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An Introduction to Normalization and Calibration Methods in Functional MRI

Published online by Cambridge University Press:  01 January 2025

Thomas T. Liu,
Gary H. Glover,
Bryon A. Mueller,
Douglas N. Greve and
Gregory G. Brown
Thomas T. Liu*
Affiliation:
Center for Functional MRI, University of California San Diego
Gary H. Glover
Affiliation:
Department of Radiology, Stanford University
Bryon A. Mueller
Affiliation:
Department of Psychiatry, University of Minnesota
Douglas N. Greve
Affiliation:
Department of Radiology, Massachusetts General Hospital
Gregory G. Brown
Affiliation:
VA San Diego Healthcare System and Department of Psychiatry, University of California San Diego
*
Requests for reprints should be sent to Thomas T. Liu, Center for Functional MRI, University of California San Diego, 9500 Gilman Drive, MC 0677, La Jolla, CA 92093, USA. E-mail: ttliu@ucsd.edu
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Abstract

In functional magnetic resonance imaging (fMRI), the blood oxygenation level dependent (BOLD) signal is often interpreted as a measure of neural activity. However, because the BOLD signal reflects the complex interplay of neural, vascular, and metabolic processes, such an interpretation is not always valid. There is growing evidence that changes in the baseline neurovascular state can result in significant modulations of the BOLD signal that are independent of changes in neural activity. This paper introduces some of the normalization and calibration methods that have been proposed for making the BOLD signal a more accurate reflection of underlying brain activity for human fMRI studies.

Keywords

functional MRIarterial spin labelingcerebral blood flowquantitative fMRIcalibrated fMRIhypercapnia

Information

Type
Original Paper
Information
Psychometrika , Volume 78 , Issue 2 , April 2013, pp. 308 - 321
Copyright
Copyright © 2012 The Psychometric Society

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References

Aguirre, G.K., Zarahn, E., D’Esposito, M. (1998). The variability of human, BOLD hemodynamic responses. NeuroImage, 8, 360–369CrossRefGoogle ScholarPubMed
Ances, B., Leontiev, O., Perthen, J.E., Liang, C., Lansing, A.E., Buxton, R.B. (2008). Regional differences in the coupling of cerebral blood flow and oxygen metabolism changes in response to activation: implications for BOLD-fMRI. NeuroImage, 39(4), 15101521. doi:10.1016/j.neuroimage.2007.11.015.CrossRefGoogle ScholarPubMed
Ances, B., Vaida, F., Ellis, R., Buxton, R. (2011). Test-retest stability of calibrated BOLD-fMRI in HIV− and HIV+ subjects. NeuroImage, 54(3), 21562162. doi:10.1016/j.neuroimage.2010.09.081.CrossRefGoogle ScholarPubMed
Ances, B.M., Liang, C.L., Leontiev, O., Perthen, J.E., Fleisher, A.S., Lansing, A.E. et al. (2008). Effects of aging on cerebral blood flow, oxygen metabolism, and blood oxygenation level dependent responses to visual stimulation. Human Brain Mapping. doi:10.1002/hbm.20574.Google Scholar
Asghar, M.S., Hansen, A.E., Pedersen, S., Larsson, H.B.W., Ashina, M. (2011). Pharmacological modulation of the BOLD response: a study of acetazolamide and glyceryl trinitrate in humans. Journal of Magnetic Resonance Imaging, 34(4), 921927. doi:10.1002/jmri.22659.CrossRefGoogle ScholarPubMed
Bandettini, P.A., Wong, E.C. (1997). A hypercapnia-based normalization method for improved spatial localization of human brain activation with fMRI. NMR in Biomedicine, 10(4–5), 1972033.0.CO;2-S>CrossRefGoogle ScholarPubMed
Behzadi, Y., Liu, T.T. (2005). An arteriolar compliance model of the cerebral blood flow response to neural stimulus. NeuroImage, 25(4), 11001111CrossRefGoogle ScholarPubMed
