2011, 8(2): 643-658. doi: 10.3934/mbe.2011.8.643

A multiscale model of the bone marrow and hematopoiesis

1. 

H Lee Moffitt Cancer Center, 12902 Magnolia Dr, Tampa, FL 33612, United States, United States

2. 

H. Lee Moffitt Cancer Center & Research Institute, Integrated Mathematical Oncology, 12902 Magnolia Drive, Tampa, FL 33612, United States

Received  March 2010 Revised  December 2010 Published  April 2011

The bone marrow is necessary for renewal of all hematopoietic cells and critical for maintenance of a wide range of physiologic functions. Multiple human diseases result from bone marrow dysfunction. It is also the site in which liquid tumors, including leukemia and multiple myeloma, develop as well as a frequent site of metastases. Understanding the complex cellular and microenvironmental interactions that govern normal bone marrow function as well as diseases and cancers of the bone marrow would be a valuable medical advance. Our goal is the development of a spatially-explicit in silico model of the bone marrow to understand both its normal function and the evolutionary dynamics that govern the emergence of bone marrow malignancy. Here we introduce a multiscale computational model of the bone marrow that incorporates three distinct spatial scales, cell, hematopoietic subunit, whole marrow. Our results, using parameter estimates from literature, recapitulates normal bone marrow function and suggest an explanation for the fractal-like structure of trabeculae and sinuses in the marrow, which would be an optimization of the hematopoietic function in order to maximize the number of mature blood cells produced daily within the volumetric restrictions of the marrow.
Citation: Ariosto Silva, Alexander R. A. Anderson, Robert Gatenby. A multiscale model of the bone marrow and hematopoiesis. Mathematical Biosciences & Engineering, 2011, 8 (2) : 643-658. doi: 10.3934/mbe.2011.8.643
References:
[1]

T. M. Fliedner, D. Graessle, C. Paulsen and K. Reimers, Structure and function of bone marrow hemopoiesis: Mechanisms of response to ionizing radiation exposure,, Cancer Biother. Radiopharm., 17 (2002), 405. doi: 10.1089/108497802760363204.

[2]

I. B. Mazo and U. H. von Andrian, Adhesion and homing of blood-borne cells in bone marrow microvessels,, J. Leukoc. Biol., 66 (1999), 25.

[3]

M. T. Valarmathi, J. M. Davis, M. J. Yost, R. L. Goodwin and J. D. Potts, A three-dimensional model of vasculogenesis,, Biomaterials, 30 (2009), 1098. doi: 10.1016/j.biomaterials.2008.10.044.

[4]

M. Adimy and F. Crauste, Mathematical model of hematopoiesis dynamics with growth factor-dependent apoptosis and proliferation regulations,, Mathematical and Computer Modelling, 49 (2009), 2128. doi: 10.1016/j.mcm.2008.07.014.

[5]

M. Adimy, O. Angulo, F. Crauste and J. C. Lopez-Marcos, Numerical integration of a mathematical model of hematopoietic stem cell dynamics,, Computers and Mathematics with Applications, 56 (2008), 594. doi: 10.1016/j.camwa.2008.01.003.

[6]

E. S. Antoniou, S. Sund, E. N. Homsi, L. F. Challenger and P. Rameshwar, A theoretical simulation of hematopoietic stem cells during oxygen fluctuations: Prediction of bone marrow responses during hemorrhagic shock.,, Shock, 22 (2004), 415. doi: 10.1097/01.shk.0000142185.88094.88.

[7]

C. Colijn and M. C. Mackey, A mathematical model of hematopoiesis-I. Periodic chronic myelogenous leukemia,, J. Theor. Biol., 237 (2005), 117. doi: 10.1016/j.jtbi.2005.03.033.

[8]

C. Colijn and M. C. Mackey, A mathematical model of hematopoiesis: II. Cyclical neutropenia,, J. Theor. Biol., 237 (2005), 133. doi: 10.1016/j.jtbi.2005.03.034.

[9]

I. Ostby, H. B. Benestad and P. Grottum, Mathematical modeling of human granulopoiesis: The possible importance of regulated apoptosis,, Math. Biosci., 186 (2003), 1. doi: 10.1016/j.mbs.2003.07.003.

[10]

O. A. Smirnova, Mathematical modeling the radiation effects on humoral immunity,, Advances in Space Research, 37 (2006), 1813. doi: 10.1016/j.asr.2006.01.003.

