational cost. The third paper by Fedosov presents a review of the stateof-the-art in modeling the various stages of malaria and also
www.drugdiscoverytoday.com
Please cite this article in press as: Drug Discov Today: Dis Model (2016), http://dx.doi.org/10.1016/j.ddmod.2016.01.001
DDMOD-423; No of Pages 3 Vol. xxx, No. xx 2016
of sickle cell anemia. While the former is an infectious disease and the latter a genetic disease, from the modeling perspective they share some similarities that the computational multiscale framework presented in the paper can effectively address. For example, they both increase the apparent blood viscosity and they can both cause vaso-occlusion episodes due to RBC stiffening and the adhesive properties of the diseased RBCs. However, in malaria it is reasonable to model the parasite inside the RBCs as a solid body whereas in sickle cell anemia the dynamic self-assembly process of sickle hemoglobin polymerization has to be modeled with sufficient accuracy as it determines the RBC shape deformation, which, in turn, affects greatly the biorheological properties of the sickle blood. Using the method of dissipative particle dynamics (DPD) – a coarse-grained molecular dynamics approach – several biophysical mechanisms of both diseases can be elucidated and quantified. Such DPD models have been carefully
Drug Discovery Today: Disease Models | Editorial
developed and validated using companion microfluidic experiments. In summary, these three papers cover some representative and diverse aspects of modeling blood flow diseases. The introduction of microfluidics into biomedicine has led to new opportunities for systematic validation of these complex models, often used patient-specific blood, which can provide calibration of parameters for the missing biochemistry details that are not currently captured with the available models. Looking into the future, a promising avenue of research in the computational modeling of blood diseases may be the integration of advances from the system biology, which can greatly advance the understanding of the adhesive properties of blood cells in the presence of inflammation, the metastasis of cancer through circulation tumor cells, and other diseases such as the formation of thrombus in the human arterial tree.
www.drugdiscoverytoday.com
Please cite this article in press as: Drug Discov Today: Dis Model (2016), http://dx.doi.org/10.1016/j.ddmod.2016.01.001
e3
Drug Discovery Today: Disease Models
DRUG DISCOVERY
TODAY
DISEASE
MODELS
Vol. xxx, No. xx 2016
Editors-in-Chief Jan Tornell – AstraZeneca, Sweden Andrew McCulloch – University of California, SanDiego, USA
Editorial
EDITORIAL
Computational models of blood disorders George Em Karniadakis Division of Applied Mathematics, Brown University, Providence, RI 02912, USA. Email: ([email protected])
Computational models for modeling blood flow in health and disease have been advanced greatly in the last ten years. Not too long ago, the state-of-the-art was based on idealized two-dimensional arterial bifurcations with the blood treated as homogeneous simple fluid but today three-dimensional patient-specific simulation studies of blood flow are performed routinely in many bioengineering labs around the world. Moreover, there is plethora of mathematical models and computational approaches in carrying out such simulations at various levels of fidelity from atomistic, to mesoscopic, to continuum. Continuum models are based on solutions of partial differential equations, for example the incompressible Navier– Stokes equations, often coupled to other advection–diffusion-reaction equations or simplified systems of ordinary differential equations that may represent complex reaction dynamics. On the other hand, atomistic level descriptions and more specifically coarse-grained versions of the molecular dynamics have emerged as powerful alternatives, especially when the discrete nature of the blood has to be considered explicitly in diseases such as malaria, sickle cell anemia, diabetes, HIV, etc. Such particle based computational methods rely on Newton’s law to describe the plasma (solvent) but they are also employed to construct virtual analogs of white cells, red blood cells, and platelets. They can also be used to construct multi-scale models of cancer cells, for example, in simulation studies of metastasis where the circulating tumor cells may have to be modeled explicitly (having different biomechanical properties) along with the red blood cells that dominate the blood composition; see a recent study in Fig. 1. In the emerging paradigm of multi-scale modeling, it may be necessary to combine the efficiency of the continuum models with the higher fidelity of the atomistic or mesoscopic models leading to hybrid type computations that can tackle 1740-6757/$ ß 2016 Elsevier Ltd. All rights reserved.
spatial and temporal scales, which may be several orders of magnitude apart. There is currently a lot of fundamental mathematical developments in this area but no single effective hybrid method has emerged yet that can be used readily by the biomedical modelers without deep knowledge of the underlying mathematics. We expect, however, that in the next few years both the mathematical and computational issues will be resolved and that robust software will be available that can be used effectively in multi-scale simulations.
George Em Karniadakis is the Charles Pitts Robinson and John Palmer Barstow Professor of Applied Mathematics at Brown University. His current research focuses on stochastic multi-scale modeling of biological systems and soft matter. He received his Ph.D. from MIT and his postdoctoral training at Stanford University. He has been a visiting faculty at Caltech, MIT, and Peking University. He has written three books and over 300 research papers. He is a Fellow of the Society for Industrial and Applied Mathematics (SIAM), Fellow of the American Physical Society (APS), Fellow of the American Society of Mechanical Engineers (ASME) and Associate Fellow of the American Institute of Aeronautics and Astronautics (AIAA). He received the CFD award (2007) and the J Tinsley Oden Medal (2013) by the US Association in Computational Mechanics, and more recently the Ralf E Kleinman award (2015) by SIAM for many outstanding contributions to Applied Mathematics in a broad range of areas, including computational fluid dynamics, spectral methods and stochastic modeling. In 2015, he received the Microcirculation Society (MCS) Wiederhielm Award for the most highly cited original article in Microcirculation over the previous five year period for the paper, ‘Blood Flow and Cell-Free Layer in Microvessels.’