Birn, R.M., Diamond, J.B., Smith, M.A., Bandettini, P.A. (2006). Separating respiratory-variation-related fluctuations from neuronal-activity-related fluctuations in fMRI. NeuroImage, 31(4), 15361548CrossRefGoogle ScholarPubMed
Birn, R.M., Saad, Z.S., Bandettini, P.A. (2001). Spatial heterogeneity of the nonlinear dynamics in the FMRI BOLD response. NeuroImage, 14, 817–826CrossRefGoogle ScholarPubMed
Biswal, B.B., Kannurpatti, S.S., Rypma, B. (2007). Hemodynamic scaling of fMRI-BOLD signal: validation of low-frequency spectral amplitude as a scalability factor. Magnetic Resonance Imaging, 25(10), 13581369CrossRefGoogle ScholarPubMed
Bolar, D.S., Sorensen, A.G., Rosen, B.R., & Adalsteinsson, E. (2009). Feasibility of QUantitative Imaging of eXtraction of Oxygen and TIssue Consumption (QUIXOTIC) to assess functional changes in venous oxygen saturation during visual stimulus. Paper presented at the 17th ISMRM scientific meeting, Honolulu. Google Scholar
Boxerman, J.L., Bandettini, P.A., Kwong, K.K., Baker, J.R., Davis, T.L., Rosen, B.R. et al. (1995). The intravascular contribution to fMRI signal change: Monte Carlo modeling and diffusion-weighted studies in vivo. Magnetic Resonance in Medicine, 34, 4–10CrossRefGoogle ScholarPubMed
Boynton, G.M., Engel, S.A., Glover, G.H., Heeger, D.J. (1996). Linear systems analysis of functional magnetic resonance imaging in human V1. The Journal of Neuroscience, 16, 4207–4221CrossRefGoogle ScholarPubMed
Brown, G.G., Zorrilla, L.T.E., Gerogy, B., Kindermann, S.S., Wong, E.C., Buxton, R.B. (2003). BOLD and perfusion response to finger-thumb apposition after acetazolamide administration: differential relationship to global perfusion. Journal of Cerebral Blood Flow and Metabolism, 23, 829–837CrossRefGoogle ScholarPubMed
Bruhn, H., Kleinschmidt, A., Boecker, H., Merboldt, K.D., Hänicke, W., Frahm, J. (1994). The effect of acetazolamide on regional cerebral blood oxygenation at rest and under stimulation as assessed by MRI. Journal of Cerebral Blood Flow and Metabolism, 14(5), 742748. doi:10.1038/jcbfm.1994.95.CrossRefGoogle ScholarPubMed
Buxton, R.B., Uludag, K., Dubowitz, D.J., Liu, T.T. (2004). Modeling the hemodynamic response to brain activation. NeuroImage, 23(Suppl 1), S220S233CrossRefGoogle ScholarPubMed
Carusone, L.M., Srinivasan, J., Gitelman, D.R., Mesulam, M.M., Parrish, T.B. (2002). Hemodynamic response changes in cerebrovascular disease: implications for functional MR imaging. American Journal of Neuroradiology, 23(7), 12221228Google ScholarPubMed
Chen, J.J., Pike, G.B. (2009). BOLD-specific cerebral blood volume and blood flow changes during neuronal activation in humans. NMR in Biomedicine, 22(10), 10541062. doi:10.1002/nbm.1411.CrossRefGoogle ScholarPubMed
Chen, J.J., Pike, G.B. (2010). Global cerebral oxidative metabolism during hypercapnia and hypocapnia in humans: implications for BOLD fMRI. Journal of Cerebral Blood Flow and Metabolism. doi:10.1038/jcbfm.2010.42.CrossRefGoogle ScholarPubMed
Chen, J.J., Pike, G.B. (2010). MRI measurement of the BOLD-specific flow-volume relationship during hypercapnia and hypocapnia in humans. NeuroImage, 53(2), 383391. doi:10.1016/j.neuroimage.2010.07.003.CrossRefGoogle ScholarPubMed
Chen, Y., Parrish, T.B. (2009). Caffeine’s effects on cerebrovascular reactivity and coupling between cerebral blood flow and oxygen metabolism. NeuroImage, 44(3), 647652. doi:10.1016/j.neuroimage.2008.09.057.CrossRefGoogle ScholarPubMed
Chiarelli, P.A., Bulte, D.P., Gallichan, D., Piechnik, S.K., Wise, R., Jezzard, P. (2007). Flow-metabolism coupling in human visual, motor, and supplementary motor areas assessed by magnetic resonance imaging. Magnetic Resonance in Medicine, 57(3), 538547. doi:10.1002/mrm.21171.CrossRefGoogle Scholar