[11]

N. Bessonov, L. Pujo-Menjouet and V. Volpert, Cell Modelling of Hematopoiesis,, Math. Model. Nat. Phenom, 2 (2008), 81.

[12]

N. Bessonov, I. Demin, L. Pujo-Menjouet and V. Volpert, A multi-agent model describing self-renewal of differentiation effects on the blood cell population,, Mathematical and Computer Modelling, 49 (2009), 2116. doi: 10.1016/j.mcm.2008.07.023.

[13]

M. B. Meads, L. A. Hazlehurst and W. S. Dalton, The bone marrow microenvironment as a tumor sanctuary and contributor to drug resistance,, Clin. Cancer Res., 14 (2008), 2519. doi: 10.1158/1078-0432.CCR-07-2223.

[14]

M. B. Meads, R. A. Gatenby and W. S. Dalton, Environment-mediated drug resistance: A major contributor to minimal residual disease,, Nat. Rev. Cancer, 9 (2009), 665. doi: 10.1038/nrc2714.

[15]

T. Albrektsson and B. Albrektsson, Microcirculation in grafted bone. A chamber technique for vital microscopy of rabbit bone transplants,, Acta Orthop. Scand., 49 (1978), 1. doi: 10.3109/17453677809005716.

[16]

P. I. Branemark, Vital microscopy of bone marrow in rabbit,, Scand. J. Clin. Lab Invest., 11 (1959), 1.

[17]

E. Passegue, A. J. Wagers, S. Giuriato, W. C. Anderson and I. L. Weissman, Global analysis of proliferation and cell cycle gene expression in the regulation of hematopoietic stem and progenitor cell fates,, J. Exp. Med., 202 (2005), 1599. doi: 10.1084/jem.20050967.

[18]

V. A. Bourke, C. J. Watchman, J. D. Reith, M. L. Jorgensen, A. Dieudonne and W. E. Bolch, Spatial gradients of blood vessels and hematopoietic stem and progenitor cells within the marrow cavities of the human skeleton,, Blood, 114 (2009), 4077. doi: 10.1182/blood-2008-12-192922.

[19]

L. M. Calvi, G. B. Adams, K. W. Weibrecht, J. M. Weber, D. P. Olson, M. C. Knight, R. P. Martin, E. Schipani, P. Divieti, F. R. Bringhurst, L. A. Milner, H. M. Kronenberg and D. T. Scadden, Osteoblastic cells regulate the haematopoietic stem cell niche,, Nature, 425 (2003), 841. doi: 10.1038/nature02040.

[20]

Y. Kubota, K. Takubo and T. Suda, Bone marrow long label-retaining cells reside in the sinusoidal hypoxic niche,, Biochem. Biophys. Res. Commun., 366 (2008), 335. doi: 10.1016/j.bbrc.2007.11.086.

[21]

X. M. Li, Z. Hu, M. L. Jorgenson, J. R. Wingard and W. B. Slayton, Bone marrow sinusoidal endothelial cells undergo nonapoptotic cell death and are replaced by proliferating sinusoidal cells in situ to maintain the vascular niche following lethal irradiation,, Exp. Hematol., 36 (2008), 1143. doi: 10.1016/j.exphem.2008.06.009.

[22]

S. G. McClugage, R. S. McCuskey Jr. and H. A. Meineke, Microscopy of living bone marrow in Situ. II. Influence of the microenvironment on hemopoiesis,, Blood, 38 (1971), 96.

[23]

S. K. Nilsson, H. M. Johnston and J. A. Coverdale, Spatial localization of transplanted hemopoietic stem cells: Inferences for the localization of stem cell niches,, Blood, 97 (2001), 2293. doi: 10.1182/blood.V97.8.2293.

[24]

C. J. Watchman, V. A. Bourke, J. R. Lyon, A. E. Knowlton, S. L. Butler, D. D. Grier, J. R. Wingard, R. C. Braylan and W. E. Bolch, Spatial distribution of blood vessels and CD34+ hematopoietic stem and progenitor cells within the marrow cavities of human cancellous bone,, J. Nucl. Med., 48 (2007), 645. doi: 10.2967/jnumed.106.035337.

[25]

T. Yahata, Y. Muguruma, S. Yumino, Y. Sheng, T. Uno, H. Matsuzawa, M. Ito, S. Kato, T. Hotta and K. Ando, Quiescent human hematopoietic stem cells in the bone marrow niches organize the hierarchical structure of hematopoiesis,, Stem Cells, 26 (2008), 3228. doi: 10.1634/stemcells.2008-0552.

