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A compartment model of VEGF distribution in blood, healthy and diseased tissues.

Stefanini MO, Wu FT, Mac Gabhann F, Popel AS - BMC Syst Biol (2008)

Bottom Line: Finally, the VEGF distribution profile in healthy tissue reveals that about half of the VEGF is complexed with the receptor tyrosine kinase VEGFR2 and the co-receptor Neuropilin-1.In diseased tissues, this binding can be reduced to 15% while VEGF bound to the extracellular matrix and basement membranes increases.This mathematical model can serve as a tool for understanding the VEGF distribution in physiological and pathological contexts as well as a foundation to investigate pro- or anti-angiogenic strategies.

View Article: PubMed Central - HTML - PubMed

Affiliation: Department of Biomedical Engineering, School of Medicine, Johns Hopkins University, Baltimore, Maryland 21205, USA. stefanini@jhmi.edu

ABSTRACT

Background: Angiogenesis is a process by which new capillaries are formed from pre-existing blood vessels in physiological (e.g., exercise, wound healing) or pathological (e.g., ischemic limb as in peripheral arterial disease, cancer) contexts. This neovascular mechanism is mediated by the vascular endothelial growth factor (VEGF) family of cytokines. Although VEGF is often targeted in anti-angiogenic therapies, there is little knowledge about how its concentration may vary between tissues and the vascular system. A compartment model is constructed to study the VEGF distribution in the tissue (including matrix-bound, cell surface receptor-bound and free VEGF isoforms) and in the blood. We analyze the sensitivity of this distribution to the secretion rate, clearance rate and vascular permeability of VEGF.

Results: We find that, in a physiological context, VEGF concentration varies approximately linearly with the VEGF secretion rate. VEGF concentration in blood but not in tissue is dependent on the vascular permeability of healthy tissue. Model simulations suggest that relative VEGF increases are similar in blood and tissue during exercise and return to baseline within several hours. In a pathological context (tumor), we find that blood VEGF concentration is relatively insensitive to increased vascular permeability in tumors, to the secretion rate of VEGF by tumors and to the clearance. However, it is sensitive to the vascular permeability in the healthy tissue. Finally, the VEGF distribution profile in healthy tissue reveals that about half of the VEGF is complexed with the receptor tyrosine kinase VEGFR2 and the co-receptor Neuropilin-1. In diseased tissues, this binding can be reduced to 15% while VEGF bound to the extracellular matrix and basement membranes increases.

Conclusion: The results are of importance for physiological conditions (e.g., exercise) and pathological conditions (e.g., peripheral arterial disease, coronary artery disease, cancer). This mathematical model can serve as a tool for understanding the VEGF distribution in physiological and pathological contexts as well as a foundation to investigate pro- or anti-angiogenic strategies.

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Whole-body changes in response to VEGF secretion by a tumor. The diseased compartment represents a 4-cm diameter tumor. Vascular permeability of the healthy tissue,  = 4 × 10-8 cm/s; VEGF plasma clearance cV = 0.0206 min-1 [28]; VEGFR1 = 10,000 and VEGFR2 = 10,000 molecules/endothelial cell; NRP1 = 10,000 molecules/endothelial cell in the healthy tissue; VEGF165 secretion rate in healthy tissue qN = 0.102 molecule/cell/s; tumor VEGF165 secretion rate qD = 0.076 or 0.025 molecule/cell/s for 10,000 (black lines) or 100,000 (dark yellow lines) NRP1 in tumor respectively. The normal tissue VEGF level is insensitive to the variation of each of the parameters considered here. A, The free VEGF concentration in the tumor and in the blood are approximately linearly dependent on tumor VEGF secretion rate. The tumor VEGF level decreases while the blood VEGF level increases when increasing the vascular permeability in tumor from  = 4 × 10-7 cm/s (dotted lines) to 4 × 10-5 cm/s (dashed lines). B, Increasing vascular permeability in tumor decreases free VEGF in the tumor and slightly increases blood VEGF. Increasing the NRP1 receptor density increases the VEGF level in tumor for vascular permeability in tumor higher than 4 × 10-7 cm/s. C, Decreasing the clearance rate of VEGF increases free VEGF in the blood and tumor. Increasing the density of NRP1 receptors in the tumor has an effect only for higher permeability  = 4 × 10-5 cm/s, drastically lowering free VEGF concentration in the tumor. D, Increasing vascular permeability in the healthy tissue results in increased free VEGF in the blood and tumor by several-fold. Vascular permeability in the tumor  = 4 × 10-7 cm/s.
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Figure 4: Whole-body changes in response to VEGF secretion by a tumor. The diseased compartment represents a 4-cm diameter tumor. Vascular permeability of the healthy tissue, = 4 × 10-8 cm/s; VEGF plasma clearance cV = 0.0206 min-1 [28]; VEGFR1 = 10,000 and VEGFR2 = 10,000 molecules/endothelial cell; NRP1 = 10,000 molecules/endothelial cell in the healthy tissue; VEGF165 secretion rate in healthy tissue qN = 0.102 molecule/cell/s; tumor VEGF165 secretion rate qD = 0.076 or 0.025 molecule/cell/s for 10,000 (black lines) or 100,000 (dark yellow lines) NRP1 in tumor respectively. The normal tissue VEGF level is insensitive to the variation of each of the parameters considered here. A, The free VEGF concentration in the tumor and in the blood are approximately linearly dependent on tumor VEGF secretion rate. The tumor VEGF level decreases while the blood VEGF level increases when increasing the vascular permeability in tumor from = 4 × 10-7 cm/s (dotted lines) to 4 × 10-5 cm/s (dashed lines). B, Increasing vascular permeability in tumor decreases free VEGF in the tumor and slightly increases blood VEGF. Increasing the NRP1 receptor density increases the VEGF level in tumor for vascular permeability in tumor higher than 4 × 10-7 cm/s. C, Decreasing the clearance rate of VEGF increases free VEGF in the blood and tumor. Increasing the density of NRP1 receptors in the tumor has an effect only for higher permeability = 4 × 10-5 cm/s, drastically lowering free VEGF concentration in the tumor. D, Increasing vascular permeability in the healthy tissue results in increased free VEGF in the blood and tumor by several-fold. Vascular permeability in the tumor = 4 × 10-7 cm/s.

