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Notebook[{
Cell[TextData[{
  "Calculations of a Neuron with 3 Dendritic\nBranches and a 25 ",
  StyleBox["m",
    FontFamily->"Symbol"],
  "m Soma"
}], "Title",
  Evaluatable->False,
  CellHorizontalScrolling->False,
  TextAlignment->Center],

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    \(Off[General::spell]\)}], "Input"],

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Cell[CellGroupData[{

Cell["Let's begin with some definitions", "Subsection",
  Evaluatable->False],

Cell["\<\
Soma with primary dendrite and two daughter dendrites, all sharing same Rm \
and Ri values\
\>", "Text"],

Cell[BoxData[
    \(\(\(Rm =. \  (*\ 
      membrane\ resistance\ applied\ to\ all\ dendrites\ and\ soma\ *) \n
    Ri =. \  (*\ internal\ resistance\ applied\ to\ entire\ cell\ *) \n
    DendDiaParent =. \  (*\ 
      Diameter\ of\ parent\ dendrite\ *) \[IndentingNewLine]
    DendDiamD1 =. \  (*\ Diameter\ of\ daughter\ #\ 1\ *) \[IndentingNewLine]
    DendDiamD2 =.  (*\ Diameter\ of\ daughter\ #\ 2\ *) \[IndentingNewLine]
    ParentLength =. \  (*\ 
      Length\ of\ parent\ diamter\ in\ cm\ \(\((\)\(um/
            10^\(-4\)\)\(\ \)\)*) \[IndentingNewLine]
    D1Length =. \  (*\ 
      Length\ of\ D1\ branch\ in\ cm\ \((um/10^4)\)\ *) \[IndentingNewLine]
    D2Length =. \  (*\ 
      length\ of\ D2\ branch\ in\ cm\ \((u\ \(\((\)\(um/
                10^\(-4\)\)\(\ \)\)\)*) \[IndentingNewLine]
    SomaDia =.  (*\ Soma\ diameter\ in\ cm\ \((um/10^\(-40\))\)\ *) \n
    SomaSa =.  (*\ Soma\ surface\ area\ cm2\ *) \n
    LambdaParent =.  (*\ Length\ constant\ of\ parent\ branch\ *) \n
    LambdaD1 =.  (*\ 
      Length\ constant\ of\ daughter\ #\ 1\ *) \[IndentingNewLine]
    LambdaD2 =.  (*\ 
      Length\ constant\ of\ daughter\ #\ 2\ *) \[IndentingNewLine]
    X1Parent =. \  (*\ 
      Real\ length\ of\ parent/LambdaParent\ *) \[IndentingNewLine]
    X1D1 =. \  (*\ Real\ length\ of\ D1/LambdaD1\ *) \[IndentingNewLine]
    X1D2 =. \  (*\ Real\ length\ of\ D2/LambdaD2\ *) \[IndentingNewLine]
    Gsoma =. \  (*\ Conductance\ of\ soma\ alone\ *) \[IndentingNewLine]
    Rsoma =. \  (*\ 
      Input\ resistance\ of\ soma\ alone\ *) \[IndentingNewLine]
    Gn =. \  (*\ Conductance\ of\ neuron\ at\ the\ soma\ *) \n
    GNeuronAtSoma =. \  (*\ 
      Input\ conductance\ of\ neuron\ at\ soma\  = 
        Gsoma + GrealParentIn\ *) \[IndentingNewLine]
    RNeuronAtSoma =.  (*\ 
      Input\ resistance\ of\ neuron\ at\ soma\ *) \[IndentingNewLine]
    GNeuronMidway =. \  (*\ 
      Input\ conductance\ of\ neuron\ at\ middle\ of\ primary/
          parent\ *) \ \[IndentingNewLine]
    RNeuronMidway =. \  (*\ 
      The\ input\ resistance\ at\ the\ middle\ of\ the\ primary\ dendrite\ \
*) \[IndentingNewLine]
    RD1Out =. \  (*\ 
      Input\ resistance\ at\ end\ of\ D1\ *) \[IndentingNewLine]
    RD2Out =. \  (*\ 
      Input\ resistance\ at\ end\ of\ D2\ *) \[IndentingNewLine]
    GinfParent =.  (*\ Infinite\ conductance\ of\ parent\ dendrite\ *) \n
    GinfD1 =.  (*\ 
      Infinite\ conductance\ of\ daughter\ branch\ #\ 1\ \
*) \[IndentingNewLine]
    GinfD2 =.  (*\ 
      Infinite\ conductance\ of\ daughter\ branch\ #\ 2\ \
*) \[IndentingNewLine]
    GrealParentIn =.  (*\ 
      The\ real\ conductance\ of\ the\ primary\ dendrite\ at\ soma\ end\ \
*) \[IndentingNewLine]
    GrealD1In =.  (*\ 
      The\ real\ conductance\ of\ daughter\ #\ 1\ at\ branch\ point\ with\ \
parent\ looking\ out\ *) \[IndentingNewLine]
