Using Strahler`s analysis to reduce realistic models (Marasco et al, 2013)

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Accession:149000
Building on our previous work (Marasco et al., (2012)), we present a general reduction method based on Strahler's analysis of neuron morphologies. We show that, without any fitting or tuning procedures, it is possible to map any morphologically and biophysically accurate neuron model into an equivalent reduced version. Using this method for Purkinje cells, we demonstrate how run times can be reduced up to 200-fold, while accurately taking into account the effects of arbitrarily located and activated synaptic inputs.
Reference:
1 . Marasco A, Limongiello A, Migliore M (2013) Using Strahler's analysis to reduce up to 200-fold the run time of realistic neuron models. Sci Rep 3:2934 [PubMed]
Model Information (Click on a link to find other models with that property)
Model Type: Neuron or other electrically excitable cell; Dendrite;
Brain Region(s)/Organism: Hippocampus; Cerebellum;
Cell Type(s): Hippocampus CA1 pyramidal GLU cell; Cerebellum Purkinje GABA cell;
Channel(s): I Na,t; I T low threshold; I K; I Calcium; Ca pump;
Gap Junctions:
Receptor(s): AMPA;
Gene(s):
Transmitter(s): Glutamate;
Simulation Environment: NEURON;
Model Concept(s): Activity Patterns; Active Dendrites; Influence of Dendritic Geometry; Detailed Neuronal Models; Action Potentials; Synaptic Integration;
Implementer(s): Limongiello, Alessandro [alessandro.limongiello at unina.it];
Search NeuronDB for information about:  Hippocampus CA1 pyramidal GLU cell; Cerebellum Purkinje GABA cell; AMPA; I Na,t; I T low threshold; I K; I Calcium; Ca pump; Glutamate;
/
PurkReductionOnLine
morphologies
readme.txt
CaE.mod *
CalciumP.mod *
CaP.mod *
CaP2.mod *
CaT.mod *
K2.mod *
K22.mod *
K23.mod *
KA.mod *
KC.mod *
KC2.mod *
KC3.mod *
KD.mod *
Kdr.mod *
Kh.mod *
Khh.mod *
KM.mod *
Leak.mod *
NaF.mod *
NaP.mod *
pj.mod
clusterisingMethods.hoc
fixnseg.hoc
mergingMethods.hoc
mosinit.hoc
ranstream.hoc *
RedPurk.hoc
stimulation1.hoc
useful&InitProc.hoc
                            
/*---------------------------------------------------------------------

   Written by Alessandro Limongiello
   University "Federico II" of Naples, 2012-2013

-----------------------------------------------------------------------*/

/*---------------------------------------------
                   USEFUL PROCEDURES
  ---------------------------------------------*/

func max(){
    if ($1 > $2){ 
       return $1
    } else {
      return $2
    }
}

/*---------------------------------------------
         Strahler Numbers Computation
  ---------------------------------------------*/	

// Useful variables
objectvar secNameList0
objectvar secaddress0	// section address	
objectvar paraddress0	// parentsection address
objectvar strahlerNumbersVect            // Vector for Strahler Numbers
objectvar stimulatedGroupVect            // Vector for Stimulated Group
objref sRef
objectvar childrenSecListVector	// a List of Vector for children of each section
objectvar parSecVect    // parent for a section

strdef str,strFile

func strahlerNumbersFunc(){ local sizeVect,ii,sN,egualBool localobj vectApp
     sizeVect = childrenSecListVector.o($1).size()
     if (sizeVect==0){
        strahlerNumbersVect.set($1,1)  
        return 1}
     
     vectApp = new Vector(sizeVect,0)
     

     egualBool = 1
     for ii = 0,sizeVect-1{
         sN = strahlerNumbersFunc(childrenSecListVector.o($1).x(ii))
         if (ii>0 && vectApp.contains(sN)==0) egualBool=0
         vectApp.set(ii,sN)
     }
     
     
     if (egualBool==1){ 
        strahlerNumbersVect.set($1,vectApp.x(0)+1) 
        return vectApp.x(0)+1
     }
     strahlerNumbersVect.set($1,vectApp.max()) 
     return vectApp.max()

}


proc strahlerNumbersComputation(){local sec,sec1,sec2,ii

    stoprun = 1
    if (optPrint==1) print "Strahler Numbers Computation"

    if (firstInit ==1){
        forall delete_section()                       
        readingFile() 
        xopen(strFile)		// read geometry file
        firstInit == 0
    }else{xopen(strFile)}

    {NSEC=0  forall if (!issection("eqSection.*")){NSEC=NSEC+1}}

	secNameList0=new List()
    strahlerNumbersVect=new Vector(NSEC,0)		    //set/reset
    stimulatedGroupVect=new Vector(NSEC,0)		    //set/reset
    secaddress0=new Vector(NSEC,0)		        //set/reset
	paraddress0=new Vector(NSEC,0)		        //set/reset
    childrenSecListVector = new List() 
   	parSecVect = new Vector(NSEC,0)		//set/reset
	
	sec = 0
	forall if (!issection("eqSection.*")){
        secNameList0.append(new String(secname()))
        secaddress0.set(sec, this_section())
        paraddress0.set(sec, parent_section(0))
        childrenSecListVector.append(new Vector())
        sec = sec+1
    }	
	
	for sec1=1,NSEC-1 {
		for sec2=0,NSEC-1 {
			if (secaddress0.x(sec2)==paraddress0.x(sec1)) {
               parSecVect.set(sec1,sec2)
               childrenSecListVector.o(sec2).append(sec1)            
            }
		}
	}    
    
    sNroot = strahlerNumbersFunc(0)
    
	if (optPrint){
        for sec1=0,100 /*NSEC-1*/{
            sizeVect = childrenSecListVector.o(sec1).size()
    		if (sizeVect==0){
               print "(sec,secname,sNum): ", sec1,secNameList0.o(sec1).s,"Leaf",strahlerNumbersVect.x(sec1)
            }else{
               printf("\nsec,secname,sNum,children): (%d,%s,%d", sec1,secNameList0.o(sec1).s,strahlerNumbersVect.x(sec1))
               for ii=0,sizeVect-1 printf(",%d",childrenSecListVector.o(sec1).x(ii))   
               printf("\n")
            }          
    	}	
     }
	
