Chapter 8: Conclusions and Future Work
8.2 Future Work
1. As pointed out in Chapters 5 and 6 our conclusions about cerebral health of patients with CHD and SCD are limited by small sizes and recruitment for these studies is ongoing.
2. Due to our ability to simultaneously measure flow and oxygenation, the method is well suited for studying dynamic neurovascular processes. The power of the method would benefit from higher temporal resolution (currently ~30s). Currently, we are
117
working towards this end by using key-hole imaging where only central low spatial frequency information is acquired in a time series scan after an initial full k-space acquisition. It is assumed that the high spatial frequency information is constant in time and does not need updating. This strategy can significantly increase the temporal resolution of the method (~2s) (depending on the number of k-space lines updated). 3. A higher temporal resolution method would also facilitate measurement of
hemodynamic and metabolic parameters in smaller cortical veins in response to task based stimulation analogous to fMRI experiments. This would enable better
understanding of the biophysical mechanisms underlying the BOLD response.
4. The method is scalable with field strength as the induced magnetization resulting from the blood-tissue susceptibility difference, , increases linearly with the applied magnetic field. Thus the method would benefit from higher SNR and spatial resolution (for above mentioned local/regional measurements) at higher fields (for example 7T).
Given its high temporal resolution and robustness, I envision this method being used adjunctively to standard clinical brain protocols. Adding simultaneous rapid measurements of absolute hemodynamic and metabolic parameters to the arsenal of noninvasively obtainable metrics by MRI will be a big step forward in the comprehensive assessment of cerebral physiology and pathology.
118
Bibliography
1. Clark, D.D. and L. Sokoloff, Basic Neurochemistry: Molecular, Cellular and
Medical Aspects. 1999(Lipincott, Philadelphia): p. 637-670.
2. Sokoloff, L., et al., The effect of mental arithmetic on cerebral circulation and metabolism. J Clin Invest, 1955. 34(7, Part 1): p. 1101-8.
3. Attwell, D. and S.B. Laughlin, An energy budget for signaling in the grey matter
of the brain. J Cereb Blood Flow Metab, 2001. 21(10): p. 1133-45.
4. Sibson, N.R., et al., Stoichiometric coupling of brain glucose metabolism and
glutamatergic neuronal activity. Proc Natl Acad Sci U S A, 1998. 95(1): p. 316- 21.
5. Shen, J., et al., Determination of the rate of the glutamate/glutamine cycle in the
human brain by in vivo 13C NMR. Proc Natl Acad Sci U S A, 1999. 96(14): p.
8235-40.
6. Salinas, E. and T.J. Sejnowski, Correlated neuronal activity and the flow of neural information. Nat Rev Neurosci, 2001. 2(8): p. 539-50.
7. Raichle, M.E. and D.A. Gusnard, Appraising the brain's energy budget. Proc Natl
Acad Sci U S A, 2002. 99(16): p. 10237-9.
8. Davis, T.L., et al., Calibrated functional MRI: mapping the dynamics of oxidative
metabolism. Proc Natl Acad Sci U S A, 1998. 95(4): p. 1834-9.
9. Kim, S.G., et al., Determination of relative CMRO2 from CBF and BOLD
changes: significant increase of oxygen consumption rate during visual
stimulation. Magn Reson Med, 1999. 41(6): p. 1152-61.
10. Jones, M., et al., The effect of hypercapnia on the neural and hemodynamic
responses to somatosensory stimulation. Neuroimage, 2005. 27(3): p. 609-23.
11. Kliefoth, A.B., R.L. Grubb, Jr., and M.E. Raichle, Depression of cerebral oxygen utilization by hypercapnia in the rhesus monkey. J Neurochem, 1979. 32(2): p. 661-3.
12. Chen, J.J. and G.B. Pike, Global cerebral oxidative metabolism during
hypercapnia and hypocapnia in humans: implications for BOLD fMRI. J Cereb Blood Flow Metab, 2010. 30(6): p. 1094-9.
13. Kety, S.S. and C.F. Schmidt, The Effects of Altered Arterial Tensions of Carbon Dioxide and Oxygen on Cerebral Blood Flow and Cerebral Oxygen Consumption of Normal Young Men. J Clin Invest, 1948. 27(4): p. 484-92.
