Scaling of Brain Metabolism and Blood Flow in Relation to Capillary and Neural Scaling
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{"title"=>"Scaling of brain metabolism and blood flow in relation to capillary and neural scaling", "type"=>"journal", "authors"=>[{"first_name"=>"Jan", "last_name"=>"Karbowski", "scopus_author_id"=>"55899735300"}], "year"=>2011, "source"=>"PLoS ONE", "identifiers"=>{"issn"=>"19326203", "arxiv"=>"1111.3610", "scopus"=>"2-s2.0-80055099916", "sgr"=>"80055099916", "pui"=>"362830202", "isbn"=>"1932-6203 (Electronic)\\r1932-6203 (Linking)", "pmid"=>"22053202", "doi"=>"10.1371/journal.pone.0026709"}, "id"=>"c2ee7a73-b952-35fd-822b-8b501b8ff20f", "abstract"=>"Brain is one of the most energy demanding organs in mammals, and its total metabolic rate scales with brain volume raised to a power of around 5/6. This value is significantly higher than the more common exponent 3/4 relating whole body resting metabolism with body mass and several other physiological variables in animals and plants. This article investigates the reasons for brain allometric distinction on a level of its microvessels. Based on collected empirical data it is found that regional cerebral blood flow CBF across gray matter scales with cortical volume $V$ as $CBF \\sim V^{-1/6}$, brain capillary diameter increases as $V^{1/12}$, and density of capillary length decreases as $V^{-1/6}$. It is predicted that velocity of capillary blood is almost invariant ($\\sim V^{\\epsilon}$), capillary transit time scales as $V^{1/6}$, capillary length increases as $V^{1/6+\\epsilon}$, and capillary number as $V^{2/3-\\epsilon}$, where $\\epsilon$ is typically a small correction for medium and large brains, due to blood viscosity dependence on capillary radius. It is shown that the amount of capillary length and blood flow per cortical neuron are essentially conserved across mammals. These results indicate that geometry and dynamics of global neuro-vascular coupling have a proportionate character. Moreover, cerebral metabolic, hemodynamic, and microvascular variables scale with allometric exponents that are simple multiples of 1/6, rather than 1/4, which suggests that brain metabolism is more similar to the metabolism of aerobic than resting body. Relation of these findings to brain functional imaging studies involving the link between cerebral metabolism and blood flow is also discussed.", "link"=>"http://www.mendeley.com/research/scaling-brain-metabolism-blood-flow-relation-capillary-neural-scaling", "reader_count"=>39, "reader_count_by_academic_status"=>{"Professor > Associate Professor"=>3, "Researcher"=>11, "Student > Ph. D. Student"=>10, "Student > Postgraduate"=>1, "Student > Master"=>5, "Student > Bachelor"=>5, "Lecturer"=>1, "Professor"=>3}, "reader_count_by_user_role"=>{"Professor > Associate Professor"=>3, "Researcher"=>11, "Student > Ph. D. Student"=>10, "Student > Postgraduate"=>1, "Student > Master"=>5, "Student > Bachelor"=>5, "Lecturer"=>1, "Professor"=>3}, "reader_count_by_subject_area"=>{"Engineering"=>5, "Unspecified"=>2, "Agricultural and Biological Sciences"=>13, "Medicine and Dentistry"=>9, "Neuroscience"=>4, "Veterinary Science and Veterinary Medicine"=>1, "Psychology"=>2, "Chemistry"=>1, "Computer Science"=>2}, "reader_count_by_subdiscipline"=>{"Engineering"=>{"Engineering"=>5}, "Medicine and Dentistry"=>{"Medicine and Dentistry"=>9}, "Neuroscience"=>{"Neuroscience"=>4}, "Chemistry"=>{"Chemistry"=>1}, "Psychology"=>{"Psychology"=>2}, "Agricultural and Biological Sciences"=>{"Agricultural and Biological Sciences"=>13}, "Computer Science"=>{"Computer Science"=>2}, "Unspecified"=>{"Unspecified"=>2}, "Veterinary Science and Veterinary Medicine"=>{"Veterinary Science and Veterinary Medicine"=>1}}, "reader_count_by_country"=>{"Greece"=>1, "Japan"=>1}, "group_count"=>2}

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Figshare

  • {"files"=>["https://ndownloader.figshare.com/files/363771", "https://ndownloader.figshare.com/files/363782", "https://ndownloader.figshare.com/files/363791", "https://ndownloader.figshare.com/files/363802"], "description"=>"<div><p>Brain is one of the most energy demanding organs in mammals, and its total metabolic rate scales with brain volume raised to a power of around 5/6. This value is significantly higher than the more common exponent 3/4 relating whole body resting metabolism with body mass and several other physiological variables in animals and plants. This article investigates the reasons for brain allometric distinction on a level of its microvessels. Based on collected empirical data it is found that regional cerebral blood flow CBF across