{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,14]],"date-time":"2026-03-14T12:55:17Z","timestamp":1773492917937,"version":"3.50.1"},"reference-count":39,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2018,11,14]],"date-time":"2018-11-14T00:00:00Z","timestamp":1542153600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/100000002","name":"National Institutes of Health","doi-asserted-by":"publisher","award":["R01 AI123093"],"award-info":[{"award-number":["R01 AI123093"]}],"id":[{"id":"10.13039\/100000002","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000002","name":"National Institutes of Health","doi-asserted-by":"publisher","award":["R01 HL110811"],"award-info":[{"award-number":["R01 HL110811"]}],"id":[{"id":"10.13039\/100000002","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000002","name":"National Institutes of Health","doi-asserted-by":"publisher","award":["U01HL131072"],"award-info":[{"award-number":["U01HL131072"]}],"id":[{"id":"10.13039\/100000002","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100004944","name":"Department of Energy, Labor and Economic Growth","doi-asserted-by":"publisher","award":["DE-AC02-05CH11231"],"award-info":[{"award-number":["DE-AC02-05CH11231"]}],"id":[{"id":"10.13039\/100004944","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["MCB140228"],"award-info":[{"award-number":["MCB140228"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Computation"],"abstract":"<jats:p>Within the first 2\u20133 months of a Mycobacterium tuberculosis (Mtb) infection, 2\u20134 mm spherical structures called granulomas develop in the lungs of the infected hosts. These are the hallmark of tuberculosis (TB) infection in humans and non-human primates. A cascade of immunological events occurs in the first 3 months of granuloma formation that likely shapes the outcome of the infection. Understanding the main mechanisms driving granuloma development and function is key to generating treatments and vaccines. In vitro, in vivo, and in silico studies have been performed in the past decades to address the complexity of granuloma dynamics. This study builds on our previous 2D spatio-temporal hybrid computational model of granuloma formation in TB (GranSim) and presents for the first time a more realistic 3D implementation. We use uncertainty and sensitivity analysis techniques to calibrate the new 3D resolution to non-human primate (NHP) experimental data on bacterial levels per granuloma during the first 100 days post infection. Due to the large computational cost associated with running a 3D agent-based model, our major goal is to assess to what extent 2D and 3D simulations differ in predictions for TB granulomas and what can be learned in the context of 3D that is missed in 2D. Our findings suggest that in terms of major mechanisms driving bacterial burden, 2D and 3D models return very similar results. For example, Mtb growth rates and molecular regulation mechanisms are very important both in 2D and 3D, as are cellular movement and modulation of cell recruitment. The main difference we found was that the 3D model is less affected by crowding when cellular recruitment and movement of cells are increased. Overall, we conclude that the use of a 2D resolution in GranSim is warranted when large scale pilot runs are to be performed and if the goal is to determine major mechanisms driving infection outcome (e.g., bacterial load). To comprehensively compare the roles of model dimensionality, further tests and experimental data will be needed to expand our conclusions to molecular scale dynamics and multi-scale resolutions.