#include <stdio.h>
#include <stdlib.h>
#include <math.h>
#include <string.h>
/***************************************************************
Function to analyse the numerical error of Generalised
Compartmental Model. A single input is simulated and
the exact solution determined using the Equivalent Cable
***************************************************************/
typedef struct SparseMatrix_t
{
double *a;
int *col;
int *StartRow;
int n;
struct SparseMatrix_t *l;
struct SparseMatrix_t *u;
} SparseMatrix;
typedef struct cond_t {
int n; /* No. timesteps in conductance profile */
double dt; /* Integration time step (msecs) */
double *g; /* Conductance profile for prescribed dt (mu a) */
double tol; /* Determines off-threshold for synapse */
double tau; /* Rise time for synapse (msecs) */
double gmax; /* Peak conductance per synapse (mu) */
} cond;
typedef struct synapse_t
{
int id; /* Identifies contact type */
double xp; /* Location of contact */
int np; /* Proximal neighbour */
int nd; /* Distal neighbour */
double wp; /* Fraction of input carried by proximal neighbour */
double wd; /* Fraction of input carried by distal neighbour */
double wpp; /* Weight of proximal potential in proximal current */
double wdp; /* Weight of distal potential in proximal current */
double wpd; /* Weight of proximal potential in distal current */
double wdd; /* Weight of distal potential in distal current */
int npp; /* Sparse entry occupied by wpp */
int ndp; /* Sparse entry occupied by wdp */
int npd; /* Sparse entry occupied by wpd */
int ndd; /* Sparse entry occupied by wdd */
double gold; /* Previous conductance */
double gnew; /* Present conductance */
/* Properties of synaptic conductance profile */
cond *SynCond; /* Address of synaptic conductance profile */
int LocalSynTime; /* Time to activation of synapse/time since activation */
int MaxLocalSynTime; /* Time of inactivation of synapse */
double vsyn; /* Reversal potential of synaptic species */
struct synapse_t *next; /* Address of next contact */
} synapse;
typedef struct branch_t
{
/* Connectivity of branch */
struct branch_t *parent; /* Address of parent branch */
struct branch_t *child; /* Address of child branch */
struct branch_t *peer; /* Addresss of peer branch */
/* Physical properties of branch */
int id; /* Branch identifier */
int nc; /* Number of compartments specifying branch */
double xl; /* X-coordinate of lefthand endpoint */
double yl; /* Y-coordinate of lefthand endpoint */
double zl; /* Z-coordinate of lefthand endpoint */
double xr; /* X-coordinate of righthand endpoint */
double yr; /* Y-coordinate of righthand endpoint */
double zr; /* Z-coordinate of righthand endpoint */
double diam; /* Branch diameter (cm) */
double plen; /* Branch length (cm) */
double hseg; /* Dendritic segment length (cm) */
/* Node information for spatial representation */
int nodes; /* Total number nodes spanning branch */
int junct; /* Junction node of the branch */
int first; /* Internal node connected to junction */
/* Contact information */
synapse *synlist; /* Branch synapse */
} branch;
typedef struct dendrite_t
{
