- Author:
- Dewan Sarwar <sarwarcse@gmail.com>
- Date:
- 2019-03-11 12:09:49+13:00
- Desc:
- added blood capillary flux model
- Permanent Source URI:
- https://models.physiomeproject.org/workspace/584/rawfile/dcab0d9157ad4fb602c5084666c323fb3e30323a/thomas_2000.cellml
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<title>Inner medullary lactate production and accumulation: a vasa recta model</title>
<author>
<firstname>Catherine</firstname>
<surname>Lloyd</surname>
<affiliation>
<shortaffil>Bioengineering Institute, University of Auckland</shortaffil>
</affiliation>
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<title>Model Status</title>
<para>This CellML version of the model has been checked in COR and PCEnv and it runs in PCEnv. The model will not run in COR because it does not contain any time derivatives - COR expects the units of the differential equations to be a function of time (not length as it is in this case). However, COR did allow for the units to be checked and they are consistent. The model runs in PCEnv but as yet it does not recreate the published results. This may be due to differences in the defined set of initial conditions. The model author has been contacted and we are currently receiving their help and advice.</para>
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<sect1 id="sec_structure">
<title>Model Structure</title>
<para>S. Randall Thomas here investigates the possibility that recycling of lactate produced by anaerobic glycolysis in the inner medulla of the kidney can provide sufficient of a lactate gradient to contributes significantly to the urine concentrating mechanism.</para>
<para>Assuming (from other sources) that 20% of the glucose delivered to the inner medulla, Thomas uses a mathematical model of the inner medullary vasa recta, based on observed mass distribution and distribution of loops, to investigate a range of plausible values of lactose and glucose permeabilities, to see which values would allow a sufficient accumulation of a lactate gradient to be a significant contributor to urine concentrating ability, in different circumstances of blood flow and diuresis.</para>
<para>The complete original paper reference is cited below:</para>
<para>
Inner medullary lactate production and accumulation: a vasa recta model, S. Randall Thomas, 2000,
<emphasis>American Journal of Physiology</emphasis>
, 279, F468-F481.
<ulink url="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=pubmed&cmd=Retrieve&dopt=AbstractPlus&list_uids=10966926&query_hl=1&itool=pubmed_docsum">PubMed ID: 10966926</ulink>
</para>
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<caption>Schematic representation of the steady-state model.</caption>
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<variable cmeta:id="model_parameters.x" initial_value="0" name="x" public_interface="out" units="mm" />
<variable cmeta:id="model_parameters.F_DVR_G_0" name="F_DVR_G_0" public_interface="out" units="pmol_min" />
<variable cmeta:id="model_parameters.F_DVR_V_0" name="F_DVR_V_0" public_interface="out" units="nl_min" />
<variable cmeta:id="model_parameters.Jv" name="Jv" public_interface="out" units="nl_min_mm" />
<variable cmeta:id="model_parameters.c_DVR_GLU_0" initial_value="10.0" name="c_DVR_GLU_0" units="millimolar" />
<variable cmeta:id="model_parameters.x_L" name="x_L" units="dimensionless" />
<variable cmeta:id="model_parameters.b" initial_value="4.0" name="b" units="dimensionless" />
<variable cmeta:id="model_parameters.F_DVR_v" name="F_DVR_v" public_interface="in" units="nl_min" />
<variable cmeta:id="model_parameters.N_x" name="N_x" public_interface="in" units="dimensionless" />
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<eq />
<ci>Jv</ci>
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<times />
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="per_mm">0.3</cn>
<apply>
<divide />
<ci>F_DVR_v</ci>
<apply>
<times />
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</apply>
</apply>
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</apply>
</apply>
<apply>
<eq />
<ci>F_DVR_V_0</ci>
<apply>
<times />
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</apply>
</apply>
<apply>
<eq />
<ci>x_L</ci>
<apply>
<divide />
<ci>x</ci>
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</apply>
</apply>
<apply>
<eq />
<ci>F_DVR_G_0</ci>
<apply>
<times />
<ci>F_DVR_V_0</ci>
<ci>c_DVR_GLU_0</ci>
</apply>
</apply>
</math>
</component>
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<map_variables variable_1="F_DVR_v" variable_2="F_DVR_v" />
</connection>
<connection>