<\/jats:p>","DOI":"10.3390\/computation6040058","type":"journal-article","created":{"date-parts":[[2018,11,14]],"date-time":"2018-11-14T10:58:22Z","timestamp":1542193102000},"page":"58","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":18,"title":["The Role of Dimensionality in Understanding Granuloma Formation"],"prefix":"10.3390","volume":"6","author":[{"given":"Simeone","family":"Marino","sequence":"first","affiliation":[{"name":"Department of Microbiology and Immunology, University of Michigan Medical School, Ann Arbor, MI 48109, USA"},{"name":"Statistics Online Computational Resource (SOCR), Department of Health Behavior and Biological Sciences, University of Michigan, Ann Arbor, MI 48109, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2641-2180","authenticated-orcid":false,"given":"Caitlin","family":"Hult","sequence":"additional","affiliation":[{"name":"Department of Microbiology and Immunology, University of Michigan Medical School, Ann Arbor, MI 48109, USA"},{"name":"Department of Chemical Engineering, University of Michigan, Ann Arbor, MI 48109, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Paul","family":"Wolberg","sequence":"additional","affiliation":[{"name":"Department of Microbiology and Immunology, University of Michigan Medical School, Ann Arbor, MI 48109, USA"},{"name":"Department of Chemical Engineering, University of Michigan, Ann Arbor, MI 48109, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jennifer J.","family":"Linderman","sequence":"additional","affiliation":[{"name":"Department of Chemical Engineering, University of Michigan, Ann Arbor, MI 48109, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1053-2591","authenticated-orcid":false,"given":"Denise E.","family":"Kirschner","sequence":"additional","affiliation":[{"name":"Department of Microbiology and Immunology, University of Michigan Medical School, Ann Arbor, MI 48109, USA"},{"name":"Department of Computational Medicine and Bioinformatics, University of Michigan, Ann Arbor, MI 48109, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2018,11,14]]},"reference":[{"key":"ref_1","unstructured":"Organization, W.H. (2016). Global Tuberculosis Report 2016, World Health Organization."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"482","DOI":"10.1038\/ng.811","article-title":"Use of whole genome sequencing to estimate the mutation rate of Mycobacterium tuberculosis during latent infection","volume":"43","author":"Ford","year":"2011","journal-title":"Nat. Genet."},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Cole, S.T., Eisenach, K.D., McMurray, D.N., and Jacobs, W.R. (2005). Animal Models of Tuberculosis. Tuberculosis and the Tubercle Bacillus, ASM Press.","DOI":"10.1128\/9781555817657"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"116","DOI":"10.1016\/S1472-9792(02)00059-8","article-title":"Non-human primates: A model for tuberculosis research","volume":"83","author":"Flynn","year":"2003","journal-title":"Tuberculosis"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"170","DOI":"10.1016\/j.coisb.2017.05.014","article-title":"A review of computational and mathematical modeling contributions to our understanding of Mycobacterium tuberculosis within-host infection and treatment","volume":"3","author":"Kirschner","year":"2017","journal-title":"Curr. Opin. Syst. Biol."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"1951","DOI":"10.4049\/jimmunol.166.3.1951","article-title":"A model to predict cell-mediated immune regulatory mechanisms during human infection with Mycobacterium tuberculosis","volume":"166","author":"Wigginton","year":"2001","journal-title":"J. Immunol."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"463","DOI":"10.1016\/j.jtbi.2003.11.023","article-title":"The human immune response to Mycobacterium tuberculosis in lung and lymph node","volume":"227","author":"Marino","year":"2004","journal-title":"J. Theor. Biol."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"494","DOI":"10.4049\/jimmunol.173.1.494","article-title":"Dendritic cell trafficking and antigen presentation in the human immune response to Mycobacterium tuberculosis","volume":"173","author":"Marino","year":"2004","journal-title":"J. Immunol."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"586","DOI":"10.1016\/j.jtbi.2010.05.012","article-title":"TNF and IL-10 are major factors in modulation of the phagocytic cell environment in lung and lymph node in tuberculosis: A next-generation two-compartmental model","volume":"265","author":"Marino","year":"2010","journal-title":"J. Theor. Biol."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"218","DOI":"10.1007\/s00285-003-0232-8","article-title":"Macrophage response to Mycobacterium tuberculosis infection","volume":"48","author":"Gammack","year":"2004","journal-title":"J. Math. Biol."