branch *root; /* Pointer to root branch of dendrite */
double plen; /* Length of dendrite */
} dendrite;
typedef struct neuron_t
{
int ndend; /* Number of dendrites */
dendrite *dendlist; /* Pointer to an array of dendrites */
} neuron;
/* Function type declarations */
cond *ConductanceProfile( double, double, double, double );
int Count_Branches( branch *, branch *),
Count_Synapses( branch *, branch *);
double branch_length( branch *, branch *),
ran(unsigned int *, unsigned int *, unsigned int *),
alfa_h( double ),
alfa_m( double ),
alfa_n( double ),
beta_h( double ),
beta_m( double ),
beta_n( double );
void Build_Test_Dendrite( branch **, branch *),
Remove_Branch( branch **, branch *),
Assign_Branch_Nodes( branch *, double *),
Enumerate_Nodes( branch *, int *),
Generate_Dendrite(branch *, int *),
Initialise_Synapses( branch *),
Update_Synapses( branch *),
Matrix_Vector_Multiply( SparseMatrix *, double *, double *),
Matrix_Malloc( SparseMatrix *, int, int),
Matrix_Free( SparseMatrix *),
cgs( int, SparseMatrix *, double *, double *, double *, double);
/* Global definitions */
#define CS 1.0
#define GS 0.091
#define GA 14.286
#define CM 1.0
#define GM 0.091
#define OUTPUT "K2Spike500.dat"
#define TEND 11
#define TAU 0.5
#define CGS 1.0e-18 /* Tolerance used in CGS algorithm */
#define GMAX 1.0e-5
#define RATE 30.0
#define VSYN 115.0
#define NT 1000
#define NODES 500
#define NSEED 2 /* Seed for random number generator */
#define CELSIUS 18.5 /* Celsius temperature of neuron */
/* Parameters for exact solution */
#define NCON 1000 /* Number of contacts */
#define RS 0.005
/* Global Variables */
SparseMatrix lhs, rhs;
double pi, *SynCurrent;
unsigned int ix, iy, iz;
int main( int argc, char **argv )
{
extern unsigned int ix, iy, iz;
extern SparseMatrix lhs, rhs;
extern double pi, *SynCurrent;
int k, j, id, nn, nodes, n, nc, i, in, nstep, maxstep, FirstNode,
NumberOfSynapses, counter, nb, connected, spk, nspk;
double *v, *x, max, AreaOfSoma, sum, tmp, vs, dt, len, h, sc,
gs, interval, dx, CellLength, LocusContact, mval,
nval, hval, aval, bval, vm0, vm1, vm2, tnow;
double *StoredLHS, *StoredRHS;
double v_na=115.0, v_k=-12.0, v_l, g_na=120.0, g_k=36.0, g_l=0.3;
void srand( unsigned int);
neuron *cell;
cond *SynCond;
synapse *newsyn, *syn;
branch *bo, *bn, *FirstBranch;
char word[20];
FILE *fp;
/* Initialise random number generator */
fp = fopen(OUTPUT,"w");
fclose(fp);
nspk = spk = 0;
dt = 1.0/((double) NT);
srand( ((unsigned int) NSEED) );
ix = rand( );
iy = rand( );
iz = rand( );
SynCond = ConductanceProfile( dt, TAU, 5.e-7, GMAX );
/* Load Test Neuron */
maxstep = 1000*NT*TEND;
pi = 4.0*atan(1.0);
AreaOfSoma = 4.0*pi*RS*RS;
if ( argc != 2 ) {
printf("\n Invoke program with load <input>\n");
return 1;
} else {
printf("\nOpening file %s\n",argv[1]);
if ( (fp=fopen(argv[1],"r")) == NULL ) {
printf("\n Test Neuron file not found");
return 1;
}
}
/* Get branch data */
bo = NULL;
while ( fscanf(fp,"%s",word) != EOF ) {
if ( strcmp(word,"Branch") == 0 || strcmp(word,"branch") == 0 ) {
bn = (branch *) malloc( sizeof(branch) );
fscanf(fp,"%d", &(bn->id) );
bn->peer = NULL;
bn->child = NULL;
bn->synlist = NULL;