14. Massik, J., et al., Hypercapnia and response of cerebral blood flow to hypoxia in newborn lambs. J Appl Physiol, 1989. 66(3): p. 1065-70.
15. Bullock, R., et al., Continuous monitoring of jugular bulb oxygen saturation and the effect of drugs acting on cerebral metabolism. Acta Neurochir Suppl (Wien), 1993. 59: p. 113-8.
16. Cruz, J., Continuous versus serial global cerebral hemometabolic monitoring:
applications in acute brain trauma. Acta Neurochir Suppl (Wien), 1988. 42: p. 35-9.
17. Cruz, J., et al., Continuous monitoring of cerebral oxygenation in acute brain injury: injection of mannitol during hyperventilation. J Neurosurg, 1990. 73(5): p. 725-30.
119
18. Sheinberg, M., et al., Continuous monitoring of jugular venous oxygen saturation
in head-injured patients. J Neurosurg, 1992. 76(2): p. 212-7.
19. Coplin, W.M., et al., Thrombotic, infectious, and procedural complications of the jugular bulb catheter in the intensive care unit. Neurosurgery, 1997. 41(1): p. 101-7; discussion 107-9.
20. Aaslid, R., T.M. Markwalder, and H. Nornes, Noninvasive transcranial Doppler
ultrasound recording of flow velocity in basal cerebral arteries. J Neurosurg, 1982. 57(6): p. 769-74.
21. McCormick, P.W., et al., Regional cerebrovascular oxygen saturation measured
by optical spectroscopy in humans. Stroke, 1991. 22(5): p. 596-602.
22. Jobsis, F.F., Noninvasive, infrared monitoring of cerebral and myocardial oxygen sufficiency and circulatory parameters. Science, 1977. 198(4323): p. 1264-7.
23. Rohlwink, U.K. and A.A. Figaji, Methods of monitoring brain oxygenation.
Childs Nerv Syst, 2010. 26(4): p. 453-64.
24. Boas, D.A., L.E. Campbell, and A.G. Yodh, Scattering and Imaging with
Diffusing Temporal Field Correlations. Phys Rev Lett, 1995. 75(9): p. 1855-
1858.
25. Durduran, T., et al., Optical measurement of cerebral hemodynamics and oxygen
metabolism in neonates with congenital heart defects. J Biomed Opt, 2010. 15(3):
p. 037004.
26. Persson, L. and L. Hillered, Chemical monitoring of neurosurgical intensive care patients using intracerebral microdialysis. J Neurosurg, 1992. 76(1): p. 72-80. 27. Hillered, L., et al., Neurometabolic monitoring of the ischaemic human brain
using microdialysis. Acta Neurochir (Wien), 1990. 102(3-4): p. 91-7.
28. Enblad, P., et al., Simultaneous intracerebral microdialysis and positron emission tomography in the detection of ischemia in patients with subarachnoid
hemorrhage. J Cereb Blood Flow Metab, 1996. 16(4): p. 637-44.
29. Raichle, M.E., Measurement of local cerebral blood flow and metabolism in man
with positron emission tomography. Fed Proc, 1981. 40(8): p. 2331-4.
30. Ter-Pogossian, M.M. and P. Herscovitch, Radioactive oxygen-15 in the study of
cerebral blood flow, blood volume, and oxygen metabolism. Semin Nucl Med, 1985. 15(4): p. 377-94.
31. Langfitt, T.W., et al., Computerized tomography, magnetic resonance imaging,
and positron emission tomography in the study of brain trauma. Preliminary observations. J Neurosurg, 1986. 64(5): p. 760-7.
32. Hovda, D.A., et al., The neurochemical and metabolic cascade following brain
injury: moving from animal models to man. J Neurotrauma, 1995. 12(5): p. 903-6.
33. Alexander, G.E., et al., Longitudinal PET Evaluation of Cerebral Metabolic
Decline in Dementia: A Potential Outcome Measure in Alzheimer's Disease Treatment Studies. Am J Psychiatry, 2002. 159(5): p. 738-45.
34. Silverman, D.H., et al., Positron emission tomography in evaluation of dementia:
Regional brain metabolism and long-term outcome. JAMA, 2001. 286(17): p.
2120-7.