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"357","DOI":"10.1016\/j.jtbi.2004.06.031","article-title":"Identifying control mechanisms of granuloma formation during M. tuberculosis infection using an agent-based model","volume":"231","author":"Ganguli","year":"2004","journal-title":"J. Theor. Biol."},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Fallahi-Sichani, M., Schaller, M.A., Kirschner, D.E., Kunkel, S.L., and Linderman, J.J. (2010). Identification of key processes that control tumor necrosis factor availability in a tuberculosis granuloma. PLoS Comput. Biol., 6.","DOI":"10.1371\/journal.pcbi.1000778"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"3706","DOI":"10.4049\/jimmunol.0802297","article-title":"Synergy between individual TNF-dependent functions determines granuloma performance for controlling Mycobacterium tuberculosis infection","volume":"182","author":"Ray","year":"2009","journal-title":"J. Immunol."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"24","DOI":"10.1016\/j.jtbi.2008.01.010","article-title":"The timing of TNF and IFN-gamma signaling affects macrophage activation strategies during Mycobacterium tuberculosis infection","volume":"252","author":"Ray","year":"2008","journal-title":"J. Theor. Biol."},{"key":"ref_15","unstructured":"Waliga, J., Marino, S., and Kirschner, D.E. (2018, November 09). The Agent-Based Model (ABM) Describing Tuberculosis (TB) Granuloma Formation and Function in the Lung. Available online: http:\/\/malthus.micro.med.umich.edu\/GranSim\/."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"2873","DOI":"10.4049\/jimmunol.0903117","article-title":"Characterizing the dynamics of CD4+ T cell priming within a lymph node","volume":"184","author":"Linderman","year":"2010","journal-title":"J. Immunol."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"169","DOI":"10.1016\/j.jtbi.2013.06.016","article-title":"Predicting lymph node output efficiency using systems biology","volume":"335C","author":"Gong","year":"2013","journal-title":"J. Theor. Biol."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"57","DOI":"10.3389\/fimmu.2014.00057","article-title":"Harnessing the heterogeneity of T cell differentiation fate to fine-tune generation of effector and memory T cells","volume":"5","author":"Gong","year":"2014","journal-title":"Front. Immunol."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"668","DOI":"10.3389\/fimmu.2016.00668","article-title":"Tissue Dimensionality Influences the Functional Response of Cytotoxic T Lymphocyte-Mediated Killing of Targets","volume":"7","author":"Gadhamsetty","year":"2017","journal-title":"Front. Immunol."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"93","DOI":"10.1146\/annurev.immunol.19.1.93","article-title":"Immunology of tuberculosis","volume":"19","author":"Flynn","year":"2001","journal-title":"Annu. Rev. Immunol."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"475","DOI":"10.1146\/annurev-immunol-032712-095939","article-title":"The immune response in tuberculosis","volume":"31","author":"Redford","year":"2013","journal-title":"Annu. Rev. Immunol."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"943","DOI":"10.1038\/ni.1781","article-title":"Foamy macrophages and the progression of the human tuberculosis granuloma","volume":"10","author":"Russell","year":"2009","journal-title":"Nat. Immunol."},{"key":"ref_23","doi-asserted-by":"crossref","unstructured":"Cilfone, N.A., Perry, C.R., Kirschner, D.E., and Linderman, J.J. (2013). Multi-scale modeling predicts a balance of tumor necrosis factor-alpha and interleukin-10 controls the granuloma environment during Mycobacterium tuberculosis infection. PLoS ONE, 8.","DOI":"10.1371\/journal.pone.0068680"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"3472","DOI":"10.4049\/jimmunol.1003299","article-title":"Multiscale computational modeling reveals a critical role for TNF-alpha receptor 1 dynamics in tuberculosis granuloma formation","volume":"186","author":"Marino","year":"2011","journal-title":"J. Immunol."},{"key":"ref_25","first-page":"170","article-title":"NF-kappaB Signaling Dynamics Play a Key Role in Infection Control in Tuberculosis","volume":"3","author":"Kirschner","year":"2012","journal-title":"Front. Physiol."