}

objref vbox00
objectvar sh00
vbox00 = new VBox() 

proc coloringStrahler(){local sec
    
    vbox00 = new VBox()
    
    vbox00.intercept(1)
    sh00 = new Shape()
    vbox00.intercept(0)
    vbox00.map("coloringStrahler", 200, 430, 300, 250)

    sec = 0
    NumSmooth = 0
    NumSpiny = 0
    sNorder1 = 0
    sNorder2 = 0
    sNorder3 = 0
    sNorder4 = 0
    sNorder5 = 0
    sNorder6 = 0
    sNorder7 = 0
    sNorderMajor7 = 0
    forall if (!issection("eqSection.*")){
           if (strahlerNumbersVect.x(sec)==1) {NumSpiny = NumSpiny+1 sNorder1 = sNorder1+1 sh00.color(2) 
           }else if (strahlerNumbersVect.x(sec)==2) {NumSpiny = NumSpiny+1 sNorder2 = sNorder2+1 sh00.color(3)
           }else if (strahlerNumbersVect.x(sec)==3) {NumSpiny = NumSpiny+1 sNorder3 = sNorder3+1 sh00.color(4)
           }else if (strahlerNumbersVect.x(sec)==4) {NumSmooth = NumSmooth+1 sNorder4 = sNorder4+1 sh00.color(5)
           }else if (strahlerNumbersVect.x(sec)==5) {NumSmooth = NumSmooth+1 sNorder5 = sNorder5+1 sh00.color(6)
           }else if (strahlerNumbersVect.x(sec)==6) {NumSmooth = NumSmooth+1 sNorder6 = sNorder6+1 sh00.color(7)
           }else if (strahlerNumbersVect.x(sec)==7) {NumSmooth = NumSmooth+1 sNorder7 = sNorder7+1 sh00.color(8)
           }else if (strahlerNumbersVect.x(sec)>7) {NumSmooth = NumSmooth+1 sNorderMajor7 = sNorderMajor7+1 sh00.color(9)}
           sec=sec+1
    }
    if (optPrint) print "(NumSmooth,NumSpiny,sNorder1,sNorder2,sNorder3,sNorder4,sNorder5,sNorder6,sNorder7,sNorderMajor7): ",\
          NumSmooth,NumSpiny,sNorder1,sNorder2,sNorder3,sNorder4,sNorder5,sNorder6,sNorder7,sNorderMajor7

    sh00.show(0)

}


objref vbox01
objectvar sh01
vbox01 = new VBox() 
objectvar stimulatedGroup1Vect            // Vector for Stimulated Group

proc coloringStimulatedClusters(){local sec
    
    vbox01 = new VBox()
    
    vbox01.intercept(1)
    sh01 = new Shape()
    vbox01.intercept(0)
    vbox01.map("coloringStimulatedClusters", 0, 130, 270, 250)


    sec = 0
    forall if (!issection("eqSection.*")){
           if (stimulatedGroup1Vect.x(sec)==1) {sh01.color(2) 
           }else if (stimulatedGroup1Vect.x(sec)==2) {sh01.color(3)
           }else if (stimulatedGroup1Vect.x(sec)==3) {sh01.color(4)
           }else if (stimulatedGroup1Vect.x(sec)==4) {sh01.color(5)
           }else if (stimulatedGroup1Vect.x(sec)==5) {sh01.color(6)
           }else if (stimulatedGroup1Vect.x(sec)==6) {sh01.color(7)
           }else if (stimulatedGroup1Vect.x(sec)==7) {sh01.color(8)
           }else if (stimulatedGroup1Vect.x(sec)==8) {sh01.color(9)
           }else if (stimulatedGroup1Vect.x(sec)==9) {sh01.color(11)
           }else if (stimulatedGroup1Vect.x(sec)==10) {sh01.color(12)
           }else if (stimulatedGroup1Vect.x(sec)==11) {sh01.color(13)
           }else if (stimulatedGroup1Vect.x(sec)==12) {sh01.color(14)
           }else if (stimulatedGroup1Vect.x(sec)==13) {sh01.color(15)
           }else if (stimulatedGroup1Vect.x(sec)==14) {sh01.color(16)
           }else if (stimulatedGroup1Vect.x(sec)==15) {sh01.color(17)
           }else if (stimulatedGroup1Vect.x(sec)==16) {sh01.color(18)
           }else if (stimulatedGroup1Vect.x(sec)>16) {sh01.color(19)}
           sec=sec+1
    }

    sh01.show(0)

}

indexStimulatedCluster = 1
objref vbox02
objectvar sh02
vbox02 = new VBox() 

proc coloringSingleStimulatedCluster(){local nCluster,sec,col,i
    
    vbox02 = new VBox()
    
    vbox02.intercept(1)
    sh02 = new Shape()
    vbox02.intercept(0)
    vbox02.map("coloringSingleStimulatedCluster", 300, 230, 500, 450)


    sec = 0
    //colNum = indexStimulatedCluster+1
    forall if (!issection("eqSection.*")){
           if (stimulatedGroup1Vect.x(sec)==indexStimulatedCluster) {sh02.color(2)}
           sec=sec+1
    }

    sh02.show(0)

}



/*---------------------------------------------
            Subroutine for setting
  ---------------------------------------------*/	


objectvar factGmaxSynMorphVect

factGmaxSynMorphVect = new Vector(100,1.0)		//set/reset


objref fIn
strdef directory

proc readingFile(){

    fIn = new File()
    fIn.chooser("", "Reading Morphologic Model", "", "Accept", "", ".\\morphologies")
    if (fIn.chooser()) {
       forall delete_section()
       firstInit = 0
       fIn.getname(strFile)
       sprint(directory,"%s",fIn.dir())
    }else firstInit = 1

}


proc PurkinjeSetting(){local sec
     
     vbox00.unmap()

     if (optPrint==1) print "AlePurkinjeFunctional Setting"
     forall delete_section() 
     xopen(strFile)		// read geometry file
     firstInit = 0
     