gray matter scales with cortical volume as , brain capillary diameter increases as , and density of capillary length decreases as . It is predicted that velocity of capillary blood is almost invariant (), capillary transit time scales as , capillary length increases as , and capillary number as , where is typically a small correction for medium and large brains, due to blood viscosity dependence on capillary radius. It is shown that the amount of capillary length and blood flow per cortical neuron are essentially conserved across mammals. These results indicate that geometry and dynamics of global neuro-vascular coupling have a proportionate character. Moreover, cerebral metabolic, hemodynamic, and microvascular variables scale with allometric exponents that are simple multiples of 1/6, rather than 1/4, which suggests that brain metabolism is more similar to the metabolism of aerobic than resting body. Relation of these findings to brain functional imaging studies involving the link between cerebral metabolism and blood flow is also discussed.</p> </div>", "links"=>[], "tags"=>["scaling", "metabolism", "capillary", "neural"], "article_id"=>131893, "categories"=>["Physiology", "Biological Sciences", "Neuroscience", "Physics"], "users"=>["Jan Karbowski"], "doi"=>["https://dx.doi.org/10.1371/journal.pone.0026709.s001", "https://dx.doi.org/10.1371/journal.pone.0026709.s002", "https://dx.doi.org/10.1371/journal.pone.0026709.s003", "https://dx.doi.org/10.1371/journal.pone.0026709.s004"], "stats"=>{"downloads"=>0, "page_views"=>0, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/Scaling_of_Brain_Metabolism_and_Blood_Flow_in_Relation_to_Capillary_and_Neural_Scaling/131893", "title"=>"Scaling of Brain Metabolism and Blood Flow in Relation to Capillary and Neural Scaling", "pos_in_sequence"=>0, "defined_type"=>4, "published_date"=>"2011-10-28 00:31:33"}
  • {"files"=>["https://ndownloader.figshare.com/files/717962"], "description"=>"<p>(A) Visual cortex: (, ). 95 confidence interval for the slope CI = (−0.168,−0.086). (B) Parietal cortex: (, ), slope CI = (−0.222,−0.078). (C) Frontal cortex: (, ), slope CI = (−0.239,−0.100). (D) Temporal cortex: (, ), slope CI = (−0.286,−0.096).</p>", "links"=>[], "tags"=>["cerebral", "cbf", "cortical"], "article_id"=>388324, "categories"=>["Physiology", "Biological Sciences", "Neuroscience", "Physics"], "users"=>["Jan Karbowski"], "doi"=>["https://dx.doi.org/10.1371/journal.pone.0026709.g001"], "stats"=>{"downloads"=>0, "page_views"=>0, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Scaling_of_cerebral_blood_flow_CBF_in_the_cortical_gray_matter_/388324", "title"=>"Scaling of cerebral blood flow CBF in the cortical gray matter.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2011-10-28 02:18:44"}
  • {"files"=>["https://ndownloader.figshare.com/files/718072"], "description"=>"<p>(A) Hippocampus: (, ), slope CI = (−0.271,0.000). (B) Thalamus: (, ), slope CI = (−0.272,−0.062). (C) Cerebellum: (, ), slope CI = (−0.252,−0.102).</p>", "links"=>[], "tags"=>["cerebral", "cbf", "subcortical"], "article_id"=>388432, "categories"=>["Physiology", "Biological Sciences", "Neuroscience", "Physics"], "users"=>["Jan Karbowski"], "doi"=>["https://dx.doi.org/10.1371/journal.pone.0026709.g002"], "stats"=>{"downloads"=>0, "page_views"=>0, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Scaling_of_cerebral_blood_flow_CBF_in_the_subcortical_gray_matter_/388432", "title"=>"Scaling of cerebral blood flow CBF in the subcortical gray matter.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2011-10-28 02:20:32"}
  • {"files"=>["https://ndownloader.figshare.com/files/718169"], "description"=>"<p>(A) Capillary diameter scales against cortical gray matter volume with the exponent 0.075 (, , ), exponent CI = (0.034,0.117). (B) Volume density of capillary length scales with the exponent (, , ), exponent CI = (−0.316,−0.008). (C) Fraction of capillary volume in gray matter is essentially independent of brain size (, , ), the same as (D) the arterial partial oxygen pressure (, , ).</p>", "links"=>[], "tags"=>["capillary", "characteristics"], "article_id"=>388537, "categories"=>["Physiology", "Biological Sciences", "Neuroscience", "Physics"], "users"=>["Jan Karbowski"], "doi"=>["https://dx.doi.org/10.1371/journal.pone.0026709.g003"], "stats"=>{"downloads"=>0, "page_views"=>0, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Scaling_of_brain_capillary_characteristics_against_brain_size_/388537", "title"=>"Scaling of brain capillary characteristics against brain size.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2011-10-28 02:22:17"}