if ( bo != NULL) {
bo->child = bn;
} else {
FirstBranch = bn;
}
bn->parent = bo;
fscanf(fp,"%lf %lf %lf", &(bn->xl), &(bn->yl), &(bn->zl) );
fscanf(fp,"%lf %lf %lf", &(bn->xr), &(bn->yr), &(bn->zr) );
fscanf(fp,"%lf %lf", &(bn->plen), &(bn->diam) );
bo = bn;
} else {
printf("Unrecognised dendritic feature\n");
return 0;
}
}
fclose(fp);
/* Compute total length of dendrite */
CellLength = 0.0;
bn = FirstBranch;
while ( bn ) {
CellLength += bn->plen;
bn = bn->child;
}
/* STEP 1. - Randomly place NCON synapses on branches */
for ( k=0 ; k<NCON ; k++ ) {
LocusContact = CellLength*ran( &ix, &iy, &iz);
bn = FirstBranch;
len = bn->plen;
while ( LocusContact > len ) {
bn = bn->child;
len += bn->plen;
}
newsyn = (synapse *) malloc( sizeof(synapse) );
newsyn->next = NULL;
newsyn->SynCond = SynCond;
newsyn->MaxLocalSynTime = SynCond->n;
newsyn->vsyn = VSYN;
newsyn->xp = LocusContact-(len-bn->plen);
syn = bn->synlist;
if ( syn ) {
while ( syn->next ) syn = syn->next;
syn->next = newsyn;
} else {
bn->synlist = newsyn;
}
}
/* STEP 2. - Count root branches */
bo = FirstBranch;
n = 0;
while ( bo ) {
bn = FirstBranch;
do {
tmp = pow(bo->xl-bn->xr,2)+pow(bo->yl-bn->yr,2)+
pow(bo->zl-bn->zr,2);
connected = ( tmp < 0.01 );
bn = bn->child;
} while ( bn && !connected );
if ( !connected ) n++;
bo = bo->child;
}
/* STEP 3. - Identify somal dendrites but extract nothing */
printf("\nTree contains %d individual dendrite(s) ...\n", n);
cell = (neuron *) malloc( sizeof(neuron) );
cell->ndend = n;
cell->dendlist = (dendrite *) malloc( n*sizeof(dendrite) );
bo = FirstBranch;
n = 0;
while ( n < cell->ndend ) {
bn = FirstBranch;
do {
tmp = pow(bo->xl-bn->xr,2)+pow(bo->yl-bn->yr,2)+
pow(bo->zl-bn->zr,2);
connected = ( tmp < 0.01 );
bn = bn->child;
} while ( bn );
if ( !connected ) cell->dendlist[n++].root = bo;
bo = bo->child;
}
/* STEP 4. - Extract root of each dendrite from dendrite list */
for ( k=0 ; k<cell->ndend ; k++ ) {
bo = cell->dendlist[k].root;
Remove_Branch( &FirstBranch, bo);
}
/* STEP 5. - Build each test dendrite from its root branch */
for ( k=0 ; k<cell->ndend ; k++ ) {
Build_Test_Dendrite( &FirstBranch, cell->dendlist[k].root );
}
if ( FirstBranch != NULL ) printf("\nWarning: Unconnected branch segments still exist\n");
/* STEP 6. - Count number of synapses on Cell */
NumberOfSynapses = 0;
for ( k=0 ; k<cell->ndend ; k++ ) {
bn = cell->dendlist[k].root;
NumberOfSynapses += Count_Synapses( cell->dendlist[k].root, bn);
}
printf("\nNumber of Synapses %d", NumberOfSynapses);
/* STEP 7. - Count number of dendritic branches */
for ( nb=k=0 ; k<cell->ndend ; k++ ) {
bn = cell->dendlist[k].root;
nb += Count_Branches( bn, bn);
}
h = CellLength/((double) NODES-nb);
for ( k=0 ; k<cell->ndend ; k++ ) Assign_Branch_Nodes( cell->dendlist[k].root, &h);
/* STEP 8. - Enumerate Nodes */
FirstNode = 0;
for ( k=0 ; k<cell->ndend ; k++ ) Enumerate_Nodes( cell->dendlist[k].root, &FirstNode );
for ( k=0 ; k<cell->ndend ; k++ ) cell->dendlist[k].root->junct = FirstNode;
printf("\nNumber of nodes is %d\n", FirstNode+1);
/* STEP 9. - Construct Sparse Matrices */
nodes = FirstNode+1;
Matrix_Malloc( &lhs, nodes, 3*nodes-2 );