35. Powers, W.J., PET studies of cerebral metabolism in Parkinson disease. J Bioenerg Biomembr, 2009. 41(6): p. 505-8.
120
36. Altman, D.I., L.L. Lich, and W.J. Powers, Brief inhalation method to measure
cerebral oxygen extraction fraction with PET: accuracy determination under pathologic conditions. J Nucl Med, 1991. 32(9): p. 1738-41.
37. Mintun, M.A., et al., Brain oxygen utilization measured with O-15 radiotracers
and positron emission tomography. J Nucl Med, 1984. 25(2): p. 177-87.
38. Pauling, L. and C.D. Coryell, The Magnetic Properties and Structure of
Hemoglobin, Oxyhemoglobin and Carbonmonoxyhemoglobin. Proc Natl Acad Sci U S A, 1936. 22(4): p. 210-6.
39. Cerdonio, M., S. Morante, and S. Vitale, Magnetic susceptibility of hemoglobins. Methods Enzymol, 1981. 76: p. 354-71.
40. McIlwain, H. and H.S. Bachelard, Biochemistry and the Central Nervous System.
1985(Churchill Livingstone, Edinburgh).
41. Haacke, E.M., et al., In Vivo Measurement of Blood Oxygen Saturation Using
Magnetic Resonance Imaging: A Direct Validation of the Blood Oxygen Level-
Dependent Concept in Functional Brain Imaging Human Brain Mapping, 1997. 5:
p. 341-346.
42. Fernández-Seara, M., et al., MR susceptometry for measuring global brain oxygen
extraction. Magn Reson Med, 2006. 55(5): p. 967-73.
43. Li, C., et al., Accuracy of the cylinder approximation for susceptometric
measurement of intravascular oxygen saturation. Magn Reson Med, 2012. 67(3):
p. 808-13.
44. Langham, M.C., et al., Accuracy and precision of MR blood oximetry based on
the long paramagnetic cylinder approximation of large vessels. Magn Reson Med, 2009. 62(2): p. 333-40.
45. Lin, W., et al., Quantitative magnetic resonance imaging in experimental
hypercapnia: improvement in the relation between changes in brain R2 and the oxygen saturation of venous blood after correction for changes in cerebral blood
volume. J Cereb Blood Flow Metab, 1999. 19(8): p. 853-62.
46. Wright, G.A., B.S. Hu, and A. Macovski, 1991 I.I. Rabi Award. Estimating
oxygen saturation of blood in vivo with MR imaging at 1.5 T. J Magn Reson Imaging, 1991. 1(3): p. 275-83.
47. Foltz, W.D., et al., Coronary venous oximetry using MRI. Magn Reson Med,
1999. 42(5): p. 837-48.
48. Gomori, J.M., et al., NMR relaxation times of blood: dependence on field
strength, oxidation state, and cell integrity. J Comput Assist Tomogr, 1987. 11(4): p. 684-90.
49. Meyer, M.E., et al., NMR relaxation rates and blood oxygenation level. Magn
Reson Med, 1995. 34(2): p. 234-41.
50. Silvennoinen, M.J., et al., Comparison of the dependence of blood R2 and R2* on
oxygen saturation at 1.5 and 4.7 Tesla. Magn Reson Med, 2003. 49(1): p. 47-60.
51. Golay, X., et al., Measurement of tissue oxygen extraction ratios from venous blood T(2): increased precision and validation of principle. Magn Reson Med, 2001. 46(2): p. 282-91.
52. Oja, J.M., et al., Determination of oxygen extraction ratios by magnetic resonance
121
53. Lu, H. and Y. Ge, Quantitative evaluation of oxygenation in venous vessels using
T2-Relaxation-Under-Spin-Tagging MRI. Magn Reson Med, 2008. 60(2): p. 357-
63.
54. van Zijl, P.C., et al., Quantitative assessment of blood flow, blood volume and blood oxygenation effects in functional magnetic resonance imaging. Nat Med, 1998. 4(2): p. 159-67.
55. Luz, Z. and S. Meiboom, Nuclear magnetic resonance study of the protolysis of
trimethylammonium ion in aqueous solution: order of the reaction with respect to the solvent. J Chem Phys, 1963. 39: p. 366-70.
56. Xu, F., Y. Ge, and H. Lu, Noninvasive quantification of whole-brain cerebral
metabolic rate of oxygen (CMRO2) by MRI. Magn Reson Med, 2009. 62(1): p.
141-8.