    GrealD2In =.  (*\ 
      The\ real\ conductance\ of\ daughter\ #\ 2\ at\ branch\ point\ with\ \
parent\ looking\ out\ *) \[IndentingNewLine]
    GrealParentOut =. \  (*\ 
      The\ real\ \((B1Out*
            GinfParent)\)\ conductance\ of\ parent\ dendrite\ at\ its\ distal\
\ end\ looking\ in\ *) \[IndentingNewLine]
    GrealD1Out =. \  (*\ 
      The\ real\ \((B1D1Out*
            GinfD1)\)\ for\ conductance\ at\ distal\ end\ of\ D1\ \
*) \[IndentingNewLine]
    GrealD2Out =. \  (*\ 
      The\ real\ \((B1D2Out*
            GinfD2)\)\ conductance\ of\ the\ distal\ end\ of\ D2\ \
*) \[IndentingNewLine]
    B1OutD1 =. \  (*\ 
      The\ B1\ factor\ at\ the\ distal\ end\ of\ D1\ to\ give\ GrealD1Out\ \
*) \[IndentingNewLine]
    B1OutD2 =. \  (*\ 
      The\ B1\ factor\ at\ the\ distal\ end\ of\ D2\ to\ give\ GrealD2Out\ \
*) \[IndentingNewLine]
    B1InParent =. \  (*\ 
      The\ B1\ factor\ at\ the\ soma\ end\ of\ the\ primary\ \((parent)\)\ \
dendrite\ to\ give\ GrealParentIn\ *) \[IndentingNewLine]
    B1InD1 =. \  (*\ 
      The\ B1\ factor\ at\ the\ proximal\ end\ of\ D1\ to\ give\ GrealD1In\ \
*) \[IndentingNewLine]
    B1InD2 =. \  (*\ 
      The\ B1\ value\ of\ daughter\ #1\ at\ branch\ point\ with\ parent\ \
\(\((\)\(multiply\ by\ GinfD2\)\(\ \)\)*) \[IndentingNewLine]
    B1OutParent =. \  (*\ 
      The\ B1\ at\ the\ distal\ end\ of\ the\ primary\ when\ move\ out\ from\ \
soma\ *) \[IndentingNewLine]
    BjoParentIn =. \  (*\ 
      Use\ when\ moving\ in\ to\ soma = \(\((\)\(\((GrealD1 + GrealD2)\)/
            GinfParent\)\(\ \)\)*) \[IndentingNewLine]
    BjoD1In =.  (*\ 
      The\ terimal\ end\ of\ D1\ when\ moving\ from\ distal\ to\ soma\ \
\((usually\ 0.0)\)\ *) \[IndentingNewLine]
    BjoD2In =. \  (*\ 
      The\ terimal\ end\ of\ D2\ when\ moving\ from\ distal\ to\ soma\ \
\((usually\ 0.0)\)\ *) \[IndentingNewLine]
    BjoParentOut =. \  (*\ 
      Convert\ soma\ to\ Bjo\ value\ for\ soma\ end\ of\ parent\ dendrite\ \
*) \[IndentingNewLine]
    BjoD1Out =. \  (*\ 
      Convert\ distal\ parent\ and\ D2\ at\ distal\ parent\ branch\ to\ Bjo\ \
going\ out\ *) \[IndentingNewLine]
    BjoD2Out\  =. \  (*\ 
      Convert\ distal\ parent\ and\ D1\ at\ distal\ parent\ branch\ to\ Bjo\ \
going\ out\ *) \[IndentingNewLine]
    GNeuronAtParentOut =. \  (*\ 
      The\ conductance\ of\ the\ cell\ at\ the\ end\ of\ the\ primary\ \
dendrite\ *) \[IndentingNewLine]
    GNeuronMidwayParent =. \  (*\ 
      The\ conductance\ of\ the\ cell\ at\ the\ middle\ of\ the\ primary\ \
dendrite\ *) \[IndentingNewLine]
    GNeuronMidwayIn =. \  (*\ 
      The\ outward\ looking\ conductance\ of\ the\ cell\ at\ the\ middle\ of\ \
the\ parent\ *) \[IndentingNewLine]
    RNeuronMidwayIn =. \  (*\ 
      The\ input\ resistance\ of\ the\ outward\ looking\ half\ of\ the\ \
parent\ dendrite\ *) \[IndentingNewLine]
    GNeuronMidwayOut =. \  (*\ 
      The\ inward\ looking\ conductance\ of\ the\ cell\ at\ the\ middle\ of\ \
the\ parent\ *) \[IndentingNewLine]
    RNeuronMidwayOut =. \  (*\ 
      The\ inward\ \((soma)\)\ looking\ conductance\ of\ the\ cell\ at\ the\ \
middle\ of\ the\ parent\ *) \[IndentingNewLine]
    Vo =. \  (*\ Initial\ starting\ voltage\ *) \[IndentingNewLine]
    Vout =. \  (*\ 
      Voltage\ profile\ moving\ outward\ from\ soma\ *) \[IndentingNewLine]
    Vin =. \  (*\ 
      Voltage\ profile\ moving\ in\ towards\ soma\ *) \[IndentingNewLine]
    Vsoma =. \)\(\ \)\( (*\ Voltage\ at\ soma\ *) \)\)\)], "Input",
  PageWidth->Infinity],