     
     LENGTHMERGINGserialMETHOD = -1
     LENGTHMERGINGparallelMETHOD = 2
     DIAMMERGINGserialMETHOD = 0
     DIAMMERGINGparallelMETHOD = 0
     RESCALEMOD = 0
     CUTTINGFACT = 100 //5
     PRESERVINGsomaMETHOD = 0
//     PRESERVINGMETHOD = 0 //0 
//     RaMERGINGMETHOD=1
//     SURFFACT_PARTIAL_TOTAL = 1
//     SURFFACT_PARTIAL_METHOD=2
     withLocation = 1 

     strahlerNumbersComputation()
      
	 sec = 0
	 forall if (!issection("eqSection.*")){
        if (issection("soma.*")){ 
           cm = cmSoma  
           Ra = Ra0 
           insert Leak gl_Leak = gl_LeakSoma el_Leak = el_Leak0  
        }else if (strahlerNumbersVect.x(sec)>3){
           cm= cmSmoothSec  
           Ra = Ra0 
           insert Leak gl_Leak = gl_LeakSmoothSec el_Leak = el_Leak0
        }else if (strahlerNumbersVect.x(sec)<=3){
           cm = cmSpinySect  
           Ra = Ra0 
           insert Leak gl_Leak = gl_LeakSpinySect el_Leak = el_Leak0
        }
        
        sec = sec+1
     }
     	
     geom_nseg()
     totOr=0
     forall {totOr=totOr+nseg}   
     if(optPrint) print "totSegIni: ", totOr 
     
     //coloringStrahler()

}



/*---------------------------------------------
                   VARIABLE DEFINITION
  ---------------------------------------------*/
	
objectvar order			// number of sections between each section and soma 
objectvar parsec        // parentsection id for each section

// section data input
objectvar secri			
objectvar secpathri		
objectvar secpathri0
objectvar secpathImp		
objectvar secpathImp0
objectvar secL			
objectvar secRa			
objectvar secCm	
objectvar secdiam
objectvar secSurf
//objectvar secApicalBasal
// section data during the merging		
objectvar mrgL		
objectvar mrgdiam	
objectvar mrgdiamSer
objectvar mrgdiamPar
objectvar mrgri	
objectvar mrgri2
objectvar mrgSurf
// equivalent section data after the merging		
objectvar eqL		
objectvar eqdiam	
objectvar eqdiamSer
objectvar eqdiamPar
objectvar eqRa


objectvar surfFactVect
objectvar eqri2
objectvar eqsecpathri
objectvar eqsecpathri0
objectvar eqsecpathImp
objectvar eqsecpathImp0
objectvar orMinpathri
objectvar orMaxpathri
//objectvar eqri	
objectvar eqSurf
objectvar orSurf	
objectvar orSurf1
objectvar orSurf2
objectvar surfFact
objectvar surfFactRmCm

// cluster data
objectvar clusterParent    // link between each cluster and its parent
objectvar clusterParentPos // position of each cluster as regards its parent
objectvar clusterList      // List of clusters
objectvar newClusterList   // List of clusters after merging Y_group_sections
objectvar clusterMarker    // Marker to identify each section belonging to its cluster
objectvar somaVector       // Vector of sections belonging to the soma
//objectvar axonVector       // Vector of sections belonging to the axon


	
	
/*---------------------------------------------
                   INIT PROCEDURE
  ---------------------------------------------*/	
	
	
proc initDataStruct(){

	order = new Vector(NSEC,0)		//set/reset
	parsec = new Vector(NSEC,0)		//set/reset

	secri = new Vector(NSEC,0)		//set/reset
	secpathri = new Vector(NSEC,0.0)		//set/reset
	secpathri0 = new Vector(NSEC,0.0)		//set/reset
	secpathImp = new Vector(NSEC,0.0)		//set/reset
	secpathImp0 = new Vector(NSEC,0.0)		//set/reset	
	secL = new Vector(NSEC,0)   		//set/reset
	secRa = new Vector(NSEC,0)   		//set/reset
	secCm = new Vector(NSEC,0)		//set/reset
	secdiam = new Vector(NSEC,0)		//set/reset
	secSurf = new Vector(NSEC,0)		//set/reset
//	secApicalBasal = new Vector(NSEC,0)		//set/reset if 1=Apical elseif 0=Basal
	
	mrgL = new Vector(NSEC,0)   		//set/reset
	mrgdiam = new Vector(NSEC,0)		//set/reset
	mrgdiamSer = new Vector(NSEC,0)		//set/reset
	mrgdiamPar = new Vector(NSEC,0)		//set/reset	
	mrgri = new Vector(NSEC,0)		//set/reset
	mrgri2 = new Vector(NSEC,0)		//set/reset
	mrgSurf = new Vector(NSEC,0)		//set/reset
	
    clusterList = new List()	
	newClusterList = new List()
	clusterMarker = new Vector(NSEC,-1)		//set/reset
	somaVector = new Vector(0,0)
    
//    axonVector = new Vector(0,0)	

}


/*---------------------------------------------
                   CELL ANALYSIS
  ---------------------------------------------*/	

// Useful variables
objectvar secNameList
objectvar secName
secNameList=new List()
objectvar secaddress	// section address	
objectvar paraddress	// parentsection address
// data to compute path from each section to the soma
objectvar rvp			
objectvar slsoma		
objectvar slroot


proc cellPurkAnalysis(){local sec,sec1,sec2, x

	strdef sname

	{NSEC=0  forall if (!issection("eqSection.*")){NSEC=NSEC+1}}		
    initDataStruct()
	secaddress=new Vector(NSEC,0)		//set/reset
	paraddress=new Vector(NSEC,0)		//set/reset
            