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"324","DOI":"10.1128\/IAI.02494-14","article-title":"Macrophage Polarization Drives Granuloma Outcome during Mycobacterium tuberculosis Infection","volume":"83","author":"Marino","year":"2015","journal-title":"Infect. Immun."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"50","DOI":"10.1016\/j.jtbi.2011.03.022","article-title":"A hybrid multi-compartment model of granuloma formation and T cell priming in Tuberculosis","volume":"280","author":"Marino","year":"2011","journal-title":"J. Theor. Biol."},{"key":"ref_28","doi-asserted-by":"crossref","unstructured":"Marino, S., Gideon, H.P., Gong, C., Mankad, S., McCrone, J.T., Lin, P.L., Linderman, J.J., Flynn, J.L., and Kirschner, D.E. (2016). Computational and Empirical Studies Predict Mycobacterium tuberculosis-Specific T Cells as a Biomarker for Infection Outcome. PLoS Comput. Biol., 12.","DOI":"10.1371\/journal.pcbi.1004804"},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"119","DOI":"10.1007\/s12195-014-0363-6","article-title":"Strategies for efficient numerical implementation of hybrid multi-scale agent-based models to describe biological systems","volume":"8","author":"Cilfone","year":"2015","journal-title":"Cell. Mol. Bioeng"},{"key":"ref_30","unstructured":"Press, W.H.T., Saul, A.T., Vetterling, W.T., and Flannery, P.B. (2007). Numerical Recipes: The Art of Scientific Computing, Cambridge University Press. [3rd ed.]."},{"key":"ref_31","doi-asserted-by":"crossref","unstructured":"Marino, S., Hult, C., Wolberg, P., Linderman, J.J., and Kirschner, D.E. (2018, November 09). The Role of Dimensionality in Understanding Granuloma Formation. Available online: http:\/\/malthus.micro.med.umich.edu\/3D-GranSim\/.","DOI":"10.3390\/computation6040058"},{"key":"ref_32","unstructured":"Nokia (2018, November 09). Qt. Available online: http:\/\/qt.nokia.com\/."},{"key":"ref_33","unstructured":"Khronos (2018, November 09). OpenGL. Available online: www.opengl.org."},{"key":"ref_34","unstructured":"Adalsteinsson, D. (2018, November 09). A Numerical Work Environment. Available online: http:\/\/www.visualdatatools.com\/DataTank\/index.html."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"178","DOI":"10.1016\/j.jtbi.2008.04.011","article-title":"A methodology for performing global uncertainty and sensitivity analysis in systems biology","volume":"254","author":"Marino","year":"2008","journal-title":"J. Theor. Biol."},{"key":"ref_36","unstructured":"Marino, S., and Kirschner, D.E. (2018, November 09). Uncertainty and Sensitivity Functions and Implementation. Available online: http:\/\/malthus.micro.med.umich.edu\/lab\/usadata\/."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"147","DOI":"10.1111\/imr.12671","article-title":"Dynamic balance of pro- and anti-inflammatory signals controls disease and limits pathology","volume":"285","author":"Cicchese","year":"2018","journal-title":"Immunol. Rev."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"664","DOI":"10.4049\/jimmunol.1400734","article-title":"Computational modeling predicts IL-10 control of lesion sterilization by balancing early host immunity-mediated antimicrobial responses with caseation during Mycobacterium tuberculosis infection","volume":"194","author":"Cilfone","year":"2015","journal-title":"J. Immunol."},{"key":"ref_39","doi-asserted-by":"crossref","unstructured":"Marino, S., Fallahi-Sichani, M., Linderman, J.J., and Kirschner, D.E. (2012). Mathematical Models of Anti-TNF Therapies and their Correlation with Tuberculosis. Antibody-Mediated Drug Delivery Systems, John Wiley & Sons, Inc.. Chapter 5.","DOI":"10.1002\/9781118229019.ch5"}],"container-title":["Computation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2079-3197\/6\/4\/58\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T15:29:37Z","timestamp":1760196577000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2079-3197\/6\/4\/58"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,11,14]]},"references-count":39,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2018,12]]}},"alternative-id":["computation6040058"],"URL":"https:\/\/doi.org\/10.3390\/computation6040058","relation":{},"ISSN":["2079-3197"],"issn-type":[{"value":"2079-3197","type":"electronic"}],"subject":[],"published":{"date-parts":[[2018,11,14]]}}}