Cell["Now Put in the data for your cell.....", "Text"],

Cell[CellGroupData[{

Cell[BoxData[
    \(cm = Centimeter\)], "Input"],

Cell[BoxData[
    TagBox[\(1\ Centimeter\),
      UnitsWrapper]], "Output"]
}, Open  ]],

Cell["\<\
For this analysis, we will use Cell 7 or the \"Golgi\" cell of the 3 branch \
neuron set\
\>", "Text"],

Cell[CellGroupData[{

Cell[BoxData[
    RowBox[{
      RowBox[{\(Rm = 27000\ Ohm\ cm\^2\  // N\), " ", 
        RowBox[{"(*", " ", 
          StyleBox[\(ohms\ cm^2\),
            FontFamily->"Courier New"], 
          StyleBox[" ",
            FontFamily->"Courier New"], 
          StyleBox["*)",
            FontFamily->"Courier New"]}], "\[IndentingNewLine]", 
        StyleBox[\(\(Ri = 220\ Ohm\ cm\ \  // N\)\(\ \)\( (*\ 
            ohms\ cm\ *) \)\),
          FontFamily->"Courier New"], 
        "\[IndentingNewLine]", \(SomaDia = 18\ 10^\(-4\)\ \ cm\ \  // N\), 
        " ", \( (*\ cm\ \((4\ 10^\(-4\))\)\ cm\ *) \), 
        "\[IndentingNewLine]", \(DendDiaParent = 4\ 10^\(-4\)\ cm\  // N\), 
        " ", \( (*\ cm\ *) \), 
        "\[IndentingNewLine]", \(ParentLength = 180\ 10^\(-4\)\ cm\  // N\), 
        "  ", \( (*\ cm\ *) \), 
        "\[IndentingNewLine]", \(DendDiamD1 = 3\ 10^\(-4\)\ cm\  // N\), 
        "  ", \( (*\ cm\ *) \), 
        "\[IndentingNewLine]", \(D1Length = 145\ 10^\(-4\)\ \ cm\ \  // N\), 
        " ", \( (*\ cm\ *) \), 
        "\[IndentingNewLine]", \(DendDiamD2 = 2\ 10^\(-4\)\ cm\ \  // N\), 
        " ", \( (*\ cm\ *) \), 
        "\[IndentingNewLine]", \(D2Length = 137\ 10^\(-4\)\ cm\ \  // N\), 
        " ", \( (*\ cm\ *) \), "\[IndentingNewLine]", \(BjoD1In = 0.0\), 
        " ", \( (*\ sealed\ end\ condition\ for\ moving\ towards\ soma\ *) \),
         "\[IndentingNewLine]", \(BjoD2In = 0.0\)}], 
      " ", \( (*\ 
        sealded\ end\ conditions\ for\ moving\ towards\ soma\ *) \)}]], \
"Input"],