	sec = 0
	forall if (!issection("eqSection.*")){
        sname =secname() secName = new String(sname) secNameList.append(secName)
        secaddress.set(sec, this_section())
        paraddress.set(sec, parent_section(0))
        secRa.set(sec,Ra)
        secL.set(sec,abs(L))
        secCm.set(sec,cm) 
        secdiam.set(sec,diam)   
        mrgL.set(sec,abs(L))
//        if (y3d(1)>=2) secApicalBasal.set(sec,1)
        if (issection("soma.*")){
              for(x) if(x>0) {
                     secSurf.set(sec,secSurf.x(sec)+area(x))
                     secri.set(sec, secri.x(sec)+ri(x))
              }
              //mrgdiam.set(sec,aaa/PI/L)
              //mrgri.set(sec,secri.x(0))
              //print sec,totSomaArea,mrgL.x(sec),mrgdiam.x(sec),secri.x(sec)
              somaVector.append(sec)
        } else {
    		  {slsoma=new SectionList() {rvp=new RangeVarPlot("v")}
    		   {soma  rvp.begin(.5)}  rvp.end(.5)  rvp.list(slsoma)}
    		  {slroot=new SectionList() {rvp=new RangeVarPlot("v")}
    		   {ss=0 forsec slsoma{ {if(ss==1) rvp.begin(.5)}  ss=ss+1}}
    		   rvp.end(.5)  rvp.list(slroot)}
    	  	  forsec slroot {order.set(sec, order.x(sec)+1) /*print sec,order.x(sec) psection()*/}
              for(x) if(x>0) {
                     secSurf.set(sec,secSurf.x(sec)+area(x))
                     secri.set(sec, secri.x(sec)+ri(x))
                     /*print sec,secri.x(sec)*/
              }
    		  if(secri.x(sec)>9999) secri.set(sec, -9999)
    		  nsecPath = 0
              forsec slroot {   nsecPath=nsecPath+1 
                                for(x) {if(x>0){secpathri.set(sec,secpathri.x(sec)+ri(x))}}
                            }
              nsecPath1 = 0
              forsec slroot {
                     nsecPath1=nsecPath1+1 
                     for(x) {if(x>0 && nsecPath1<nsecPath) secpathri0.set(sec,secpathri0.x(sec)+ri(x))}
              }

              if (PRESERVINGMETHOD==0){             //PRESERVINGMETHOD = 0 by Destexhe
                     mrgdiamSer.set(sec,secdiam.x(sec))
                     mrgdiamPar.set(sec,secdiam.x(sec)^2)
                     //print mrgdiamPar.x(sec)
                     mrgdiam.set(sec,sqrt(secRa.x(sec)*secL.x(sec)*4/secri.x(sec)/100/PI))                     
              }else if (PRESERVINGMETHOD==1){
                     mrgdiam.set(sec,secSurf.x(sec)/secL.x(sec)/PI)
              }
              mrgri.set(sec,secri.x(sec))		  
              mrgri2.set(sec,secri.x(sec))	
              mrgSurf.set(sec, secSurf.x(sec))
        }
    sec=sec+1}	
	for sec1=1,NSEC-1 {
		for sec2=0,NSEC-1 {
			if(secaddress.x(sec2)==paraddress.x(sec1)) {parsec.set(sec1,sec2)}
		}
	}
}





/*---------------------------------------------
                   CLUSTERISING PROCEDURES
  ---------------------------------------------*/
xopen("clusterisingMethods.hoc")

/*---------------------------------------------
                   MERGING PROCEDURES
  ---------------------------------------------*/
xopen("mergingMethods.hoc")

/*---------------------------------------------
                   REDUCTION PROCEDURES
  ---------------------------------------------*/


// Useful variables
objectvar searchAvailable
objectvar mergeAvailable



// seaching the next Y_group_sections / output:  {secA,secB,secP} 
proc getNextY(){local ii, nsect, idA, idB, sec   //input: Vector of id sections

    // seaching the last available section
	secA=0			
	nsect = $o1.size()-1
	idA = 0 
	for ii=0,nsect {
        if(searchAvailable.x(ii)){
        	sec = $o1.x(ii)	
            if(order.x(sec)>=order.x(secA)) {secA=sec idA = ii}
        }
    }
    
    // seaching the brother section of secA
	secB=0
	idB = 0
	for ii=0,nsect {
        if(searchAvailable.x(ii)){
        	sec = $o1.x(ii)		
            if(parsec.x(sec)==parsec.x(secA)&&sec!=secA) {secB=sec idB = ii}
        }
    }

    // seaching the parent section of secA
	secP=0
	if ($o1.contains(parsec.x(secA))) secP=parsec.x(secA)	

    // marking unavailable sections already visited	
	searchAvailable.set(idA,0)
	if (secB!=0) searchAvailable.set(idB,0)
	
    if (secA!=0){
    	if (secP==0){ 
           mergeAvailable.set(idA,1)
    	   if (secB!=0) mergeAvailable.set(idB,1)
        }
    }
}


// Useful proc used in PurkReduction() after each call of getNextY() and before each call of merge2() or mergeY()
//        input:   {secA,secB,secP}
//        output:  {AmRa,AmL,Amdiam,Amri,BmRa,BmL,Bmdiam,Bmri,PmRa,PmL,Pmdiam,Pmri}
proc shortnms(){
	{AmRa=0 AmL=0 Amdiam=0 Amri=0 Amsurf=0 AmdiamSer=0 AmdiamPar=0}
	{BmRa=0 BmL=0 Bmdiam=0 Bmri=0 Bmsurf=0 BmdiamSer=0 BmdiamPar=0}
	{PmRa=0 PmL=0 Pmdiam=0 Pmri=0 Pmsurf=0 PmdiamSer=0 PmdiamPar=0}
	if(secA>0) {
		AmRa=secRa.x(secA)
		AmL=mrgL.x(secA)  
		Amdiam=mrgdiam.x(secA)
		AmdiamSer=mrgdiamSer.x(secA)
        AmdiamPar=mrgdiamPar.x(secA)
		Amri=(AmRa*AmL)/(PI*((Amdiam^2)/4)*100)
		Amsurf = AmL*Amdiam*PI
	}
	if(secB>0) {
		BmRa=secRa.x(secB)
		BmL=mrgL.x(secB)  
		Bmdiam=mrgdiam.x(secB) 
		BmdiamSer=mrgdiamSer.x(secB)
        BmdiamPar=mrgdiamPar.x(secB)
		Bmri=(BmRa*BmL)/(PI*((Bmdiam^2)/4)*100)
		Bmsurf = BmL*Bmdiam*PI
	}
	if(secP>0) {
		PmRa=secRa.x(secP)
		PmL=mrgL.x(secP)  
		Pmdiam=mrgdiam.x(secP) 
		PmdiamSer=mrgdiamSer.x(secP)
        PmdiamPar=mrgdiamPar.x(secP)
		Pmri=(PmRa*PmL)/(PI*((Pmdiam^2)/4)*100)
		Pmsurf = PmL*Pmdiam*PI
	}
    