57. Yablonskiy, D.A. and E.M. Haacke, Theory of NMR signal behavior in
magnetically inhomogeneous tissues: the static dephasing regime. Magn Reson Med, 1994. 32(6): p. 749-63.
58. An, H., et al., Quantitative measurements of cerebral metabolic rate of oxygen
utilization using MRI: a volunteer study. NMR Biomed, 2001. 14(7-8): p. 441-7.
59. He, X. and D.A. Yablonskiy, Quantitative BOLD: mapping of human cerebral
deoxygenated blood volume and oxygen extraction fraction: default state. Magn Reson Med, 2007. 57(1): p. 115-26.
60. He, X., M. Zhu, and D.A. Yablonskiy, Validation of oxygen extraction fraction
measurement by qBOLD technique. Magn Reson Med, 2008. 60(4): p. 882-8.
61. Boxerman, J.L., et al., MR contrast due to intravascular magnetic susceptibility
perturbations. Magn Reson Med, 1995. 34(4): p. 555-66.
62. Boxerman, J.L., et al., The intravascular contribution to fMRI signal change: Monte Carlo modeling and diffusion-weighted studies in vivo. Magn Reson Med, 1995. 34(1): p. 4-10.
63. Kennan, R.P., J. Zhong, and J.C. Gore, Intravascular susceptibility contrast
mechanisms in tissues. Magn Reson Med, 1994. 31(1): p. 9-21.
64. Greene, A.E., M.T. Todorova, and T.N. Seyfried, Perspectives on the metabolic
management of epilepsy through dietary reduction of glucose and elevation of ketone bodies. J Neurochem, 2003. 86(3): p. 529-37.
65. Lowry, O.H., et al., Effect of Ischemia on Known Substrates and Cofactors of the Glycolytic Pathway in Brain. J Biol Chem, 1964. 239: p. 18-30.
66. Magistretti, P.J. and L. Pellerin, Cellular mechanisms of brain energy metabolism. Relevance to functional brain imaging and to neurodegenerative disorders. Ann N Y Acad Sci, 1996. 777: p. 380-7.
67. Quastel, J.H. and A.H. Wheatley, Oxidations by the brain. Biochem J, 1932.
26(3): p. 725-44.
68. Leenders, K.L., et al., Brain energy metabolism and dopaminergic function in
Huntington's disease measured in vivo using positron emission tomography. Mov Disord, 1986. 1(1): p. 69-77.
69. Ishii, K., et al., Decreased medial temporal oxygen metabolism in Alzheimer's
122
70. Shishido, F., et al., Cerebral oxygen and glucose metabolism and blood flow in
mitochondrial encephalomyopathy: a PET study. Neuroradiology, 1996. 38(2): p.
102-7.
71. Santens, P., et al., Cerebral oxygen metabolism in patients with progressive supranuclear palsy: a positron emission tomography study. Eur Neurol, 1997. 37(1): p. 18-22.
72. Tanaka, M., et al., Cerebral perfusion and oxygen metabolism in Parkinson's
disease: positron emission tomographic study using oxygen-15-labeled CO2 and O2. Nippon Rinsho, 1997. 55(1): p. 218-21.
73. Ito, H., et al., Changes in cerebral blood flow and cerebral oxygen metabolism during neural activation measured by positron emission tomography: comparison with blood oxygenation level-dependent contrast measured by functional
magnetic resonance imaging. J Cereb Blood Flow Metab, 2005. 25(3): p. 371-7.
74. Mayberg, T.S. and A.M. Lam, Jugular bulb oximetry for the monitoring of
cerebral blood flow and metabolism. Neurosurg Clin N Am, 1996. 7(4): p. 755-
65.
75. Fernandez-Seara, M.A., et al., MR susceptometry for measuring global brain
oxygen extraction. Magn Reson Med, 2006. 55(5): p. 967-73.
76. Dumoulin, C.L. and H.R. Hart, Jr., Magnetic resonance angiography. Radiology,
1986. 161(3): p. 717-20.
77. Bryant, D.J., et al., Measurement of flow with NMR imaging using a gradient
pulse and phase difference technique. J Comput Assist Tomogr, 1984. 8(4): p.
588-93.
78. B.West, J., Pulmonary Physiology and Pathophysiology: An Integrated, Case-
Based Approach 2nd ed. 2007, Philadelphia,PA: Lippincott Williams & Wilkins.