Cell[BoxData[
    TagBox[\(27000.`\ \(Centimeter\^2\ Ohm\)\),
      UnitsWrapper]], "Output"],

Cell[BoxData[
    TagBox[\(220.`\ \(Centimeter\ Ohm\)\),
      UnitsWrapper]], "Output"],

Cell[BoxData[
    TagBox[\(0.0018`\ Centimeter\),
      UnitsWrapper]], "Output"],

Cell[BoxData[
    TagBox[\(0.0004`\ Centimeter\),
      UnitsWrapper]], "Output"],

Cell[BoxData[
    TagBox[\(0.018`\ Centimeter\),
      UnitsWrapper]], "Output"],

Cell[BoxData[
    TagBox[\(0.0003`\ Centimeter\),
      UnitsWrapper]], "Output"],

Cell[BoxData[
    TagBox[\(0.0145`\ Centimeter\),
      UnitsWrapper]], "Output"],

Cell[BoxData[
    TagBox[\(0.0002`\ Centimeter\),
      UnitsWrapper]], "Output"],

Cell[BoxData[
    TagBox[\(0.0137`\ Centimeter\),
      UnitsWrapper]], "Output"],

Cell[BoxData[
    \(0.`\)], "Output"],

Cell[BoxData[
    \(0.`\)], "Output"]
}, Open  ]],

Cell["\<\

The soma surface area\
\>", "Text"],

Cell[CellGroupData[{

Cell[BoxData[
    \(\(\(\[IndentingNewLine]\)\(N[SomaSa = \[Pi]\ SomaDia\^2]\)\)\)], "Input"],

Cell[BoxData[
    TagBox[\(0.000010178760197630929`\ Centimeter\^2\),
      UnitsWrapper]], "Output"]
}, Open  ]],

Cell["The input conductance of the soma", "Text"],

Cell[CellGroupData[{

Cell[BoxData[
    \(\(\(\n\)\(Gsoma = Convert[SomaSa\/Rm, \ Mho] // N\)\)\)], "Input",
  PageWidth->Infinity],

Cell[BoxData[
    TagBox[\(3.7699111843077513`*^-10\ Mho\),
      UnitsWrapper]], "Output"]
}, Open  ]],

Cell["This value is in Mhos or Siemens", "Text"],

Cell[CellGroupData[{

Cell[BoxData[
    \(Rsoma = Convert[1/Gsoma, \ Ohm] // N\)], "Input"],

Cell[BoxData[
    TagBox[\(2.6525823848649225`*^9\ Ohm\),
      UnitsWrapper]], "Output"]
}, Open  ]],

Cell["This value is in ohms", "Text"],

Cell[CellGroupData[{

Cell[BoxData[
    \(Convert[Rsoma, \ Mega\ Ohm] // N\)], "Input"],

Cell[BoxData[
    TagBox[\(2652.5823848649225`\ \(Mega\ Ohm\)\),
      UnitsWrapper]], "Output"]
}, Open  ]],

Cell["Megohms (small diameter cell body)", "Text"],

Cell[TextData[{
  "\nNow define 3 different ",
  StyleBox["l ",
    FontFamily->"Symbol"]
}], "Text"],