	if(RESCALEMOD==1){
	  if(secA>0 && secB>0){
	    if(AmL>BmL){
	      {BmL=AmL  mrgL.set(secB,BmL)}
          if (PRESERVINGMETHOD==0){             //PRESERVINGMETHOD = 0 by Destexhe
               Bmdiam=sqrt((BmRa*BmL*4)/(Bmri*PI*100))
        	   BmdiamSer=Bmdiam
               BmdiamPar=Bmdiam
          }else if (PRESERVINGMETHOD==1){
               Bmdiam=Bmsurf/BmL/PI } 
          mrgdiam.set(secB,Bmdiam) 
          {Bmsurf = BmL*Bmdiam*PI}
	    }else if(BmL>AmL){
	      {AmL=BmL  mrgL.set(secA,AmL)}
	      if (PRESERVINGMETHOD==0){             //PRESERVINGMETHOD = 0 by Destexhe
               Amdiam=sqrt((AmRa*AmL*4)/(Amri*PI*100))
        	   AmdiamSer=Amdiam
               AmdiamPar=Amdiam               
          }else if (PRESERVINGMETHOD==1){
               Amdiam=Amsurf/AmL/PI } 
          mrgdiam.set(secA,Amdiam)
	      {Amsurf = AmL*Amdiam*PI}
	    }
	  }
	}
}


// merging procedure of the section secA with its parent secP
proc mergingParentSec(){
    mergingSerialMethod(AmRa,PmRa,AmL,PmL,Amdiam,Pmdiam,Amri,Pmri,Amsurf,Pmsurf,AmdiamSer,PmdiamSer,AmdiamPar,PmdiamPar)
    mrgL.set(secP, newL)
	mrgri.set(secP, newri)
	mrgri2.set(secP, Amri+Pmri)
	mrgSurf.set(secP, max(Amsurf,Pmsurf))
	mrgdiam.set(secP, newdiam) 
	mrgdiamSer.set(secP, newdiamSer) 
	mrgdiamPar.set(secP, newdiamPar) 
	//print "newdiamPar",newdiamPar,"secP",secNameList.o(secP).s
}


// merging procedure of Y_group_sections
proc mergingYSec(){local AmL2BmL,BmL2AmL
	AmL2BmL=AmL/BmL
	BmL2AmL=BmL/AmL
	if(AmL2BmL>=CUTTINGFACT){mergingSerialMethod(AmRa,PmRa,AmL,PmL,Amdiam,Pmdiam,Amri,Pmri,Amsurf,Pmsurf,AmdiamSer,PmdiamSer,AmdiamPar,PmdiamPar)}
    if(BmL2AmL>=CUTTINGFACT){mergingSerialMethod(BmRa,PmRa,BmL,PmL,Bmdiam,Pmdiam,Bmri,Pmri,Bmsurf,Pmsurf,BmdiamSer,PmdiamSer,BmdiamPar,PmdiamPar)} 
	if(AmL2BmL<CUTTINGFACT && BmL2AmL<CUTTINGFACT){
       mergingYMethod(AmRa,BmRa,PmRa,AmL,BmL,PmL,Amdiam,Bmdiam,Pmdiam,Amri,Bmri,Pmri,AmdiamSer,BmdiamSer,PmdiamSer,AmdiamPar,BmdiamPar,PmdiamPar)}
	
    mrgL.set(secP, newL)
	mrgri.set(secP, newri)
	mrgri2.set(secP, newri2)
	mrgSurf.set(secP, newSurf)
	mrgdiam.set(secP, newdiam)  
	mrgdiamSer.set(secP, newdiamSer) 
	mrgdiamPar.set(secP, newdiamPar) 	
    //print "newdiamPar da Y",newdiamPar,"secP",secNameList.o(secP).s	
}

// Useful variables
objectvar clusterVectApp
objectvar mergeAvailableApp

// procedure to create a new Cluster List after merging Y_group_sections
proc newClusters(){local nsect, sec
    {clusterVectApp = $o1 mergeAvailableApp = $o2}
    nsect = clusterVectApp.size()
    clusterVect = new Vector(0,0)

	for ii=0,nsect-1 {
        if(mergeAvailableApp.x(ii)) {/*print clusterVectApp.x(ii)*/ clusterVect.append(clusterVectApp.x(ii))}
    }    
    newClusterList.append(clusterVect)

}

objectvar appVect

proc PurkReduction(){local i, ii, nsect

	eqL=new Vector(clusterList.count,0)   		//set/reset
	eqdiam=new Vector(clusterList.count,0)		//set/reset
	eqdiamSer=new Vector(clusterList.count,0)		//set/reset
	eqdiamPar=new Vector(clusterList.count,0)		//set/reset	
	//eqRa=new Vector(clusterList.count,0)		//set/reset	
	eqri2=new Vector(clusterList.count,0)		//set/reset	
	eqSurf=new Vector(clusterList.count,0)		//set/reset	
	orSurf=new Vector(clusterList.count,0)		//set/reset
	orSurf1=new Vector(clusterList.count,0)		//set/reset
	orSurf2=new Vector(clusterList.count,0)		//set/reset
	surfFact=new Vector(clusterList.count,1)		//set/reset
	surfFactRmCm=new Vector(clusterList.count,1)		//set/reset	
	//eqri=new Vector(clusterList.count,0)		//set/reset
		
	newClusterList.append(somaVector)
	mergingSoma(newClusterList.o(0))
	iniClusterList = 1
    	
	for i=iniClusterList,clusterList.count-1 {
        nsect = clusterList.o(i).size()   
        searchAvailable = new Vector(nsect,1)
        mergeAvailable = new Vector(nsect,0)
		getNextY(clusterList.o(i))
		shortnms()
		while(secA>0) {	
			if (secB==0 && secP!=0) mergingParentSec()
			if (secB!=0 && secP!=0) mergingYSec()
            //print secNameList.o(secA).s,secA,secNameList.o(secB).s,secB,secNameList.o(secP).s,secP
			getNextY(clusterList.o(i))
			shortnms()
		}
		newClusters(clusterList.o(i),mergeAvailable)
		mergingAllMethod(newClusterList.o(i),i,nsect)

        totSurf = 0
        appVect = new Vector(0,0)
        for ii=0,nsect-1 {
            appVect.append(secSurf.x(clusterList.o(i).x(ii)))
            totSurf = totSurf + secSurf.x(clusterList.o(i).x(ii))
        }
        //print totSurf
        