Cohen, E.R., Rostrup, E., Sidaros, K., Lund, T.E., Paulson, O.B., Ugurbil, K. et al. (2004). Hypercapnic normalization of BOLD fMRI: comparison across field strengths and pulse sequences. NeuroImage, 23(2), 613624CrossRefGoogle ScholarPubMed
Cohen, E.R., Ugurbil, K., Kim, S.G. (2002). Effect of basal conditions on the magnitude and dynamics of the blood oxygenation level-dependent fMRI response. Journal of Cerebral Blood Flow and Metabolism, 22(9), 10421053CrossRefGoogle ScholarPubMed
D’Esposito, M., Deouell, L.Y., Gazzaley, A. (2003). Alterations in the BOLD fMRI signal with ageing and disease: a challenge for neuroimaging. Nature Reviews. Neuroscience, 4(11), 863872CrossRefGoogle ScholarPubMed
Davis, T.L., Kwong, K.K., Weisskoff, R.M., Rosen, B.R. (1998). Calibrated functional MRI: mapping the dynamics of oxidative metabolism. Proceedings of the National Academy of Sciences of the United States of America, 95, 1834–1839CrossRefGoogle ScholarPubMed
de Zwart, J.A., van Gelderen, P., Jansma, J.M., Fukunaga, M., Bianciardi, M., Duyn, J.H. (2009). Hemodynamic nonlinearities affect BOLD fMRI response timing and amplitude. NeuroImage, 47(4), 16491658. doi:10.1016/j.neuroimage.2009.06.001.CrossRefGoogle ScholarPubMed
Detre, J.A., Rao, H., Wang, D.J.J., Chen, Y.F., Wang, Z. (2012). Applications of arterial spin labeled MRI in the brain. Journal of Magnetic Resonance Imaging. doi:10.1002/jmri.23581.CrossRefGoogle ScholarPubMed
Detre, J.A., Wang, J., Wang, Z., Rao, H. (2009). Arterial spin-labeled perfusion MRI in basic and clinical neuroscience. Current Opinion in Neurology, 22(4), 348355. doi:10.1097/WCO.0b013e32832d9505.CrossRefGoogle ScholarPubMed
Devor, A., Dunn, A.K., Andermann, M.L., Ulbert, I., Boas, D.A., Dale, A.M. (2003). Coupling of total hemoglobin concentration, oxygenation, and neural activity in rat somatosensory cortex. Neuron, 39(2), 353359CrossRefGoogle ScholarPubMed
Formaggio, E., Storti, S., Avesani, M., Cerini, R., Milanese, F., Gasparini, A. et al. (2008). EEG and FMRI coregistration to investigate the cortical oscillatory activities during finger movement. Brain Topography, 21(2), 100111. doi:10.1007/s10548-008-0058-1.CrossRefGoogle ScholarPubMed
Friston, K.J., Josephs, O., Rees, G., Turner, R. (1998). Nonlinear event-related responses in fMRI. Magnetic Resonance in Medicine, 39, 41–52CrossRefGoogle ScholarPubMed
Griffeth, V.E.M., Buxton, R.B. (2011). A theoretical framework for estimating cerebral oxygen metabolism changes using the calibrated-BOLD method: modeling the effects of blood volume distribution, hematocrit, oxygen extraction fraction, and tissue signal properties on the BOLD signal. NeuroImage, 58(1), 198212. doi:10.1016/j.neuroimage.2011.05.077.CrossRefGoogle ScholarPubMed
Handwerker, D.A., Gazzaley, A., Inglis, B.A., D’Esposito, M. (2007). Reducing vascular variability of fMRI data across aging populations using a breathholding task. Human Brain Mapping, 28(9), 846859. doi:10.1002/hbm.20307.CrossRefGoogle ScholarPubMed
Handwerker, D.A., Ollinger, J.M., D’Esposito, M. (2004). Variation of BOLD hemodynamic responses across subjects and brain regions and their effects on statistical analyses. NeuroImage, 21(4), 16391651CrossRefGoogle ScholarPubMed
Hewson-Stoate, N., Jones, M., Martindale, J., Berwick, J., Mayhew, J. (2005). Further nonlinearities in neurovascular coupling in rodent barrel cortex. NeuroImage, 24(2), 565574. doi:10.1016/j.neuroimage.2004.08.040.CrossRefGoogle ScholarPubMed