Cell[CellGroupData[{

Cell[BoxData[
    \(LambdaParent = N[\@\(\(Rm\ DendDiaParent\)\/\(Ri\ 4\)\)]\)], "Input",
  PageWidth->Infinity],

Cell[BoxData[
    TagBox[\(0.11078234188139946`\ Centimeter\),
      UnitsWrapper]], "Output"]
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Cell[CellGroupData[{

Cell[BoxData[
    \(Convert[LambdaParent, \ Micron]\)], "Input"],

Cell[BoxData[
    TagBox[\(1107.8234188139945`\ Micron\),
      UnitsWrapper]], "Output"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
    \(LambdaD1 = N[\@\(\(Rm\ DendDiamD1\)\/\(Ri\ 4\)\)]\)], "Input"],

Cell[BoxData[
    TagBox[\(0.09594032236002469`\ Centimeter\),
      UnitsWrapper]], "Output"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
    \(Convert[LambdaD1, \ Micron]\)], "Input"],

Cell[BoxData[
    TagBox[\(959.4032236002469`\ Micron\),
      UnitsWrapper]], "Output"]
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Cell[CellGroupData[{

Cell[BoxData[
    \(LambdaD2 = N[\@\(\(Rm\ DendDiamD2\)\/\(Ri\ 4\)\)]\)], "Input"],

Cell[BoxData[
    TagBox[\(0.07833494518006402`\ Centimeter\),
      UnitsWrapper]], "Output"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
    \(Convert[LambdaD2, \ Micron]\)], "Input"],

Cell[BoxData[
    TagBox[\(783.3494518006402`\ Micron\),
      UnitsWrapper]], "Output"]
}, Open  ]],

Cell["\<\

Define an infinite length cylinder branch for each branch\
\>", "Text"],

Cell[CellGroupData[{

Cell[BoxData[
    \(GinfParent = 
      Convert[1\/2\ \[Pi]\ 1\/\@\(Rm\ Ri\)\ DendDiaParent\^\(3/2\), \ Mho] // 
        N\)], "Input",
  PageWidth->Infinity],

Cell[BoxData[
    TagBox[\(5.156044317067813`*^-9\ Mho\),
      UnitsWrapper]], "Output"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
    \(GinfD1 = 
      Convert[1\/2\ \[Pi]\ 1\/\@\(Rm\ Ri\)\ DendDiamD1\^\(3/2\), \ 
        Mho]\)], "Input"],

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    TagBox[\(3.348949021214334`*^-9\ Mho\),
      UnitsWrapper]], "Output"]
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Cell[CellGroupData[{

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      Convert[1\/2\ \[Pi]\ 1\/\@\(Rm\ Ri\)\ DendDiamD2\^\(3/2\), \ 
        Mho]\)], "Input"],

Cell[BoxData[
    TagBox[\(1.822936950348506`*^-9\ Mho\),
      UnitsWrapper]], "Output"]
}, Open  ]],

Cell["Need to define X1 values", "Text"],

Cell[CellGroupData[{

Cell[BoxData[{
    \(X1Parent = ParentLength/LambdaParent\), "\[IndentingNewLine]", 
    \(X1D1 = D1Length/LambdaD1\), "\[IndentingNewLine]", 
    \(X1D2 = D2Length/LambdaD2\)}], "Input"],

Cell[BoxData[
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Cell[BoxData[
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Cell[BoxData[
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}, Open  ]],

Cell["\<\

Define the B1 factor which determines the input resistance of a dendritic \
branch at its proximal origin\
\>", "Text"],

Cell[CellGroupData[{

Cell[BoxData[
    \(B1InD1 = 
      N[\(BjoD1In + Tanh[X1D1]\)\/\(1 + BjoD1In\ Tanh[X1D1]\)]\)], "Input",
  PageWidth->Infinity],

Cell[BoxData[
    \(0.14999529137047338`\)], "Output"]
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Cell[CellGroupData[{

Cell[BoxData[
    \(\(\(B1InD2 = 
      N[\(BjoD2In + Tanh[X1D2]\)\/\(1 + BjoD2In\ Tanh[X1D2]\)]\)\(\
\[IndentingNewLine]\)
    \)\)], "Input"],