  • {"files"=>["https://ndownloader.figshare.com/files/718258"], "description"=>"<p>(A) Across our sample of mammals, the cortical neuron number density scales against cortical volume with the exponent (, , ), exponent CI = (−0.221,−0.036). (B) The ratio of the density of capillary length to the density of neurons in the cortex does not correlate with brain size (, , ), exponent CI = (−0.228,0.161). (C) The log-log dependence of the capillary length density on neuron density gives the exponent of 1.05 (, , ).</p>", "links"=>[], "tags"=>["capillary", "cerebral"], "article_id"=>388624, "categories"=>["Physiology", "Biological Sciences", "Neuroscience", "Physics"], "users"=>["Jan Karbowski"], "doi"=>["https://dx.doi.org/10.1371/journal.pone.0026709.g004"], "stats"=>{"downloads"=>0, "page_views"=>0, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Neuron_density_versus_capillary_length_density_in_the_cerebral_cortex_/388624", "title"=>"Neuron density versus capillary length density in the cerebral cortex.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2011-10-28 02:23:44"}
  • {"files"=>["https://ndownloader.figshare.com/files/718354"], "description"=>"<p>The ratio of CBF to neuron density in the cerebral cortex does not correlate significantly with brain size (log-log plot yields , , ). The value of CBF for each species is the arithmetic mean of regional CBF across cerebral cortex.</p>", "links"=>[], "tags"=>["cerebral", "cortical", "neuron"], "article_id"=>388720, "categories"=>["Physiology", "Biological Sciences", "Neuroscience", "Physics"], "users"=>["Jan Karbowski"], "doi"=>["https://dx.doi.org/10.1371/journal.pone.0026709.g005"], "stats"=>{"downloads"=>0, "page_views"=>0, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Invariance_of_cerebral_blood_flow_per_cortical_neuron_across_mammals_/388720", "title"=>"Invariance of cerebral blood flow per cortical neuron across mammals.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2011-10-28 02:25:20"}
  • {"files"=>["https://ndownloader.figshare.com/files/718395"], "description"=>"<p>Data for were taken from Suppl. Inform. <a href=\"http://www.plosone.org/article/info:doi/10.1371/journal.pone.0026709#pone.0026709.s003\" target=\"_blank\">Table S2</a> (references therein).</p>", "links"=>[], "tags"=>["capillary"], "article_id"=>388766, "categories"=>["Physiology", "Biological Sciences", "Neuroscience", "Physics"], "users"=>["Jan Karbowski"], "doi"=>["https://dx.doi.org/10.1371/journal.pone.0026709.t002"], "stats"=>{"downloads"=>0, "page_views"=>0, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Exponent_as_a_function_of_capillary_diameter_/388766", "title"=>"Exponent as a function of capillary diameter.", "pos_in_sequence"=>0, "defined_type"=>3, "published_date"=>"2011-10-28 02:26:06"}
  • {"files"=>["https://ndownloader.figshare.com/files/718422"], "description"=>"<p>Summary of scalings for brain capillaries and hemodynamics against cortical gray matter volume .</p>", "links"=>[], "tags"=>["scalings", "capillaries", "hemodynamics", "cortical"], "article_id"=>388787, "categories"=>["Physiology", "Biological Sciences", "Neuroscience", "Physics"], "users"=>["Jan Karbowski"], "doi"=>["https://dx.doi.org/10.1371/journal.pone.0026709.t003"], "stats"=>{"downloads"=>0, "page_views"=>0, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Summary_of_scalings_for_brain_capillaries_and_hemodynamics_against_cortical_gray_matter_volume_/388787", "title"=>"Summary of scalings for brain capillaries and hemodynamics against cortical gray matter volume .", "pos_in_sequence"=>0, "defined_type"=>3, "published_date"=>"2011-10-28 02:26:27"}
  • {"files"=>["https://ndownloader.figshare.com/files/718447"], "description"=>"<p>Data for and were collected from <a href=\"http://www.plosone.org/article/info:doi/10.1371/journal.pone.0026709#pone.0026709-SugiharaSeki1\" target=\"_blank\">[35]</a>. The value of was taken as 1/8. The last column represents values of the fitting function to the function in the fourth column.</p>", "links"=>[], "tags"=>["affecting"], "article_id"=>388818, "categories"=>["Physiology", "Biological Sciences", "Neuroscience", "Physics"], "users"=>["Jan Karbowski"], "doi"=>["https://dx.doi.org/10.1371/journal.pone.0026709.t001"], "stats"=>{"downloads"=>0, "page_views"=>0, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Parameters_affecting_the_effective_blood_viscosity_/388818", "title"=>"Parameters affecting the effective blood viscosity.", "pos_in_sequence"=>0, "defined_type"=>3, "published_date"=>"2011-10-28 02:26:58"}

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Relative Metric

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