Hoge, R.D., Atkinson, J., Gill, B., Crelier, G.R., Marrett, S., Pike, G.B. (1999). Investigation of BOLD signal dependence on cerebral blood flow and oxygen consumption: the deoxyhemoglobin dilution model. Magnetic Resonance in Medicine, 42(5), 8498633.0.CO;2-Z>CrossRefGoogle ScholarPubMed
Hoge, R.D., Atkinson, J., Gill, B., Crelier, G.R., Marrett, S., Pike, G.B. (1999). Linear coupling between cerebral blood flow and oxygen consumption in activated human cortex. Proceedings of the National Academy of Sciences of the United States of America, 96(16), 94039408CrossRefGoogle ScholarPubMed
Huttunen, J.K., Gröhn, O., Penttonen, M. (2008). Coupling between simultaneously recorded BOLD response and neuronal activity in the rat somatosensory cortex. NeuroImage, 39(2), 775785. doi:10.1016/j.neuroimage.2007.06.042.CrossRefGoogle ScholarPubMed
Hyder, F. (2004). Neuroimaging with calibrated FMRI. Stroke, 35(11 Suppl 1), 26352641CrossRefGoogle ScholarPubMed
Hyder, F., Rothman, D.L., Shulman, R.G. (2002). Total neuroenergetics support localized brain activity: implications for the interpretation of fMRI. Proceedings of the National Academy of Sciences of the United States of America, 99(16), 1077110776. doi:10.1073/pnas.132272299.CrossRefGoogle ScholarPubMed
Iannetti, G., Wise, R. (2007). BOLD functional MRI in disease and pharmacological studies: room for improvement?. Magnetic Resonance Imaging, 25(6), 978988. doi:10.1016/j.mri.2007.03.018.CrossRefGoogle ScholarPubMed
Jain, V., Langham, M.C., Floyd, T.F., Jain, G., Magland, J.F., Wehrli, F.W. (2011). Rapid magnetic resonance measurement of global cerebral metabolic rate of oxygen consumption in humans during rest and hypercapnia. Journal of Cerebral Blood Flow and Metabolism. doi:10.1038/jcbfm.2011.34.CrossRefGoogle ScholarPubMed
Jones, M., Berwick, J., Hewson-Stoate, N., Gias, C., Mayhew, J. (2005). The effect of hypercapnia on the neural and hemodynamic responses to somatosensory stimulation. NeuroImage, 27(3), 609623. doi:10.1016/j.neuroimage.2005.04.036.CrossRefGoogle ScholarPubMed
Kannurpatti, S.S., Biswal, B.B. (2008). Detection and scaling of task-induced fMRI-BOLD response using resting state fluctuations. NeuroImage, 40(4), 15671574. doi:10.1016/j.neuroimage.2007.09.040.CrossRefGoogle ScholarPubMed
Kida, I., Rothman, D.L., Hyder, F. (2007). Dynamics of changes in blood flow, volume, and oxygenation: implications for dynamic functional magnetic resonance imaging calibration. Journal of Cerebral Blood Flow and Metabolism, 27(4), 690696. doi:10.1038/sj.jcbfm.9600409.CrossRefGoogle ScholarPubMed
Kim, T., Hendrich, K.S., Masamoto, K., Kim, S.-G. (2007). Arterial versus total blood volume changes during neural activity-induced cerebral blood flow change: implication for BOLD fMRI. Journal of Cerebral Blood Flow and Metabolism, 27(6), 12351247. doi:10.1038/sj.jcbfm.9600429.CrossRefGoogle ScholarPubMed
Koch, S.P., Koendgen, S., Bourayou, R., Steinbrink, J., Obrig, H. (2008). Individual alpha-frequency correlates with amplitude of visual evoked potential and hemodynamic response. NeuroImage, 41(2), 233242. doi:10.1016/j.neuroimage.2008.02.018.CrossRefGoogle ScholarPubMed
Leuchter, A.F., Uijtdehaage, S.H., Cook, I.A., O’Hara, R., Mandelkern, M. (1999). Relationship between brain electrical activity and cortical perfusion in normal subjects. Psychiatry Research, 90(2), 125140CrossRefGoogle ScholarPubMed
Li, T.Q., Haefelin, T.N., Chan, B., Kastrup, A., Jonsson, T., Glover, G.H. et al. (2000). Assessment of hemodynamic response during focal neural activity in human using bolus tracking, arterial spin labeling and BOLD techniques. NeuroImage, 12(4), 442451. doi:10.1006/nimg.2000.0634.CrossRefGoogle Scholar
Liau, J., Liu, T.T. (2009). Inter-subject variability in hypercapnic normalization of the BOLD fMRI response. NeuroImage, 45(2), 420430. doi:10.1016/j.neuroimage.2008.11.032.CrossRefGoogle ScholarPubMed