79. Pelc, N.J., et al., Quantitative magnetic resonance flow imaging. Magn Reson Q,
1994. 10(3): p. 125-47.
80. Magland, Pulse sequence programming in a dynamic visual environment.
Proceedings of the 14th Annual Meeting of ISMRM, Seattle, WA, USA, 2006. Abstract 578.
81. Magland J, W.F., Pulse sequence programming in a dynamic visual environment.
Proceedings of the 14th Annual Meeting of ISMRM, Seattle, WA, USA, 2006. Abstract 578.
82. Mugler, J.P., 3rd and J.R. Brookeman, Three-dimensional magnetization-
prepared rapid gradient-echo imaging (3D MP RAGE). Magn Reson Med, 1990. 15(1): p. 152-7.
83. Kretschmann, H.J., et al., Brain growth in man. Bibl Anat, 1986(28): p. 1-26. 84. Cooper, E.R., The vertebral venous plexus. Acta Anat (Basel), 1960. 42: p. 333-
51.
85. Langham, M.C., et al., Retrospective correction for induced magnetic field inhomogeneity in measurements of large-vessel hemoglobin oxygen saturation by
MR susceptometry. Magn Reson Med, 2009. 61(3): p. 626-33.
86. Abduljalil, A.M., et al., Enhanced gray and white matter contrast of phase susceptibility-weighted images in ultra-high-field magnetic resonance imaging. J Magn Reson Imaging, 2003. 18(3): p. 284-90.
123
87. Yushkevich, P.A., et al., User-guided 3D active contour segmentation of
anatomical structures: significantly improved efficiency and reliability. Neuroimage, 2006. 31(3): p. 1116-28.
88. Hattori, N., et al., Accuracy of a method using short inhalation of (15)O-O(2) for measuring cerebral oxygen extraction fraction with PET in healthy humans. J Nucl Med, 2004. 45(5): p. 765-70.
89. Ibaraki, M., et al., Quantification of cerebral blood flow and oxygen metabolism with 3-dimensional PET and 15O: validation by comparison with 2-dimensional PET. J Nucl Med, 2008. 49(1): p. 50-9.
90. Nagdyman, N., et al., Comparison between cerebral tissue oxygenation index
measured by near-infrared spectroscopy and venous jugular bulb saturation in children. Intensive Care Med, 2005. 31(6): p. 846-50.
91. Coles, J.P., et al., Effect of hyperventilation on cerebral blood flow in traumatic head injury: clinical relevance and monitoring correlates. Crit Care Med, 2002. 30(9): p. 1950-9.
92. Powers, W.J., et al., Cerebral blood flow and cerebral metabolic rate of oxygen requirements for cerebral function and viability in humans. J Cereb Blood Flow Metab, 1985. 5(4): p. 600-8.
93. Li, D., Y. Wang, and D.J. Waight, Blood oxygen saturation assessment in vivo
using T2* estimation. Magn Reson Med, 1998. 39(5): p. 685-90.
94. Chien, D., D.L. Levin, and C.M. Anderson, MR gradient echo imaging of
intravascular blood oxygenation: T2* determination in the presence of flow. Magn Reson Med, 1994. 32(4): p. 540-5.
95. Stainsby, J.A. and G.A. Wright, Partial volume effects on vascular T2
measurements. Magn Reson Med, 1998. 40(3): p. 494-9.
96. Frackowiak, R.S., et al., Quantitative measurement of regional cerebral blood
flow and oxygen metabolism in man using 15O and positron emission
tomography: theory, procedure, and normal values. J Comput Assist Tomogr, 1980. 4(6): p. 727-36.
97. Schenck, J.F., The role of magnetic susceptibility in magnetic resonance imaging: MRI magnetic compatibility of the first and second kinds. Med Phys, 1996. 23(6): p. 815-50.
98. An, H. and W. Lin, Impact of intravascular signal on quantitative measures of
cerebral oxygen extraction and blood volume under normo- and hypercapnic conditions using an asymmetric spin echo approach. Magn Reson Med, 2003. 50(4): p. 708-16.
99. Ogawa, S., et al., Intrinsic signal changes accompanying sensory stimulation: functional brain mapping with magnetic resonance imaging. Proc Natl Acad Sci U S A, 1992. 89(13): p. 5951-5.