<map_components component_1="model_parameters" component_2="F_DVR_LAC" />
<map_variables variable_1="ksh" variable_2="ksh" />
<map_variables variable_1="x" variable_2="x" />
</connection>
<connection>
<map_components component_1="J_ABS_V" component_2="F_AVR_v" />
<map_variables variable_1="J_ABS_V" variable_2="J_ABS_V" />
</connection>
<connection>
<map_components component_1="c_DVR_GLU" component_2="JLAC" />
<map_variables variable_1="c_DVR_GLU" variable_2="c_DVR_LAC" />
</connection>
<connection>
<map_components component_1="model_parameters" component_2="F_AVR_v" />
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<map_variables variable_1="x" variable_2="x" />
</connection>
<connection>
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<map_variables variable_1="F_AVR_v" variable_2="F_AVR_v" />
</connection>
<connection>
<map_components component_1="model_parameters" component_2="JGLU" />
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</connection>
<connection>
<map_components component_1="model_parameters" component_2="kv" />
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<map_variables variable_1="L" variable_2="L" />
<map_variables variable_1="N_0" variable_2="N_0" />
<map_variables variable_1="F_DVR_V_0" variable_2="F_DVR_V_0" />
</connection>
<connection>
<map_components component_1="JLAC" component_2="F_AVR_LAC" />
<map_variables variable_1="JLAC" variable_2="JLAC" />
</connection>
<connection>
<map_components component_1="JGLY" component_2="F_AVR_LAC" />
<map_variables variable_1="JGLY" variable_2="JGLY" />
</connection>
<connection>
<map_components component_1="model_parameters" component_2="F_AVR_LAC" />
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<connection>
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</connection>
<connection>
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<map_variables variable_1="JGLU" variable_2="JGLU" />
</connection>
<connection>
<map_components component_1="JGLU" component_2="F_AVR_GLU" />
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<connection>
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</connection>
<connection>
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</connection>
<connection>
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<map_variables variable_1="N_x" variable_2="N_x" />
</connection>
<connection>
<map_components component_1="N_x" component_2="JGLY" />
<map_variables variable_1="N_x" variable_2="N_x" />
</connection>
<connection>
<map_components component_1="F_DVR_v" component_2="F_AVR_v" />
<map_variables variable_1="F_DVR_v" variable_2="F_DVR_v" />
</connection>
<connection>
<map_components component_1="F_AVR_LAC" component_2="c_AVR_LAC" />
<map_variables variable_1="F_AVR_LAC" variable_2="F_AVR_LAC" />
</connection>
<connection>
<map_components component_1="F_DVR_GLU" component_2="c_DVR_GLU" />
<map_variables variable_1="F_DVR_GLU" variable_2="F_DVR_GLU" />
</connection>
<connection>
<map_components component_1="c_AVR_GLU" component_2="JGLY" />
<map_variables variable_1="c_AVR_GLU" variable_2="c_AVR_GLU" />
</connection>
<connection>
<map_components component_1="c_AVR_LAC" component_2="JLAC" />
<map_variables variable_1="c_AVR_LAC" variable_2="c_AVR_LAC" />
</connection>
<connection>
<map_components component_1="F_DVR_LAC" component_2="F_AVR_LAC" />
<map_variables variable_1="F_DVR_LAC" variable_2="F_DVR_LAC" />
</connection>
<connection>
<map_components component_1="model_parameters" component_2="N_x" />
<map_variables variable_1="ksh" variable_2="ksh" />
<map_variables variable_1="N_0" variable_2="N_0" />
<map_variables variable_1="x" variable_2="x" />
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<connection>
<map_components component_1="model_parameters" component_2="JGLY" />
<map_variables variable_1="ksh" variable_2="ksh" />
<map_variables variable_1="L" variable_2="L" />
<map_variables variable_1="F_DVR_G_0" variable_2="F_DVR_G_0" />
<map_variables variable_1="N_0" variable_2="N_0" />
</connection>
<connection>
<map_components component_1="F_DVR_LAC" component_2="c_DVR_LAC" />
<map_variables variable_1="F_DVR_LAC" variable_2="F_DVR_LAC" />
</connection>
<connection>
<map_components component_1="N_x" component_2="J_ABS_V" />
<map_variables variable_1="N_x" variable_2="N_x" />
</connection>
<connection>
<map_components component_1="model_parameters" component_2="JLAC" />
<map_variables variable_1="Jv" variable_2="Jv" />
</connection>
<connection>
<map_components component_1="JLAC" component_2="F_DVR_LAC" />
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</connection>