        if (SURFFACT_PARTIAL_METHOD==0 || SURFFACT_PARTIAL_METHOD==3){
            orSurf.set(i,appVect.sum())
            surfFact.set(i,surfFactVect.x(i)*orSurf.x(i)/eqSurf.x(i))
            surfFactRmCm.set(i,surfFactVect.x(i)*orSurf.x(i)/eqSurf.x(i))
        }else if (SURFFACT_PARTIAL_METHOD==1 || SURFFACT_PARTIAL_METHOD==4){
            orSurf.set(i,orSurf1.x(i))
            surfFact.set(i,surfFactVect.x(i)*orSurf.x(i)/eqSurf.x(i))
            surfFactRmCm.set(i,surfFactVect.x(i)*orSurf.x(i)/eqSurf.x(i))    
            //print surfFact.x(i),surfFactRmCm.x(i)
        }        
  
              
        		
	}
}



/*---------------------------------------------
            OUTPUT DATA:
            PRINT CLUSTERLIST
            CREATING EQUIVALENT CELL
  ---------------------------------------------*/

// Useful variables
objectvar clusterListApp

proc printClusterList(){local nCluster,secApp,i,j,ii
    clusterListApp = $o1
    nCluster = clusterListApp.count
    
    for i=0,nCluster-1{
        print "_____________________"
        print "cluster n. ", i
        
        for j=0,clusterListApp.o(i).size()-1{
            secApp = clusterListApp.o(i).x(j)
            
            print secApp, secNameList.o(secApp).s, secL.x(secApp),secdiam.x(secApp),mrgdiamPar.x(secApp), secSurf.x(secApp),secpathri0.x(secApp),secpathri.x(secApp)
        }
        
    }    
    print "Section\tLength (um)\tDiameter (um)\tOld Area (um^2)\tNew Area (um^2)\tArea Fact"
    
    for ii=0,nCluster-1 print ii, "\t", eqL.x(ii),"\t", eqdiam.x(ii),"\t",orSurf.x(ii),"\t",eqSurf.x(ii),"\t",surfFactRmCm.x(ii)

    print "eqRa\t orMinpathri\t orMaxpathri\t eqri2\t eqriEffettiva\t eqpathri0\t eqpathri"
    
    for ii=0,nCluster-1 {
        eqSection[ii] {
             if(RaMERGINGMETHOD==0){RaEq = factEqRa*eqRa.x(ii)}\
             else if(RaMERGINGMETHOD==1){RaEq = factEqRa*eqri2.x(ii)*PI*(diam/2)^2*100/L}\
             else if(RaMERGINGMETHOD==2){RaEq = factEqRa*(orMaxpathri.x(ii)-orMinpathri.x(ii))*PI*(diam/2)^2*100/L}
        }
        print RaEq,"\t",orMinpathri.x(ii),"\t",orMaxpathri.x(ii),"\t",eqri2.x(ii),"\t",(eqRa.x(ii)*eqL.x(ii))/(PI*((eqdiam.x(ii)^2)/4)*100),"\t",eqsecpathri0.x(ii),"\t",eqsecpathri.x(ii)
        }
    
     
}


// data to compute path from each section to the soma
objectvar eqrvp			
objectvar eqslsoma		
objectvar eqslroot

{create eqSection[2000]}

factEqRa = 1

objref tgAlph
objref signDx
objref signDy

proc createPurkEqCell(){local nCluster,appLun,sec,col,i,j,jj,secApp
    
    clusterListApp = $o1
    nCluster = clusterListApp.count
    eqsecpathri = new Vector(nCluster,0.0)		//set/reset
    eqsecpathri0 = new Vector(nCluster,0.0)		//set/reset
    orMinpathri = new Vector(nCluster,10^6)		//set/reset
    orMaxpathri = new Vector(nCluster,0.0)		//set/reset
    eqRa = new Vector(nCluster,0.0)		//set/reset
        
    TotOrSurf = orSurf.sum(1,orSurf.size-1)
    TotEqSurf = eqSurf.sum(1,eqSurf.size-1)


    for (i = 0; i < nCluster; i = i + 1){
        
        for jj=0,clusterListApp.o(i).size()-1{
            secApp = clusterListApp.o(i).x(jj)
            eqRa.set(i,eqRa.x(i)+secRa.x(secApp))
        
            if (secpathri.x(secApp)>orMaxpathri.x(i)){
               orMaxpathri.set(i,secpathri.x(secApp))
            }
            if (secpathri0.x(secApp)<orMinpathri.x(i)){
               orMinpathri.set(i,secpathri0.x(secApp))
            }                
        }
        
        
        if (clusterListApp.o(i).size()==1){
          if (parsec.x(secApp)!=0){ //Mod Ale: era secApp invece di 0
             orMinpathri.set(i,secpathri.x(parsec.x(secApp)))
          }else{orMinpathri.set(i,0)}
          orMaxpathri.set(i,secpathri.x(secApp))
        }
        
        appp = orMinpathri.x(i)  
        if (orMinpathri.x(i)>orMaxpathri.x(i)){
           orMinpathri.x(i) = orMaxpathri.x(i)
           orMaxpathri.x(i) = appp
        }
        
        
        if(optPrint) print "orMinpathri di ",i,"è: ", orMinpathri.x(i)
        if(optPrint) print "orMaxpathri di ",i,"è: ", orMaxpathri.x(i)
        
        
        eqRa.set(i,eqRa.x(i)/clusterListApp.o(i).size())
        
        
        
        for (j = 1; j < nCluster; j = j + 1){
            if (clusterParent.x(j)==i) {eqSection[i] connect eqSection[j](0), clusterParentPos.x(j)} 
        }       
        
        aaa = 0
        if (SURFFACT_PARTIAL_TOTAL==0 && i>0) {surfFact.set(i,TotOrSurf/TotEqSurf) surfFactRmCm.set(i,TotOrSurf/TotEqSurf)}