100. Reichenbach, J.R., et al., High-resolution venography of the brain using magnetic
resonance imaging. MAGMA, 1998. 6(1): p. 62-9.
101. Gomori, J.M., et al., Intracranial hematomas: imaging by high-field MR. Radiology, 1985. 157(1): p. 87-93.
102. An, H. and W. Lin, Quantitative measurements of cerebral blood oxygen
saturation using magnetic resonance imaging. J Cereb Blood Flow Metab, 2000. 20(8): p. 1225-36.
124
103. Hoogenraad, F.G., et al., In vivo measurement of changes in venous blood-
oxygenation with high resolution functional MRI at 0.95 tesla by measuring changes in susceptibility and velocity. Magn Reson Med, 1998. 39(1): p. 97-107.
104. Fan, A.P., et al., Phase-based regional oxygen metabolism (PROM) using MRI.
Magn Reson Med, 2011.
105. Jain, V., M.C. Langham, and F.W. Wehrli, MRI estimation of global brain oxygen
consumption rate. J Cereb Blood Flow Metab, 2010. 26.
106. Weisskoff, R.M. and S. Kiihne, MRI susceptometry: image-based measurement of
absolute susceptibility of MR contrast agents and human blood. Magn Reson Med, 1992. 24(2): p. 375-83.
107. Spees, W.M., et al., Water proton MR properties of human blood at 1.5 Tesla:
magnetic susceptibility, T(1), T(2), T*(2), and non-Lorentzian signal behavior. Magn Reson Med, 2001. 45(4): p. 533-42.
108. Fabry, M.E. and R.C. San George, Effect of magnetic susceptibility on nuclear magnetic resonance signals arising from red cells: a warning. Biochemistry, 1983. 22(17): p. 4119-25.
109. Thulborn, K.R., et al., Oxygenation dependence of the transverse relaxation time of water protons in whole blood at high field. Biochim Biophys Acta, 1982. 714(2): p. 265-70.
110. Jain, V., et al., Rapid magnetic resonance measurement of global cerebral metabolic rate of oxygen consumption in humans during rest and hypercapnia. J Cereb Blood Flow Metab, 2011. 31(7): p. 1504-12.
111. Jain, V., et al., Regional Cerebral Metabolic Rate of Oxygen Consumption in the Middle Cerebral Artery Territory. International Soceity of Magnetic Resonance in Medicine, Montreal,Canada, 2011.
112. Bland, J.M. and D.G. Altman, Statistical methods for assessing agreement
between two methods of clinical measurement. Lancet, 1986. 1(8476): p. 307-10.
113. Kondroskii, E.I., et al., Magnetic Susceptibility of Single Human Erythrocytes. Biofizika, 1981. 26(6): p. 1104-6.
114. Zborowski, M., et al., Red blood cell magnetophoresis. Biophys J, 2003. 84(4): p. 2638-45.
115. Sezdi, M., et al., Changes in electrical and physiological properties of human
blood during storage. Conf Proc IEEE Eng Med Biol Soc, 2005. 7: p. 6710-3.
116. Bennett-Guerrero, E., et al., Evolution of adverse changes in stored RBCs. Proc Natl Acad Sci U S A, 2007. 104(43): p. 17063-8.
117. Cerdonio, M., et al., Magnetic properties of oxyhemoglobin. Proc Natl Acad Sci U
S A, 1977. 74(2): p. 398-400.
118. Cerdonio, M., et al., Magnetic and spectral properties of carp
carbonmonoxyhemoglobin. Competitive effects of chloride ions and inositol
hexakisphosphate. Eur J Biochem, 1983. 132(3): p. 461-7.
119. Savicki, J.P., G. Lang, and M. Ikeda-Saito, Magnetic susceptibility of oxy- and
carbonmonoxyhemoglobins. Proc Natl Acad Sci U S A, 1984. 81(17): p. 5417-9.
120. Jain, V., M.C. Langham, and F.W. Wehrli, MRI estimation of global brain oxygen
125
121. Sakhnini, L., Magnetic measurements on human erythrocytes: Normal, beta
thalassemia major, and sickle. Journal of Applied Physics, 2003. 93(10): p. Part 2&3.
122. Taylor, D.S., The Magnetic Properties of Myoglobin and Ferrimyoglobin, and