http://dx.doi.org/10.1016/j.ddmod.2016.01.001
Please cite this article in press as: Drug Discov Today: Dis Model (2016), http://dx.doi.org/10.1016/j.ddmod.2016.01.001
e1
DDMOD-423; No of Pages 3 Drug Discovery Today: Disease Models | Editorial
Vol. xxx, No. xx 2016
Drug Discovery Today: Disease Models
Figure 1. Red blood cells (red) and circulating tumor cells (green) traveling through a microfluidic cell sorting device as simulated by uDeviceX, a GPUaccelerated parallel solver developed by a joint team of researchers from Brown University, ETH Zurich, University of Lugano. These results were obtained based on the Dissipative Particle Dynamics (DPD) method on the Titan supercomputer at Oak Ridge Leadership Computing facility. The solvent (plasma), the red blood cells, as well as the cancel cells are all represented by DPD. The image is rendered using ray tracing by Yu-Hang Tang of Brown University.
In this special issue, we have included three papers focusing on different aspects of blood diseases. The first paper by Clapp and Levy reviews mathematical models for leukemia and lymphoma, which affect over one million people in the United States according to the Leukemia and Lymphoma Society. The paper first discusses hematopoiesis, which is often modeled as system of discrete maturity stages starting with hematopoietic stem cells and ending with mature blood cells. Despite its complexity, simple ordinary differential equation (ODE) models have already provided useful insight into the process. Moreover, delay ODEs (DDEs) can be employed to capture events such as cell divisions. Stochasticity may also be important, especially for small cell populations in order to capture the emerging dynamics. The second part of the paper examines the utility of mathematical models for treatment, specifically how to improve and optimize the way various therapies are administered. To this end, parametric sensitivity analysis and numerical simulation can determine the dependence of a treatment outcome on a specific model. The final part of the paper reviews how mathematical models can be used to evaluate drug resistance, what combinations of drugs may be the most effective, and also how to quantify the probability of treatment failure. The second paper by Kunz et al. presents a review of flow, structure and biochemistry models of the tumor microenvironment. The focus is on melanoma metastasis, where the biochemical and dynamic interactions between e2
polymorphonuclear neutrophils (PMNs) and tumor cells (TCs) are of interest; PMNs comprise 50–70% of all circulating leukocytes. PMN-mediated tumor cell adhesion to the endothelium under shear flow conditions is a critical step in metastasis. The paper presents first cell-scale fluid dynamics methods, followed by a discussion on geometric and structural dynamics modeling of cells in blood flow. Then, the authors review the adhesive dynamics method applied to adherent leukocytes that participate in TC capture. Adhesion kinetics are modeled as probabilistic interactions between receptor and ligand molecules with the adhesion molecules modeled as springs. The specific biochemistry of adhesion kinetics models of relevance to PMN-TC and PMN-EC (endothelium cell) bonding are then presented. Finally, they briefly touch on scale-bridging approaches that have appeared for molecular-to-cell and cell-to-cell-population interactions. The authors also present a new method for predicting adhesion efficiency at the cell-population-scale using a statistical technique. They pose the important modeling question on when to model at the cell-resolving level and what modeling fidelity to employ at the cell-population level. Simplified models where the expensive fluid dynamics is taken into account only implicitly allow for systematic parametric studies on adhesion biochemistry, cell deformation and margination, without excessive computational cost. The third paper by Fedosov presents a review of the stateof-the-art in modeling the various stages of malaria and also
www.drugdiscoverytoday.com
Please cite this article in press as: Drug Discov Today: Dis Model (2016), http://dx.doi.org/10.1016/j.ddmod.2016.01.001
DDMOD-423; No of Pages 3 Vol. xxx, No. xx 2016
of sickle cell anemia. While the former is an infectious disease and the latter a genetic disease, from the modeling perspective they share some similarities that the computational multiscale framework presented in the paper can effectively address. For example, they both increase the apparent blood viscosity and they can both cause vaso-occlusion episodes due to RBC stiffening and the adhesive properties of the diseased RBCs. However, in malaria it is reasonable to model the parasite inside the RBCs as a solid body whereas in sickle cell anemia the dynamic self-assembly process of sickle hemoglobin polymerization has to be modeled with sufficient accuracy as it determines the RBC shape deformation, which, in turn, affects greatly the biorheological properties of the sickle blood. Using the method of dissipative particle dynamics (DPD) – a coarse-grained molecular dynamics approach – several biophysical mechanisms of both diseases can be elucidated and quantified. Such DPD models have been carefully
Drug Discovery Today: Disease Models | Editorial
developed and validated using companion microfluidic experiments. In summary, these three papers cover some representative and diverse aspects of modeling blood flow diseases. The introduction of microfluidics into biomedicine has led to new opportunities for systematic validation of these complex models, often used patient-specific blood, which can provide calibration of parameters for the missing biochemistry details that are not currently captured with the available models. Looking into the future, a promising avenue of research in the computational modeling of blood diseases may be the integration of advances from the system biology, which can greatly advance the understanding of the adhesive properties of blood cells in the presence of inflammation, the metastasis of cancer through circulation tumor cells, and other diseases such as the formation of thrombus in the human arterial tree.
www.drugdiscoverytoday.com
Please cite this article in press as: Drug Discov Today: Dis Model (2016), http://dx.doi.org/10.1016/j.ddmod.2016.01.001
e3