Mentions: We performed a sensitivity analysis on the tumor VEGF secretion rate. For the selected parameters we found that regardless of the vascular permeability in the tumor, free VEGF concentration in available interstitial fluid in the normal tissue is insensitive to the VEGF secretion rate in the tumor and to the vascular permeability of the tumor (Figures 4A). This qualitative behavior is independent of the density of the NRP1 in the tumor. At a vascular permeability in the tumor of 4 × 10-7 cm/s (dotted lines), the free VEGF level in the available tumor interstitial fluid is approximately proportional to the secretion rate of VEGF in the tumor while the VEGF concentration in the blood plasma is rather insensitive to the change in the tumor VEGF secretion. When increasing the permeability by two orders of magnitude (4 × 10-5 cm/s, dashed lines), more VEGF molecules secreted from the tumor enter the blood. This results in an increase of VEGF level in the blood plasma and a decrease of VEGF level in the tumor for a given VEGF secretion rate in tumor. However, even at a high VEGF secretion rate in the tumor, the plasma VEGF concentration increases by less that 50%. Thus, an increase in the VEGF secretion rate alone cannot explain the several-fold increase reported for cancer patients [11], at least for the selected parameters of the model. For a given secretion rate in tumor, our calculations show that for the plasma VEGF level to double, the tumor size would have to increase approximately to 25-cm diameter.


A compartment model of VEGF distribution in blood, healthy and diseased tissues.

Stefanini MO, Wu FT, Mac Gabhann F, Popel AS - BMC Syst Biol (2008)