Cell[BoxData[
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Cell["The input conductance of a dendritic branch at its origin", "Text"],

Cell[CellGroupData[{

Cell[BoxData[
    \(GrealD1In = N[GinfD1\ B1InD1]\)], "Input"],

Cell[BoxData[
    TagBox[\(5.023265842219057`*^-10\ Mho\),
      UnitsWrapper]], "Output"]
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Cell[CellGroupData[{

Cell[BoxData[{
    \(GrealD2In = N[GinfD2\ B1InD2]\), "\[IndentingNewLine]", 
    \(BjoParentIn = 
      N[\((\((GrealD1In + 
                GrealD2In)\)/\((GinfParent)\))\)]\), "\[IndentingNewLine]", 
    \(B1InParent = 
      N[\((\((BjoParentIn + Tanh[X1Parent])\)/\((1 + 
                BjoParentIn\ Tanh[X1Parent])\))\)]\), "\[IndentingNewLine]", 
    \(GrealParentIn = N[B1InParent\ GinfParent]\)}], "Input"],

Cell[BoxData[
    TagBox[\(3.156022937758674`*^-10\ Mho\),
      UnitsWrapper]], "Output"],

Cell[BoxData[
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Cell[BoxData[
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Cell[BoxData[
    TagBox[\(1.6073234706822149`*^-9\ Mho\),
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}, Open  ]],

Cell["\<\
The input conductance of the neuron adds the conductance of the dendrite and \
the soma\
\>", "Text"],

Cell[CellGroupData[{

Cell[BoxData[
    \(GNeuronAtSoma = N[Gsoma + GrealParentIn]\)], "Input"],

Cell[BoxData[
    TagBox[\(1.98431458911299`*^-9\ Mho\),
      UnitsWrapper]], "Output"]
}, Open  ]],

Cell["Note that this value is in siemens", "Text"],

Cell[CellGroupData[{

Cell[BoxData[
    \(RNeuronAtSoma = Convert[1/GNeuronAtSoma, \ Ohm]\)], "Input"],

Cell[BoxData[
    TagBox[\(5.039523498373364`*^8\ Ohm\),
      UnitsWrapper]], "Output"]
}, Open  ]],

Cell["\<\
This is the input resistance in ohms....so convert to megohms\
\>", "Text"],

Cell[CellGroupData[{

Cell[BoxData[
    \(Convert[RNeuronAtSoma, \ Mega\ Ohm]\)], "Input"],

Cell[BoxData[
    TagBox[\(503.9523498373364`\ \(Mega\ Ohm\)\),
      UnitsWrapper]], "Output"]
}, Open  ]],

Cell["Value in Megohms (compare to soma alone)", "Text"],

Cell["\<\
Now we can move out towards periphery. First convert soma into an extension \
of parent dendrite\
\>", "Text"],

Cell[CellGroupData[{

Cell[BoxData[
    \(BjoParentOut = Gsoma/GinfParent\)], "Input"],

Cell[BoxData[
    \(0.07311634564172363`\)], "Output"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
    \(B1ParentOut = \(BjoParentOut + Tanh[X1Parent]\)\/\(1 + BjoParentOut\ \
Tanh[X1Parent]\)\)], "Input",
  PageWidth->Infinity],

Cell[BoxData[
    \(0.23145646412011261`\)], "Output"]
}, Open  ]],

Cell["\<\
Now the input conductance of the cell measured at the distal end of the \
dendrite using GrealDIn values calculated on way in\
\>", "Text"],

Cell[CellGroupData[{

Cell[BoxData[
    \(GNeuronAtDendrite = 
      GinfParent\ B1ParentOut + GrealD1In + GrealD2In\)], "Input"],

Cell[BoxData[
    TagBox[\(2.01132866447289`*^-9\ Mho\),
      UnitsWrapper]], "Output"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
    \(N[GNeuronAtDendrite]\)], "Input"],

Cell[BoxData[
    TagBox[\(2.01132866447289`*^-9\ Mho\),
      UnitsWrapper]], "Output"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
    \(\(\(RNeuronAtDendrite = 
      Convert[1/GNeuronAtDendrite, \ Ohm]\)\(\[IndentingNewLine]\)
    \)\)], "Input"],