[26]

T. Yin and L. Li, The stem cell niches in bone,, J. Clin. Invest., 116 (2006), 1195. doi: 10.1172/JCI28568.

[27]

J. Zhang, C. Niu, L. Ye, H. Huang, X. He, W. G. Tong, J. Ross, J. Haug, T. Johnson, J. Q. Feng, S. Harris, L. M. Wiedemann, Y. Mishina and L. Li, Identification of the haematopoietic stem cell niche and control of the niche size,, Nature, 425 (2003), 836. doi: 10.1038/nature02041.

[28]

G. B. Adams, K. T. Chabner, I. R. Alley, D. P. Olson, Z. M. Szczepiorkowski, M. C. Poznansky, C. H. Kos, M. R. Pollak, E. M. Brown and D. T. Scadden, Stem cell engraftment at the endosteal niche is specified by the calcium-sensing receptor,, Nature, 439 (2006), 599.

[29]

P. Eliasson and J. I. Jonsson, The hematopoietic stem cell niche: Low in oxygen but a nice place to be,, J. Cell Physiol., 222 (2010), 17. doi: 10.1002/jcp.21908.

[30]

M. J. Kiel and S. J. Morrison, Uncertainty in the niches that maintain haematopoietic stem cells,, Nat. Rev. Immunol., 8 (2008), 290. doi: 10.1038/nri2279.

[31]

A. S. Silva, J. A. Yunes, R. J. Gillies and R. A. Gatenby, The potential role of systemic buffers in reducing intratumoral extracellular pH and acid-mediated invasion,, Cancer Res., 69 (2009), 2677. doi: 10.1158/0008-5472.CAN-08-2394.

[32]

A. S. Silva, R. A. Gatenby, R. J. Gillies and J. A. Yunes, A quantitative theoretical model for the development of malignancy in ductal carcinoma in situ,, J. Theor. Biol., 262 (2010), 601. doi: 10.1016/j.jtbi.2009.10.031.

[33]

D. Bray, "Cell movements: From Molecules to Motility,", 1$^{st}$ edition, (2001).

[34]

H. R. De Raeve, K. Asosingh, E. Wisse, B. Van Camp, E. Van Marck and K. Vanderkerken, Part of the multiple myeloma-associated microvessels is functionally connected to the systemic circulation: A study in the murine 5T33MM model,, Virchows Arch., 445 (2004), 389. doi: 10.1007/s00428-004-1064-7.

[35]

O. Sezer, K. Niemoller, O. Kaufmann, J. Eucker, C. Jakob, I. Zavrski and K. Possinger, Decrease of bone marrow angiogenesis in myeloma patients achieving a remission after chemotherapy,, Eur. J. Haematol., 66 (2001), 238. doi: 10.1034/j.1600-0609.2001.066004238.x.

[36]

A. Orazi, D. P. O'Malley and D. A. Arber, "Illustrated Pathology of the Bone Marrow,", 1$^{st}$ edition, (2006). doi: 10.1017/CBO9780511543531.

[37]

R. C. Furze and S. M. Rankin, Neutrophil mobilization and clearance in the bone marrow,, Immunology, 125 (2008), 281. doi: 10.1111/j.1365-2567.2008.02950.x.

[38]

N. C. Jain, "Essentials of Veterinary Hematology,", 1$^{st}$ edition, (1993).

show all references

References:
[1]

T. M. Fliedner, D. Graessle, C. Paulsen and K. Reimers, Structure and function of bone marrow hemopoiesis: Mechanisms of response to ionizing radiation exposure,, Cancer Biother. Radiopharm., 17 (2002), 405. doi: 10.1089/108497802760363204.

[2]

I. B. Mazo and U. H. von Andrian, Adhesion and homing of blood-borne cells in bone marrow microvessels,, J. Leukoc. Biol., 66 (1999), 25.

[3]

M. T. Valarmathi, J. M. Davis, M. J. Yost, R. L. Goodwin and J. D. Potts, A three-dimensional model of vasculogenesis,, Biomaterials, 30 (2009), 1098. doi: 10.1016/j.biomaterials.2008.10.044.

[4]

M. Adimy and F. Crauste, Mathematical model of hematopoiesis dynamics with growth factor-dependent apoptosis and proliferation regulations,, Mathematical and Computer Modelling, 49 (2009), 2128. doi: 10.1016/j.mcm.2008.07.014.

[5]

M. Adimy, O. Angulo, F. Crauste and J. C. Lopez-Marcos, Numerical integration of a mathematical model of hematopoietic stem cell dynamics,, Computers and Mathematics with Applications, 56 (2008), 594. doi: 10.1016/j.camwa.2008.01.003.