Whole-body changes in response to VEGF secretion by a tumor. The diseased compartment represents a 4-cm diameter tumor. Vascular permeability of the healthy tissue,  = 4 × 10-8 cm/s; VEGF plasma clearance cV = 0.0206 min-1 [28]; VEGFR1 = 10,000 and VEGFR2 = 10,000 molecules/endothelial cell; NRP1 = 10,000 molecules/endothelial cell in the healthy tissue; VEGF165 secretion rate in healthy tissue qN = 0.102 molecule/cell/s; tumor VEGF165 secretion rate qD = 0.076 or 0.025 molecule/cell/s for 10,000 (black lines) or 100,000 (dark yellow lines) NRP1 in tumor respectively. The normal tissue VEGF level is insensitive to the variation of each of the parameters considered here. A, The free VEGF concentration in the tumor and in the blood are approximately linearly dependent on tumor VEGF secretion rate. The tumor VEGF level decreases while the blood VEGF level increases when increasing the vascular permeability in tumor from  = 4 × 10-7 cm/s (dotted lines) to 4 × 10-5 cm/s (dashed lines). B, Increasing vascular permeability in tumor decreases free VEGF in the tumor and slightly increases blood VEGF. Increasing the NRP1 receptor density increases the VEGF level in tumor for vascular permeability in tumor higher than 4 × 10-7 cm/s. C, Decreasing the clearance rate of VEGF increases free VEGF in the blood and tumor. Increasing the density of NRP1 receptors in the tumor has an effect only for higher permeability  = 4 × 10-5 cm/s, drastically lowering free VEGF concentration in the tumor. D, Increasing vascular permeability in the healthy tissue results in increased free VEGF in the blood and tumor by several-fold. Vascular permeability in the tumor  = 4 × 10-7 cm/s.
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Figure 4: Whole-body changes in response to VEGF secretion by a tumor. The diseased compartment represents a 4-cm diameter tumor. Vascular permeability of the healthy tissue, = 4 × 10-8 cm/s; VEGF plasma clearance cV = 0.0206 min-1 [28]; VEGFR1 = 10,000 and VEGFR2 = 10,000 molecules/endothelial cell; NRP1 = 10,000 molecules/endothelial cell in the healthy tissue; VEGF165 secretion rate in healthy tissue qN = 0.102 molecule/cell/s; tumor VEGF165 secretion rate qD = 0.076 or 0.025 molecule/cell/s for 10,000 (black lines) or 100,000 (dark yellow lines) NRP1 in tumor respectively. The normal tissue VEGF level is insensitive to the variation of each of the parameters considered here. A, The free VEGF concentration in the tumor and in the blood are approximately linearly dependent on tumor VEGF secretion rate. The tumor VEGF level decreases while the blood VEGF level increases when increasing the vascular permeability in tumor from = 4 × 10-7 cm/s (dotted lines) to 4 × 10-5 cm/s (dashed lines). B, Increasing vascular permeability in tumor decreases free VEGF in the tumor and slightly increases blood VEGF. Increasing the NRP1 receptor density increases the VEGF level in tumor for vascular permeability in tumor higher than 4 × 10-7 cm/s. C, Decreasing the clearance rate of VEGF increases free VEGF in the blood and tumor. Increasing the density of NRP1 receptors in the tumor has an effect only for higher permeability = 4 × 10-5 cm/s, drastically lowering free VEGF concentration in the tumor. D, Increasing vascular permeability in the healthy tissue results in increased free VEGF in the blood and tumor by several-fold. Vascular permeability in the tumor = 4 × 10-7 cm/s.
Mentions: We performed a sensitivity analysis on the tumor VEGF secretion rate. For the selected parameters we found that regardless of the vascular permeability in the tumor, free VEGF concentration in available interstitial fluid in the normal tissue is insensitive to the VEGF secretion rate in the tumor and to the vascular permeability of the tumor (Figures 4A). This qualitative behavior is independent of the density of the NRP1 in the tumor. At a vascular permeability in the tumor of 4 × 10-7 cm/s (dotted lines), the free VEGF level in the available tumor interstitial fluid is approximately proportional to the secretion rate of VEGF in the tumor while the VEGF concentration in the blood plasma is rather insensitive to the change in the tumor VEGF secretion. When increasing the permeability by two orders of magnitude (4 × 10-5 cm/s, dashed lines), more VEGF molecules secreted from the tumor enter the blood. This results in an increase of VEGF level in the blood plasma and a decrease of VEGF level in the tumor for a given VEGF secretion rate in tumor. However, even at a high VEGF secretion rate in the tumor, the plasma VEGF concentration increases by less that 50%. Thus, an increase in the VEGF secretion rate alone cannot explain the several-fold increase reported for cancer patients [11], at least for the selected parameters of the model. For a given secretion rate in tumor, our calculations show that for the plasma VEGF level to double, the tumor size would have to increase approximately to 25-cm diameter.

Bottom Line: Finally, the VEGF distribution profile in healthy tissue reveals that about half of the VEGF is complexed with the receptor tyrosine kinase VEGFR2 and the co-receptor Neuropilin-1.In diseased tissues, this binding can be reduced to 15% while VEGF bound to the extracellular matrix and basement membranes increases.This mathematical model can serve as a tool for understanding the VEGF distribution in physiological and pathological contexts as well as a foundation to investigate pro- or anti-angiogenic strategies.

View Article: PubMed Central - HTML - PubMed

Affiliation: Department of Biomedical Engineering, School of Medicine, Johns Hopkins University, Baltimore, Maryland 21205, USA. stefanini@jhmi.edu

ABSTRACT

Background: Angiogenesis is a process by which new capillaries are formed from pre-existing blood vessels in physiological (e.g., exercise, wound healing) or pathological (e.g., ischemic limb as in peripheral arterial disease, cancer) contexts. This neovascular mechanism is mediated by the vascular endothelial growth factor (VEGF) family of cytokines. Although VEGF is often targeted in anti-angiogenic therapies, there is little knowledge about how its concentration may vary between tissues and the vascular system. A compartment model is constructed to study the VEGF distribution in the tissue (including matrix-bound, cell surface receptor-bound and free VEGF isoforms) and in the blood. We analyze the sensitivity of this distribution to the secretion rate, clearance rate and vascular permeability of VEGF.

Results: We find that, in a physiological context, VEGF concentration varies approximately linearly with the VEGF secretion rate. VEGF concentration in blood but not in tissue is dependent on the vascular permeability of healthy tissue. Model simulations suggest that relative VEGF increases are similar in blood and tissue during exercise and return to baseline within several hours. In a pathological context (tumor), we find that blood VEGF concentration is relatively insensitive to increased vascular permeability in tumors, to the secretion rate of VEGF by tumors and to the clearance. However, it is sensitive to the vascular permeability in the healthy tissue. Finally, the VEGF distribution profile in healthy tissue reveals that about half of the VEGF is complexed with the receptor tyrosine kinase VEGFR2 and the co-receptor Neuropilin-1. In diseased tissues, this binding can be reduced to 15% while VEGF bound to the extracellular matrix and basement membranes increases.

Conclusion: The results are of importance for physiological conditions (e.g., exercise) and pathological conditions (e.g., peripheral arterial disease, coronary artery disease, cancer). This mathematical model can serve as a tool for understanding the VEGF distribution in physiological and pathological contexts as well as a foundation to investigate pro- or anti-angiogenic strategies.

Show MeSH
Related in: MedlinePlus