Cell[BoxData[
    TagBox[\(4.9718378585434747`*^8\ Ohm\),
      UnitsWrapper]], "Output"]
}, Open  ]],

Cell["Convert to Mohms", "Text"],

Cell[CellGroupData[{

Cell[BoxData[
    \(Convert[RNeuronAtDendrite, \ Mega\ Ohm]\)], "Input"],

Cell[BoxData[
    TagBox[\(497.18378585434743`\ \(Mega\ Ohm\)\),
      UnitsWrapper]], "Output"]
}, Open  ]],

Cell["\<\
The Input Resistance of the cell at the end of the primary or parent dendrite
Now go to the end of each daughter branch of the primary or parent (D1 and \
D2); first for D1\
\>", "Text"],

Cell[CellGroupData[{

Cell[BoxData[
    \(BjoD1Out = \((GNeuronAtDendrite - GrealD1In)\)/GinfD1\)], "Input"],

Cell[BoxData[
    \(0.45058974343652974`\)], "Output"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
    \(B1OutD1 = \((BjoD1Out + \ Tanh[X1D1])\)/\((1 + 
            BjoD1Out\ Tanh[X1D1])\)\)], "Input"],

Cell[BoxData[
    \(0.5625634315332293`\)], "Output"]
}, Open  ]],

Cell["This is the conductance at the distal end of D1", "Text"],

Cell[CellGroupData[{

Cell[BoxData[
    \(GrealD1Out = B1OutD1\ GinfD1\)], "Input"],

Cell[BoxData[
    TagBox[\(1.8839962534041855`*^-9\ Mho\),
      UnitsWrapper]], "Output"]
}, Open  ]],

Cell["This is the input resistance at the end of D1", "Text"],

Cell[CellGroupData[{

Cell[BoxData[
    \(RD1Out = Convert[1/GrealD1Out, \ Ohm]\)], "Input"],

Cell[BoxData[
    TagBox[\(5.307866181756486`*^8\ Ohm\),
      UnitsWrapper]], "Output"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
    \(Convert[RD1Out, \ Mega\ Ohm]\)], "Input"],

Cell[BoxData[
    TagBox[\(530.7866181756486`\ \(Mega\ Ohm\)\),
      UnitsWrapper]], "Output"]
}, Open  ]],

Cell["Now for D2", "Text"],

Cell[CellGroupData[{

Cell[BoxData[
    \(BjoD2Out = \((GNeuronAtDendrite - GrealD2In)\)/GinfD2\)], "Input"],

Cell[BoxData[
    \(0.9302166870734814`\)], "Output"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
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      N[\((BjoD2Out + Tanh[X1D2])\)/\((1 + 
              BjoD2Out\ Tanh[X1D2])\)]\)], "Input"],

Cell[BoxData[
    \(0.9503018959743909`\)], "Output"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
    \(GrealD2Out = B1OutD2\ GinfD2\)], "Input"],

Cell[BoxData[
    TagBox[\(1.7323404401579594`*^-9\ Mho\),
      UnitsWrapper]], "Output"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
    \(RD2Out = Convert[1/GrealD2Out, \ Ohm]\)], "Input"],

Cell[BoxData[
    TagBox[\(5.772537411346337`*^8\ Ohm\),
      UnitsWrapper]], "Output"]
}, Open  ]],

Cell["This value is in ohms", "Text"],

Cell[CellGroupData[{

Cell[BoxData[
    \(Convert[RD2Out, Mega\ Ohm]\)], "Input"],

Cell[BoxData[
    TagBox[\(577.2537411346336`\ \(Mega\ Ohm\)\),
      UnitsWrapper]], "Output"]
}, Open  ]],

Cell["Value in Mohms", "Text"],

Cell["\<\
How about the input resistance of the cell measured in the middle of the \
parent or primary dendrite?\
\>", "Text",
  FontSize->14],

Cell[CellGroupData[{

Cell[BoxData[
    \(X1Midway = X1Parent/2\)], "Input"],

Cell[BoxData[
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Cell[CellGroupData[{