[6]

E. S. Antoniou, S. Sund, E. N. Homsi, L. F. Challenger and P. Rameshwar, A theoretical simulation of hematopoietic stem cells during oxygen fluctuations: Prediction of bone marrow responses during hemorrhagic shock.,, Shock, 22 (2004), 415. doi: 10.1097/01.shk.0000142185.88094.88.

[7]

C. Colijn and M. C. Mackey, A mathematical model of hematopoiesis-I. Periodic chronic myelogenous leukemia,, J. Theor. Biol., 237 (2005), 117. doi: 10.1016/j.jtbi.2005.03.033.

[8]

C. Colijn and M. C. Mackey, A mathematical model of hematopoiesis: II. Cyclical neutropenia,, J. Theor. Biol., 237 (2005), 133. doi: 10.1016/j.jtbi.2005.03.034.

[9]

I. Ostby, H. B. Benestad and P. Grottum, Mathematical modeling of human granulopoiesis: The possible importance of regulated apoptosis,, Math. Biosci., 186 (2003), 1. doi: 10.1016/j.mbs.2003.07.003.

[10]

O. A. Smirnova, Mathematical modeling the radiation effects on humoral immunity,, Advances in Space Research, 37 (2006), 1813. doi: 10.1016/j.asr.2006.01.003.

[11]

N. Bessonov, L. Pujo-Menjouet and V. Volpert, Cell Modelling of Hematopoiesis,, Math. Model. Nat. Phenom, 2 (2008), 81.

[12]

N. Bessonov, I. Demin, L. Pujo-Menjouet and V. Volpert, A multi-agent model describing self-renewal of differentiation effects on the blood cell population,, Mathematical and Computer Modelling, 49 (2009), 2116. doi: 10.1016/j.mcm.2008.07.023.

[13]

M. B. Meads, L. A. Hazlehurst and W. S. Dalton, The bone marrow microenvironment as a tumor sanctuary and contributor to drug resistance,, Clin. Cancer Res., 14 (2008), 2519. doi: 10.1158/1078-0432.CCR-07-2223.

[14]

M. B. Meads, R. A. Gatenby and W. S. Dalton, Environment-mediated drug resistance: A major contributor to minimal residual disease,, Nat. Rev. Cancer, 9 (2009), 665. doi: 10.1038/nrc2714.

[15]

T. Albrektsson and B. Albrektsson, Microcirculation in grafted bone. A chamber technique for vital microscopy of rabbit bone transplants,, Acta Orthop. Scand., 49 (1978), 1. doi: 10.3109/17453677809005716.

[16]

P. I. Branemark, Vital microscopy of bone marrow in rabbit,, Scand. J. Clin. Lab Invest., 11 (1959), 1.

[17]

E. Passegue, A. J. Wagers, S. Giuriato, W. C. Anderson and I. L. Weissman, Global analysis of proliferation and cell cycle gene expression in the regulation of hematopoietic stem and progenitor cell fates,, J. Exp. Med., 202 (2005), 1599. doi: 10.1084/jem.20050967.

[18]

V. A. Bourke, C. J. Watchman, J. D. Reith, M. L. Jorgensen, A. Dieudonne and W. E. Bolch, Spatial gradients of blood vessels and hematopoietic stem and progenitor cells within the marrow cavities of the human skeleton,, Blood, 114 (2009), 4077. doi: 10.1182/blood-2008-12-192922.

[19]

L. M. Calvi, G. B. Adams, K. W. Weibrecht, J. M. Weber, D. P. Olson, M. C. Knight, R. P. Martin, E. Schipani, P. Divieti, F. R. Bringhurst, L. A. Milner, H. M. Kronenberg and D. T. Scadden, Osteoblastic cells regulate the haematopoietic stem cell niche,, Nature, 425 (2003), 841. doi: 10.1038/nature02040.

[20]

Y. Kubota, K. Takubo and T. Suda, Bone marrow long label-retaining cells reside in the sinusoidal hypoxic niche,, Biochem. Biophys. Res. Commun., 366 (2008), 335. doi: 10.1016/j.bbrc.2007.11.086.

[21]

X. M. Li, Z. Hu, M. L. Jorgenson, J. R. Wingard and W. B. Slayton, Bone marrow sinusoidal endothelial cells undergo nonapoptotic cell death and are replaced by proliferating sinusoidal cells in situ to maintain the vascular niche following lethal irradiation,, Exp. Hematol., 36 (2008), 1143. doi: 10.1016/j.exphem.2008.06.009.