    }
    
    for (j = 0; j < eqSomaVector.size(); j = j + 1){ 
        jj = eqSomaVector.x(j)
        eqSection[jj] {insert Leak el_Leak = el_Leak0 gl_Leak = factRm*surfFactRmCm.x(jj)*gl_LeakSoma el_Leak = el_Leak0
                       L = eqL.x(jj) diam = eqdiam.x(jj) 
                       cm=factCm*cmSoma*surfFactRmCm.x(jj)
                       if($2==0){Ra = factEqRa*eqRa.x(jj)}\
                       else if($2==1){Ra = factEqRa*eqri2.x(jj)*PI*(diam/2)^2*100/L}\
                       else if($2==2){Ra = factEqRa*(orMaxpathri.x(jj)-orMinpathri.x(jj))*PI*(diam/2)^2*100/L}
        } 
    }       
    for (j = 0; j < eqTrunkVector.size(); j = j + 1){
        jj = eqTrunkVector.x(j)
        eqSection[jj] {insert Leak el_Leak = el_Leak0 gl_Leak = factRm*surfFactRmCm.x(jj)*gl_LeakSmoothSec el_Leak = el_Leak0
                       L = eqL.x(jj) diam = eqdiam.x(jj) 
                       cm=factCm*cmSmoothSec*surfFactRmCm.x(jj)
                       if($2==0){Ra = factEqRa*eqRa.x(jj)}\
                       else if($2==1){Ra = factEqRa*eqri2.x(jj)*PI*(diam/2)^2*100/L}\
                       else if($2==2){Ra = factEqRa*(orMaxpathri.x(jj)-orMinpathri.x(jj))*PI*(diam/2)^2*100/L}
        }         
    }
    for (j = 0; j < eqSmoothVector.size(); j = j + 1){
        jj = eqSmoothVector.x(j)
        eqSection[jj] {insert Leak el_Leak = el_Leak0 gl_Leak = factRm*surfFactRmCm.x(jj)*gl_LeakSmoothSec el_Leak = el_Leak0
                       L = eqL.x(jj) diam = eqdiam.x(jj) 
                       cm=factCm*cmSmoothSec*surfFactRmCm.x(jj)
                       if($2==0){Ra = factEqRa*eqRa.x(jj)}\
                       else if($2==1){Ra = factEqRa*eqri2.x(jj)*PI*(diam/2)^2*100/L}\
                       else if($2==2){Ra = factEqRa*(orMaxpathri.x(jj)-orMinpathri.x(jj))*PI*(diam/2)^2*100/L}
        } 
    }
    for (j = 0; j < eqSpinyVector.size(); j = j + 1){
        jj = eqSpinyVector.x(j)
        eqSection[jj] {insert Leak el_Leak = el_Leak0 gl_Leak = factRm*surfFactRmCm.x(jj)*gl_LeakSpinySect el_Leak = el_Leak0
                       L = eqL.x(jj) diam = eqdiam.x(jj) 
                       cm=factCm*cmSpinySect*surfFactRmCm.x(jj)
                       if($2==0){Ra = factEqRa*eqRa.x(jj)}\
                       else if($2==1){Ra = factEqRa*eqri2.x(jj)*PI*(diam/2)^2*100/L}\
                       else if($2==2){Ra = factEqRa*(orMaxpathri.x(jj)-orMinpathri.x(jj))*PI*(diam/2)^2*100/L}
        } 
    }    
    
    
    totEq=0
    for (i = 0; i < nCluster; i = i + 1){
        eqSection[i] {
               nseg = int((L/(d_lambda*lambda_f(freqEq))+0.9)/2)*2 + 1  
               totEq=totEq+nseg
        } 
    }       
      
    if(optPrint) print "totSegEq: ", totEq
  
    sec = 1
    forsec "eqSection.*" if (!issection("eqSection[0]")){
	  {eqslsoma=new SectionList() eqrvp=new RangeVarPlot("v")
	   {eqSection[0]  eqrvp.begin(.5)}  eqrvp.end(.5) eqrvp.list(eqslsoma) }
	  {eqslroot=new SectionList() eqrvp=new RangeVarPlot("v")
	   {ss=0 forsec eqslsoma{ {if(ss==1) eqrvp.begin(.5)}  ss=ss+1}}
	   eqrvp.end(.5)  eqrvp.list(eqslroot)}
	   
	  nsecPath = 0 
	  forsec eqslroot {nsecPath=nsecPath+1 for(x) if(x>0) eqsecpathri.set(sec,eqsecpathri.x(sec)+ri(x))}
      nsecPath1 = 0
      forsec eqslroot {
             nsecPath1=nsecPath1+1 
             for(x) if(x>0 && nsecPath1<nsecPath) eqsecpathri0.set(sec,eqsecpathri0.x(sec)+ri(x))
      }      
        
	  sec = sec+1
    }    
    forsec "eqSection[0]" {for(x) if(x>0) eqsecpathri.set(0,eqsecpathri.x(0)+ri(x))}

    
    tgAlph = new Vector(0,0)
    signDx = new Vector(0,0)
    signDy = new Vector(0,0)
    
    access soma[0]
    distance()
    xx0 = x3d(1)
    yy0 = y3d(1)
    yyPrec = yy0

    iii = 0
    forsec TrunkSectList{
         if (distance(0)==0){yyPrec = yy0}
         if (x3d(1)-xx0==0){
            tgAlph.append(1e10)
         }else {tgAlph.append(abs((y3d(1)-yyPrec)/(x3d(1)-xx0)))}
         if (x3d(1)-xx0>=0){signDx.append(1)}else{signDx.append(-1)}
         if (y3d(1)-yyPrec>=0){signDy.append(1)}else{signDy.append(-1)}                            
         //print tgAlph.x(iii)
         iii =iii+1
                  
         yyPrec = yyPrec+y3d(1)-y3d(0)
    }

    access soma[0]
    if (x3d(1)-x3d(0)==0){
     tgAlph0 = 1e10
    }else {tgAlph0 = abs((y3d(1)-y3d(0))/(x3d(1)-x3d(0)))} 

    appLun = eqSection[0].L
    access eqSection[0]
   
    pt3dclear()
    DeltaY = appLun*sin(atan(tgAlph0))
    DeltaX = appLun*cos(atan(tgAlph0))
    pt3dadd(300,0,0,eqSection[0].diam)
    pt3dadd(300+DeltaX,DeltaY,0,eqSection[0].diam)
    
    
    for (j = 0; j < 1; j = j + 1){ //eqTrunkVector.size()
        jj = eqTrunkVector.x(j)
        jjParent = clusterParent.x(jj)
        eqSection[jjParent]{xxParent = x3d(1) yyParent = y3d(1)}
                
        eqSection[jj] {
            pt3dclear()
            DeltaY = L*sin(atan(tgAlph.x(j)))
            DeltaX = L*cos(atan(tgAlph.x(j)))/10
        
            pt3dadd(xxParent,yyParent,0,diam)
            pt3dadd(xxParent+signDx.x(j)*DeltaX,yyParent+signDy.x(j)*DeltaY,0,diam)        
        }       
    }



