Data-driven modelling of the FRC network for studying the fluid flow in the conduit system

Abstract The human immune system is characterized by enormous cellular and anatomical complexity. Lymph nodes are key centers of immune reactivity, organized into distinct structural and functional modules including the T-cell zone, fibroblastic reticular cell (FRC) network and the conduit system. A thorough understanding of the modular organization is a prerequisite for lymphoid organ tissue-engineering. Due to the biological complexity of lymphoid organs, the development of mathematical models capable of elaborating the lymph node architecture and functional organization, has remained a major challenge in computational biology. Here, we present a computational method to model the geometry of the FRC network and fluid flow in the conduit system. It differs from the blood vascular network image-based reconstruction approaches as it develops the parameterized geometric model using the real statistics of the node degree and the edge length distributions. The FRC network model is then used to analyze the fluid flow through the underlying conduit system. A first observation is that the pressure gradient is approximately linear, which suggests homogeneity of the network. Furthermore, calculated permeability values ( ≈ 0.0033 μ m 2 ) show the generated network is isotropic, while investigating random variations of pipe radii (with a given mean and standard deviation) shows a significant effect on the permeability. This framework can now be further explored to systematically correlate fundamental characteristics of the FRC conduit system to more global material properties such as permeability.

[1]  Georg Kraal,et al.  The conduit system of the lymph node. , 2008, International immunology.

[2]  Paul S. Andrews,et al.  Pairing experimentation and computational modeling to understand the role of tissue inducer cells in the development of lymphoid organs , 2012, Front. Immun..

[3]  R. Black,et al.  Modelling the lymphatic system: challenges and opportunities , 2012, Journal of The Royal Society Interface.

[4]  Richard Manasseh,et al.  Development of optimized vascular fractal tree models using level set distance function. , 2010, Medical engineering & physics.

[5]  Mohammad Jafarnejad,et al.  Modeling Lymph Flow and Fluid Exchange with Blood Vessels in Lymph Nodes. , 2015, Lymphatic research and biology.

[6]  Timoteo Carletti,et al.  The Stochastic Evolution of a Protocell: The Gillespie Algorithm in a Dynamically Varying Volume , 2011, Comput. Math. Methods Medicine.

[7]  Bharathram Ganapathisubramani,et al.  An Image-Based Model of Fluid Flow Through Lymph Nodes , 2016, Bulletin of mathematical biology.

[8]  Jens V. Stein,et al.  Quantitative Measurements in 3-Dimensional Datasets of Mouse Lymph Nodes Resolve Organ-Wide Functional Dependencies , 2012, Comput. Math. Methods Medicine.

[9]  D. Dasgupta.  Artificial Immune Systems and Their Applications , 1998, Springer Berlin Heidelberg.

[10]  Stephen G. Kobourov,et al.  Spring Embedders and Force Directed Graph Drawing Algorithms , 2012, ArXiv.

[11]  Richard Manasseh,et al.  Dynamics of pulsatile flow in fractal models of vascular branching networks , 2009, Medical & Biological Engineering & Computing.

[12]  Mark Coles,et al.  IL-7-producing stromal cells are critical for lymph node remodeling. , 2012, Blood.

[13]  Hazel M. Dockrell,et al.  Roitt's essential immunology: book review , 2002 .

[14]  Jonathan Timmis,et al.  An immune-inspired swarm aggregation algorithm for self-healing swarm robotic systems , 2016, Biosyst..

[15]  L. Munn,et al.  Imaging the lymphatic system. , 2014, Microvascular research.

[16]  Gregory B. Sands,et al.  Organ-wide 3D-imaging and topological analysis of the continuous microvascular network in a murine lymph node , 2015, Scientific Reports.

[17]  S. Turley,et al.  Fibroblastic Reticular Cells: Organization and Regulation of the T Lymphocyte Life Cycle , 2015, The Journal of Immunology.

[18]  Michael Sixt,et al.  The conduit system transports soluble antigens from the afferent lymph to resident dendritic cells in the T cell area of the lymph node. , 2005, Immunity.

[19]  Yoshinori Fukui,et al.  Global lymphoid tissue remodeling during a viral infection is orchestrated by a B cell-lymphotoxin-dependent pathway. , 2010, Blood.

[20]  Paul S. Andrews,et al.  Using argument notation to engineer biological simulations with increased confidence , 2015, Journal of The Royal Society Interface.

[21]  Emma Hart,et al.  An Engineering-Informed Modelling Approach to AIS , 2011, ICARIS.

[22]  A. Haase,et al.  Lymphoid tissue structure and HIV-1 infection: life or death for T cells. , 2012, Trends in immunology.

[23]  C. Herndon,et al.  Contextual analysis of immunological response through whole-organ fluorescent imaging. , 2013, Lymphatic research and biology.

[24]  Burkhard Ludewig,et al.  Topological Small-World Organization of the Fibroblastic Reticular Cell Network Determines Lymph Node Functionality , 2016, PLoS biology.

[25]  Yongsheng Ding,et al.  An immune system-inspired rescheduling algorithm for workflow in Cloud systems , 2016, Knowl. Based Syst..

[26]  Irun R. Cohen,et al.  Real and artificial immune systems: computing the state of the body , 2007, Nature Reviews Immunology.

[27]  Gennady Bocharov,et al.  Computational Approach to 3D Modeling of the Lymph Node Geometry , 2015, Comput..

[28]  A Danilov,et al.  Methods of graph network reconstruction in personalized medicine , 2016, International journal for numerical methods in biomedical engineering.

[29]  S. McDougall,et al.  Mathematical modelling of flow through vascular networks: Implications for tumour-induced angiogenesis and chemotherapy strategies , 2002, Bulletin of mathematical biology.

[30]  L. Leserman,et al.  Disrupted Lymph Node and Splenic Stroma in Mice with Induced Inflammatory Melanomas Is Associated with Impaired Recruitment of T and Dendritic Cells , 2011, PloS one.

[31]  G. Bokoch,et al.  Sophisticated strategies for information encounter in the lymph node: the reticular network as a conduit of soluble information and a highway for cell traffic. , 1996, Journal of immunology.

[32]  Brian E. Chapman,et al.  Automated generation of directed graphs from vascular segmentations , 2015, J. Biomed. Informatics.

[33]  Mark Coles,et al.  Application of tissue engineering to the immune system: development of artificial lymph nodes , 2012, Front. Immun..

[34]  Jonathan Timmis,et al.  Application areas of AIS: The past, the present and the future , 2008, Appl. Soft Comput..

[35]  Ashutosh Kumar Singh,et al.  Ex vivo engineered immune organoids for controlled germinal center reactions. , 2015, Biomaterials.

[36]  M. Swartz,et al.  Interstitial flow and its effects in soft tissues. , 2007, Annual review of biomedical engineering.

[37]  Thomas Rülicke,et al.  Maturation of Lymph Node Fibroblastic Reticular Cells from Myofibroblastic Precursors Is Critical for Antiviral Immunity , 2013, Immunity.

[38]  L Preziosi,et al.  A review of mathematical models for the formation of vascular networks. , 2013, Journal of theoretical biology.

[39]  Stephen Shaw,et al.  Lymph-Borne Chemokines and Other Low Molecular Weight Molecules Reach High Endothelial Venules via Specialized Conduits While a Functional Barrier Limits Access to the Lymphocyte Microenvironments in Lymph Node Cortex , 2000, The Journal of experimental medicine.

[40]  S Aharinejad,et al.  The influence of optimization target selection on the structure of arterial tree models generated by constrained constructive optimization , 1995, The Journal of general physiology.