<connection>
<map_components component_1="F_DVR_v" component_2="c_DVR_LAC" />
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</connection>
<connection>
<map_components component_1="F_AVR_v" component_2="c_AVR_GLU" />
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</connection>
<connection>
<map_components component_1="c_AVR_GLU" component_2="JGLU" />
<map_variables variable_1="c_AVR_GLU" variable_2="c_AVR_GLU" />
</connection>
<connection>
<map_components component_1="F_DVR_GLU" component_2="F_AVR_GLU" />
<map_variables variable_1="F_DVR_GLU" variable_2="F_DVR_GLU" />
</connection>
<connection>
<map_components component_1="c_DVR_GLU" component_2="JGLU" />
<map_variables variable_1="c_DVR_GLU" variable_2="c_DVR_GLU" />
</connection>
<connection>
<map_components component_1="F_DVR_v" component_2="c_DVR_GLU" />
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</connection>
<connection>
<map_components component_1="N_x" component_2="model_parameters" />
<map_variables variable_1="N_x" variable_2="N_x" />
</connection>
<connection>
<map_components component_1="kv" component_2="J_ABS_V" />
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</connection>
<connection>
<map_components component_1="model_parameters" component_2="F_AVR_GLU" />
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<map_variables variable_1="x" variable_2="x" />
</connection>
<connection>
<map_components component_1="JGLY" component_2="F_AVR_GLU" />
<map_variables variable_1="JGLY" variable_2="JGLY" />
</connection>
<connection>
<map_components component_1="model_parameters" component_2="F_DVR_v" />
<map_variables variable_1="ksh" variable_2="ksh" />
<map_variables variable_1="Jv" variable_2="Jv" />
<map_variables variable_1="x" variable_2="x" />
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</semsim:hasSourceParticipant>
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</semsim:hasMediatorParticipant>
<semsim:name>permeation velocity of lactate</semsim:name>
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<vCard:FN>S. Randall Thomas</vCard:FN>
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<dcterms:description>Since anaerobic glycolysis yields two lactates for each glucose consumed and since it is reported to be a major source of ATP for inner medullary (IM) cell maintenance, it is a likely source of "external" IM osmoles. It has long been known that such an osmole source could theoretically contribute to the "single-effect" of the urine concentrating mechanism, but there was previously no suggestion of a plausible source. I used numerical simulation to estimate axial gradients of lactate and glucose that might be accumulated by countercurrent recycling in IM vasa recta (IMVR). Based on measurements in other tissues, anaerobic glycolysis (assumed to be independent of diuretic state) was estimated to consume approximately 20% of the glucose delivered to the IM. IM tissue mass and axial distribution of loops and vasa recta were according to reported values for rat and other rodents. Lactate (P(LAC)) and glucose (P(GLU)) permeabilities were varied over a range of plausible values. The model results suggest that P(LAC) of 100 x 10(-5) cm/s (similar to measured permeabilities for other small solutes) is sufficiently high to ensure efficient lactate recycling. By contrast, it was necessary in the model to reduce P(GLU) to a small fraction of this value (1/25th) to avoid papillary glucose depletion by countercurrent shunting. The results predict that IM lactate production could suffice to build a significant steady-state axial lactate gradient in the IM interstitium. Other modeling studies (Jen JF and Stephenson JL. Bull Math Biol 56: 491-514, 1994; and Thomas SR and Wexler AS. Am J Physiol Renal Fluid Electrolyte Physiol 269: F159-F171, 1995) have shown that 20-100 mosmol/kgH(2)O of unspecified external, interstitial, osmolytes could greatly improve IM concentrating ability. The present study gives several plausible scenarios consistent with accumulation of metabolically produced lactate osmoles, although only to the lower end of this range. For example, if 20% of entering glucose is consumed, the model predicts that papillary lactate would attain about 15 mM assuming vasa recta outflow is increased 30% by fluid absorbed from the nephrons and collecting ducts and that this lactate gradient would double if IM blood flow were reduced by one-half, as may occur in antidiuresis. Several experimental tests of the hypothesis are indicated.</dcterms:description>
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