Liu, T.T., Brown, G.G. (2007). Measurement of cerebral perfusion with arterial spin labeling: Part 1. Methods. Journal of the International Neuropsychological Society, 13(3), 517525. doi:10.1017/S1355617707070646.CrossRefGoogle Scholar
Liu, T.T., Liau, J. (2010). Caffeine increases the linearity of the visual BOLD response. NeuroImage, 49(3), 23112317. doi:10.1016/j.neuroimage.2009.10.040.CrossRefGoogle ScholarPubMed
Liu, T.T., Wong, E.C. (2005). A signal processing model for arterial spin labeling functional MRI. NeuroImage, 24(1), 207215CrossRefGoogle ScholarPubMed
Lu, H., Ge, Y. (2008). Quantitative evaluation of oxygenation in venous vessels using T2-Relaxation-Under-Spin-Tagging MRI. Magnetic Resonance in Medicine, 60(2), 357363. doi:10.1002/mrm.21627.CrossRefGoogle ScholarPubMed
Lu, H., Yezhuvath, U.S., Xiao, G. (2010). Improving fMRI sensitivity by normalization of basal physiologic state. Human Brain Mapping, 31(1), 8087. doi:10.1002/hbm.20846.CrossRefGoogle ScholarPubMed
Lu, H., Zhao, C., Ge, Y., Lewis-Amezcua, K. (2008). Baseline blood oxygenation modulates response amplitude: physiologic basis for intersubject variations in functional MRI signals. Magnetic Resonance in Medicine, 60(2), 364372. doi:10.1002/mrm.21686.CrossRefGoogle ScholarPubMed
Maandag, N.J., Coman, D., Sanganahalli, B.G., Herman, P., Smith, A.J., Blumenfeld, H. et al. (2007). Energetics of neuronal signaling and fMRI activity. Proceedings of the National Academy of Sciences of the United States of America, 104(51), 2054620551. doi:10.1073/pnas.0709515104.CrossRefGoogle ScholarPubMed
Meltzer, J., Negishi, M., Mayes, L.C., Constable, R.T. (2007). Individual differences in EEG theta and alpha dynamics during working memory correlate with fMRI responses across subjects. Clinical Neurophysiology, 118(11), 24192436. doi:10.1016/j.clinph.2007.07.023.CrossRefGoogle ScholarPubMed
Nangini, C., Hlushchuk, Y., Hari, R. (2009). Predicting stimulus-rate sensitivity of human somatosensory fMRI signals with MEG. Human Brain Mapping, 30(6), 18241832. doi:10.1002/hbm.20787.CrossRefGoogle ScholarPubMed
Oakes, T.R., Pizzagalli, D.A., Hendrick, A.M., Horras, K.A., Larson, C.L., Abercrombie, H.C. et al. (2004). Functional coupling of simultaneous electrical and metabolic activity in the human brain. Human Brain Mapping, 21(4), 257270. doi:10.1002/hbm.20004.CrossRefGoogle ScholarPubMed
Ogawa, S., Menon, R.S., Tank, D.W., Kim, S.-G., Merkle, H., Ellerman, J.M. et al. (1993). Functional brain mapping by blood oxygenation level—dependent contrast magnetic resonance imaging: a comparison of signal characteristics with a biophysical model. Biophysical Journal, 64, 803–812CrossRefGoogle ScholarPubMed
Ou, W., Golland, P., Hämäläinen, M. (2007). Sources of variability in MEG. Medical image computing and computer-assisted intervention: MICCAI International Conference on Medical Image Computing and Computer-Assisted Intervention, 10(Pt 2), 751759Google Scholar
Perthen, J.E., Lansing, A.E., Liau, J., Liu, T.T., Buxton, R.B. (2008). Caffeine-induced uncoupling of cerebral blood flow and oxygen metabolism: a calibrated BOLD fMRI study. NeuroImage, 40(1), 237247CrossRefGoogle ScholarPubMed
Pigeau, R.A., Frame, A.M. (1992). Steady-state visual evoked responses in high and low alpha subjects. Electroencephalography and Clinical Neurophysiology, 84(2), 101109CrossRefGoogle ScholarPubMed
Polich, J. (1997). On the relationship between EEG and P300: individual differences, aging, and ultradian rhythms. International Journal of Psychophysiology, 26(1–3), 299317CrossRefGoogle ScholarPubMed