[22]

S. G. McClugage, R. S. McCuskey Jr. and H. A. Meineke, Microscopy of living bone marrow in Situ. II. Influence of the microenvironment on hemopoiesis,, Blood, 38 (1971), 96.

[23]

S. K. Nilsson, H. M. Johnston and J. A. Coverdale, Spatial localization of transplanted hemopoietic stem cells: Inferences for the localization of stem cell niches,, Blood, 97 (2001), 2293. doi: 10.1182/blood.V97.8.2293.

[24]

C. J. Watchman, V. A. Bourke, J. R. Lyon, A. E. Knowlton, S. L. Butler, D. D. Grier, J. R. Wingard, R. C. Braylan and W. E. Bolch, Spatial distribution of blood vessels and CD34+ hematopoietic stem and progenitor cells within the marrow cavities of human cancellous bone,, J. Nucl. Med., 48 (2007), 645. doi: 10.2967/jnumed.106.035337.

[25]

T. Yahata, Y. Muguruma, S. Yumino, Y. Sheng, T. Uno, H. Matsuzawa, M. Ito, S. Kato, T. Hotta and K. Ando, Quiescent human hematopoietic stem cells in the bone marrow niches organize the hierarchical structure of hematopoiesis,, Stem Cells, 26 (2008), 3228. doi: 10.1634/stemcells.2008-0552.

[26]

T. Yin and L. Li, The stem cell niches in bone,, J. Clin. Invest., 116 (2006), 1195. doi: 10.1172/JCI28568.

[27]

J. Zhang, C. Niu, L. Ye, H. Huang, X. He, W. G. Tong, J. Ross, J. Haug, T. Johnson, J. Q. Feng, S. Harris, L. M. Wiedemann, Y. Mishina and L. Li, Identification of the haematopoietic stem cell niche and control of the niche size,, Nature, 425 (2003), 836. doi: 10.1038/nature02041.

[28]

G. B. Adams, K. T. Chabner, I. R. Alley, D. P. Olson, Z. M. Szczepiorkowski, M. C. Poznansky, C. H. Kos, M. R. Pollak, E. M. Brown and D. T. Scadden, Stem cell engraftment at the endosteal niche is specified by the calcium-sensing receptor,, Nature, 439 (2006), 599.

[29]

P. Eliasson and J. I. Jonsson, The hematopoietic stem cell niche: Low in oxygen but a nice place to be,, J. Cell Physiol., 222 (2010), 17. doi: 10.1002/jcp.21908.

[30]

M. J. Kiel and S. J. Morrison, Uncertainty in the niches that maintain haematopoietic stem cells,, Nat. Rev. Immunol., 8 (2008), 290. doi: 10.1038/nri2279.

[31]

A. S. Silva, J. A. Yunes, R. J. Gillies and R. A. Gatenby, The potential role of systemic buffers in reducing intratumoral extracellular pH and acid-mediated invasion,, Cancer Res., 69 (2009), 2677. doi: 10.1158/0008-5472.CAN-08-2394.

[32]

A. S. Silva, R. A. Gatenby, R. J. Gillies and J. A. Yunes, A quantitative theoretical model for the development of malignancy in ductal carcinoma in situ,, J. Theor. Biol., 262 (2010), 601. doi: 10.1016/j.jtbi.2009.10.031.

[33]

D. Bray, "Cell movements: From Molecules to Motility,", 1$^{st}$ edition, (2001).

[34]

H. R. De Raeve, K. Asosingh, E. Wisse, B. Van Camp, E. Van Marck and K. Vanderkerken, Part of the multiple myeloma-associated microvessels is functionally connected to the systemic circulation: A study in the murine 5T33MM model,, Virchows Arch., 445 (2004), 389. doi: 10.1007/s00428-004-1064-7.

[35]

O. Sezer, K. Niemoller, O. Kaufmann, J. Eucker, C. Jakob, I. Zavrski and K. Possinger, Decrease of bone marrow angiogenesis in myeloma patients achieving a remission after chemotherapy,, Eur. J. Haematol., 66 (2001), 238. doi: 10.1034/j.1600-0609.2001.066004238.x.

[36]

A. Orazi, D. P. O'Malley and D. A. Arber, "Illustrated Pathology of the Bone Marrow,", 1$^{st}$ edition, (2006). doi: 10.1017/CBO9780511543531.

[37]

R. C. Furze and S. M. Rankin, Neutrophil mobilization and clearance in the bone marrow,, Immunology, 125 (2008), 281. doi: 10.1111/j.1365-2567.2008.02950.x.

[38]

N. C. Jain, "Essentials of Veterinary Hematology,", 1$^{st}$ edition, (1993).

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