Cell[BoxData[
    \(B1MidwayIn = \(BjoParentIn + Tanh[X1Midway]\)\/\(1 + BjoParentIn\ \
Tanh[X1Midway]\)\)], "Input",
  PageWidth->Infinity],

Cell[BoxData[
    \(0.23665388440872245`\)], "Output"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
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Cell[BoxData[
    TagBox[\(1.2201979158176166`*^-9\ Mho\),
      UnitsWrapper]], "Output"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
    \(B1MidwayOut = \(BjoParentOut + Tanh[X1Midway]\)\/\(1 + BjoParentOut\ \
Tanh[X1Midway]\)\)], "Input",
  PageWidth->Infinity],

Cell[BoxData[
    \(0.15327004502205854`\)], "Output"]
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Cell[CellGroupData[{

Cell[BoxData[
    \(GNeuronMidwayOut = B1MidwayOut\ GinfParent\)], "Input"],

Cell[BoxData[
    TagBox[\(7.902671446127128`*^-10\ Mho\),
      UnitsWrapper]], "Output"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
    \(GNeuronMidway = GNeuronMidwayIn + GNeuronMidwayOut\)], "Input"],

Cell[BoxData[
    TagBox[\(2.0104650604303294`*^-9\ Mho\),
      UnitsWrapper]], "Output"]
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Cell[CellGroupData[{

Cell[BoxData[
    \(RNeuronMidway = Convert[1/GNeuronMidway, \ Ohm]\)], "Input"],

Cell[BoxData[
    TagBox[\(4.973973533198111`*^8\ Ohm\),
      UnitsWrapper]], "Output"]
}, Open  ]],

Cell["This value is on ohms, convert to Mohms", "Text"],

Cell[CellGroupData[{

Cell[BoxData[
    \(Convert[RNeuronMidway, \ Mega\ Ohm]\)], "Input"],

Cell[BoxData[
    TagBox[\(497.3973533198111`\ \(Mega\ Ohm\)\),
      UnitsWrapper]], "Output"]
}, Open  ]],

Cell["\<\

What about current flowing from soma towards the peripher. For a three \
branched cell, you have to consider first the decay from the soma into the \
end of the parent dendrite, then how current will spread from the proximal \
end of each dendrite into the distal \"sealed\" end.  \
\>", "Text"],

Cell[BoxData[{
    \(X =. \), "\[IndentingNewLine]", 
    \(X1 =. \), "\[IndentingNewLine]", 
    \(Vo =. \), "\[IndentingNewLine]", 
    \(B1 =. \)}], "Input"],

Cell[CellGroupData[{

Cell[BoxData[
    \(Vin = \(Vo\ \((Cosh[X1 - X] + B1\ Sinh[X1 - X])\)\)\/\(Cosh[X1] + B1\ \
Sinh[X1]\)\)], "Input",
  PageWidth->Infinity],

Cell[BoxData[
    \(\(Vo\ \((Cosh[X - X1] - B1\ Sinh[X - X1])\)\)\/\(Cosh[X1] + B1\ \
Sinh[X1]\)\)], "Output"]
}, Open  ]],

Cell["\<\
Let's calculate how voltage would decay from the soma to the end of each \
dendrite\
\>", "Text"],

Cell[CellGroupData[{

Cell[BoxData[{
    \(B1 = BjoParentIn\  (*\ 
      This\ is\ what\ you\ calculated\ on\ your\ way\ in\ from\ the\ distal\ \
ends\ of\ the\ two\ daughters\ *) \), "\[IndentingNewLine]", 
    \(X1 = X1Parent\), "\[IndentingNewLine]", 
    \(Vo = 100. \)}], "Input"],

Cell[BoxData[
    \(0.15863495883660683`\)], "Output"],

Cell[BoxData[
    \(0.1624807680927192`\)], "Output"],

Cell[BoxData[
    \(100.`\)], "Output"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
    \(ya = 
      Plot[Vin, {X, 0, X1}, PlotRange \[Rule] {{0, 0.4}, {0, 100}}, \ 
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(*******************************************************************
End of Mathematica Notebook file.
*******************************************************************)