Restom, K., Bangen, K.J., Bondi, M.W., Perthen, J.E., Liu, T.T. (2007). Cerebral blood flow and BOLD responses to a memory encoding task: a comparison between healthy young and elderly adults. NeuroImage, 37(2), 430439CrossRefGoogle Scholar
Restom, K., Behzadi, Y., Liu, T.T. (2006). Physiological noise reduction for arterial spin labeling functional MRI. NeuroImage, 31(3), 11041115CrossRefGoogle ScholarPubMed
Restom, K., Perthen, J.E., Liu, T.T. (2008). Calibrated fMRI in the medial temporal lobe during a memory-encoding task. NeuroImage, 40(4), 14951502CrossRefGoogle ScholarPubMed
Sheth, S.A., Nemoto, M., Guiou, M., Walker, M., Pouratian, N., Toga, A.W. (2004). Linear and nonlinear relationships between neuronal activity, oxygen metabolism, and hemodynamic responses. Neuron, 42(2), 347355CrossRefGoogle ScholarPubMed
Sicard, K., Duong, T. (2005). Effects of hypoxia, hyperoxia, and hypercapnia on baseline and stimulus-evoked BOLD, CBF, and CMRO in spontaneously breathing animals. NeuroImage, 25(3), 850858. doi:10.1016/j.neuroimage.2004.12.010.CrossRefGoogle Scholar
Smith, A.J., Blumenfeld, H., Behar, K.L., Rothman, D.L., Shulman, R.G., Hyder, F. (2002). Cerebral energetics and spiking frequency: the neurophysiological basis of fMRI. Proceedings of the National Academy of Sciences of the United States of America, 99(16), 1076510770. doi:10.1073/pnas.132272199.CrossRefGoogle ScholarPubMed
St Lawrence, K.S., Ye, F.Q., Lewis, B.K., Frank, J.A., McLaughlin, A.C. (2003). Measuring the effects of indomethacin on changes in cerebral oxidative metabolism and cerebral blood flow during sensorimotor activation. Magnetic Resonance in Medicine, 50(1), 99106CrossRefGoogle ScholarPubMed
Stefanovic, B., Warnking, J.M., Kobayashi, E., Bagshaw, A.P., Hawco, C., Dubeau, F. et al. (2005). Hemodynamic and metabolic responses to activation, deactivation and epileptic discharges. NeuroImage, 28(1), 205215CrossRefGoogle ScholarPubMed
Thomason, M.E., Foland, L.C., Glover, G.H. (2007). Calibration of BOLD fMRI using breath holding reduces group variance during a cognitive task. Human Brain Mapping, 28(1), 5968CrossRefGoogle ScholarPubMed
Thomason, M.E., Glover, G.H. (2008). Controlled inspiration depth reduces variance in breath-holding-induced BOLD signal. NeuroImage, 39(1), 206214. doi:10.1016/j.neuroimage.2007.08.014.CrossRefGoogle ScholarPubMed
Tobimatsu, S., Tomoda, H., Kato, M. (1996). Normal variability of the amplitude and phase of steady-state VEPs. Electroencephalography and Clinical Neurophysiology, 100(3), 171176CrossRefGoogle ScholarPubMed
Vasquez, A.L., Noll, D.C. (1998). Nonlinear aspects of the BOLD response in functional MRI. NeuroImage, 7, 108–118CrossRefGoogle Scholar
Wager, T.D., Vazquez, A., Hernandez, L., Noll, D.C. (2005). Accounting for nonlinear BOLD effects in fMRI: parameter estimates and a model for prediction in rapid event-related studies. NeuroImage, 25(1), 206218CrossRefGoogle Scholar
Wise, R.G., Ide, K., Poulin, M.J., Tracey, I. (2004). Resting fluctuations in arterial carbon dioxide induce significant low frequency variations in BOLD signal. NeuroImage, 21(4), 16521664CrossRefGoogle ScholarPubMed
Xu, F., Uh, J., Brier, M.R., Hart, J., Yezhuvath, U.S., Gu, H. et al. (2011). The influence of carbon dioxide on brain activity and metabolism in conscious humans. Journal of Cerebral Blood Flow and Metabolism, 31(1), 5867. doi:10.1038/jcbfm.2010.153.CrossRefGoogle ScholarPubMed
Zappe, A.C., Uludağ, K., Oeltermann, A., Uğurbil, K., Logothetis, N.K. (2008). The influence of moderate hypercapnia on neural activity in the anesthetized nonhuman primate. Cerebral Cortex, 18(11), 26662673. doi:10.1093/cercor/bhn023.CrossRefGoogle ScholarPubMed