    
}


// Useful variables
objectvar sh
objectvar shPlot
objref vbox0, vbox1

strdef app
objref strobj,rr,gg,bb
strobj = new StringFunctions()

proc coloringClusterList(){local nCluster,sec,col,i,j
    clusterListApp = $o1
    nCluster = clusterListApp.count
   
    vbox0 = new VBox()  
    vbox1 = new VBox()  
    strdef strApp 
    
    vbox0.intercept(1)

    sh = new Shape() //PlotShape

    app = ""
    sh.action("app = secname() secApp=-1 forall {secApp=secApp+1 if (issection(app)) break} print secApp,app coloringClusterList(clusterListApp)")  
    
    vbox0.intercept(0)
    sprint(strApp, "Plotting %s", str)
    vbox0.map(strApp, 0, 530, 270, 250)
    
    sec = 0
    forall if (!issection("eqSection.*")){
           col = 1
           for (i = 0; i < nCluster; i = i + 1){
               //print "pippo",i,col,col-int(col/10)
               if (col-int(col/10)*10==2 || col-int(col/10)*10==0) col = col-int(col/10)*10+1
               //print "pluto",i,col
               if (clusterListApp.o(i).contains(sec)&&!issection(app)) sh.color(col)
               col = col + 1
           }
           sec=sec+1
    }
    
    col = 1
    forsec "eqSection.*" {if (col-int(col/10)*10==2 || col-int(col/10)*10==0) {col = col-int(col/10)*10+1} sh.color(col) col=col+1}    
    
    length = strobj.len(app)
    if (length>0) forsec "eqSection.*" if(issection(app)){sh.color(2)}

    
    if(optPrint2) {
        vbox1.intercept(1)
        shPlot = new PlotShape()
        shPlot.scale(-70, 0)  //-70,30,-50
        shPlot.exec_menu("Show Diam")
        shPlot.exec_menu("Shape Plot")
        vbox1.intercept(0)
        vbox1.map(strApp, 400, 295, 500, 420)
    }

    sh.show(0)

}







/*---------------------------------------------
                   ACCURACY FUNCTION
  ---------------------------------------------*/
  
accu = -1
fact2 = 0.35
TmaxNeg = 10
TmaxPos = 10

// Useful variables
objectvar vecTTSpikeOrApp, vecTTSpikeEqApp

func accuracy(){local i, j, nn
     
    tstop = t
    vecTTSpikeOrApp = $o1
    vecTTSpikeEqApp = $o2
    
    
	TP = 0
	TN = 0
	FP = 0
	FN = 0
	
	if(vecTTSpikeOrApp.size()==0) vecTTSpikeOrApp.append(tstop)
	if(vecTTSpikeEqApp.size()==0) vecTTSpikeEqApp.append(tstop)
	
	for i = 0,vecTTSpikeOrApp.size()-1{
        if (i == 0){tprec = 0
        }else{tprec = vecTTSpikeOrApp.x(i - 1)}
        if (i == vecTTSpikeOrApp.size()-1){tsucc = tstop
        }else{tsucc = vecTTSpikeOrApp.x(i + 1)}
        if (fact2*(vecTTSpikeOrApp.x(i) - tprec) <= TmaxPos){DeltaT1 = fact2*(vecTTSpikeOrApp.x(i) - tprec)
        }else{DeltaT1 = TmaxPos}
        if (i == 0){initNeg = 0
        }else{initNeg = tprec + DeltaT1}
        fineNeg = vecTTSpikeOrApp.x(i) - DeltaT1
        initPos = fineNeg
        if (fact2*(tsucc - vecTTSpikeOrApp.x(i)) <= TmaxPos){DeltaT2 = fact2*(tsucc - vecTTSpikeOrApp.x(i))
        }else{DeltaT2 = TmaxPos}        
        finePos = vecTTSpikeOrApp.x(i) + DeltaT2
        
        for (nn = initNeg; nn <= fineNeg; nn = nn + TmaxNeg) {
            
            inizioInter = nn
			if (nn + TmaxNeg <= fineNeg) {fineInter = nn + TmaxNeg
            }else(fineInter = fineNeg)	
            
            nEq = 0
            for j = 0,vecTTSpikeEqApp.size()-1{
                if (vecTTSpikeEqApp.x(j) > inizioInter && vecTTSpikeEqApp.x(j) < fineInter) nEq = nEq+1
            }
            if (nEq == 0) {TN = TN + 1
            }else{FP = FP + nEq}   
        }	

        nEq = 0
        for j = 0,vecTTSpikeEqApp.size()-1{
            if (vecTTSpikeEqApp.x(j) >= initPos && vecTTSpikeEqApp.x(j) <= finePos) nEq = nEq+1
        }
        
        
        if (nEq == 0) { FN = FN + 1
        }else{TP = TP + 1 FP = FP + nEq - 1}        	


    }
		
    initNeg = finePos
	fineNeg = tstop
     
    
    for (nn = initNeg; nn <= fineNeg; nn = nn + TmaxNeg) {
        
        inizioInter = nn
		if (nn + TmaxNeg <= fineNeg) {fineInter = nn + TmaxNeg
        }else(fineInter = fineNeg)	
        
        nEq = 0
        for j = 0,vecTTSpikeEqApp.size()-1{
            if (vecTTSpikeEqApp.x(j) > inizioInter && vecTTSpikeEqApp.x(j) < fineInter) nEq = nEq+1
        }
        if (nEq == 0) {TN = TN + 1
        }else{FP = FP + nEq}   
    }    
   
    if(TP + TN + FP + FN != 0){ accu = (TP + TN)/(TP + TN + FP + FN) }
        	
    
    return accu
}


surfFactVect = new Vector(2000,1.0)		//set/reset

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