Matrix_Malloc( &rhs, nodes, 3*nodes-2 );
lhs.StartRow[0] = rhs.StartRow[0] = 0;
for ( counter=k=0 ; k<cell->ndend ; k++ ) {
bn = cell->dendlist[k].root;
Generate_Dendrite( bn, &counter);
}
lhs.n = rhs.n = nodes;
/* STEP 10. - Do somal node */
lhs.a[3*nodes-3] = rhs.a[3*nodes-3] = 0.0;
for ( k=0 ; k<cell->ndend ; k++ ) {
bn = cell->dendlist[k].root;
lhs.a[counter] = (bn->diam)*(bn->hseg)/6.0;
rhs.a[counter] = -0.25*pi*pow(bn->diam,2)/(bn->hseg);
lhs.col[counter] = rhs.col[counter] = bn->first;
lhs.a[3*nodes-3] += 2.0*pi*(bn->diam)*(bn->hseg)/6.0;
rhs.a[3*nodes-3] += 0.25*pi*pow(bn->diam,2)/(bn->hseg);
counter++;
}
lhs.col[counter] = rhs.col[counter] = nodes-1;
lhs.StartRow[nodes] = rhs.StartRow[nodes] = counter+1;
/* STEP 12. - Fill in properties of synapses */
for( k=0 ; k<cell->ndend ; k++ ) Initialise_Synapses(cell->dendlist[k].root);
for ( k=0 ; k<3*nodes-2 ; k++ ) {
rhs.a[k] = 0.5*dt*(GA*rhs.a[k]+GM*lhs.a[k]);
rhs.a[k] = CM*lhs.a[k]-rhs.a[k];
lhs.a[k] = 2.0*CM*lhs.a[k]-rhs.a[k];
}
lhs.a[3*nodes-3] += AreaOfSoma*CS;
rhs.a[3*nodes-3] += AreaOfSoma*CS;
/* STEP 13. - Construct and load vectors to hold transient information */
StoredLHS = (double *) malloc( (3*nodes-2)*sizeof(double) );
StoredRHS = (double *) malloc( (3*nodes-2)*sizeof(double) );
for ( k=0 ; k<3*nodes-2 ; k++ ) {
StoredLHS[k] = lhs.a[k];
StoredRHS[k] = rhs.a[k];
}
/* STEP 14. - Compute somal conductances and the leakage potential */
g_na *= AreaOfSoma;
g_k *= AreaOfSoma;
g_l *= AreaOfSoma;
hval = alfa_h(0.0)/(alfa_h(0.0)+beta_h(0.0));
mval = alfa_m(0.0)/(alfa_m(0.0)+beta_m(0.0));
nval = alfa_n(0.0)/(alfa_n(0.0)+beta_n(0.0));
v_l = g_na*pow(mval,3)*hval*v_na+g_k*pow(nval,4)*v_k;
v_l = -v_l/g_l;
/* STEP 15. - Construct and initialise potentials and currents */
v = (double *) malloc( (nodes)*sizeof(double) );
x = (double *) malloc( (nodes)*sizeof(double) );
SynCurrent = (double *) malloc( (nodes)*sizeof(double) );
for ( k=0 ; k<nodes ; k++ ) v[k] = 0.0;
/* Initialise temporal integration and integrate forward */
nstep = 0;
while ( nstep < maxstep ) {
nstep++;
/* Phase 1. - Update HH channel variables */
vs = v[nodes-1];
aval = dt*alfa_h(vs);
bval = dt*beta_h(vs);
tmp = 0.5*(aval+bval);
hval = (aval+(1.0-tmp)*hval)/(1.0+tmp);
aval = dt*alfa_m(vs);
bval = dt*beta_m(vs);
tmp = 0.5*(aval+bval);
mval = (aval+(1.0-tmp)*mval)/(1.0+tmp);
aval = dt*alfa_n(vs);
bval = dt*beta_n(vs);
tmp = 0.5*(aval+bval);
nval = (aval+(1.0-tmp)*nval)/(1.0+tmp);
/* Phase 2. - Compute somal conductance and contribution to current */
gs = g_l; /* Leakage conductance */
sc = g_l*v_l; /* Leakage contribution to somal current */
tmp = g_na*hval*pow(mval,3); /* Sodium conductance */
gs += tmp;
sc += tmp*v_na; /* Sodium contribution to somal current */
tmp = g_k*pow(nval,4); /* Potassium conductance */
gs += tmp;
sc += tmp*v_k; /* Potasium contribution to somal current */
/* Phase 3. - Zero LHS, RHS and SynCurrent */
for ( k=0 ; k<3*nodes-2 ; k++ ) lhs.a[k] = rhs.a[k] = 0.0;
for ( k=0 ; k<nodes ; k++ ) SynCurrent[k] = 0.0;
/* Phase 4. - Update synaptic conductances and input */
for ( k=0 ; k<cell->ndend ; k++ ) {
bn = cell->dendlist[k].root;
Update_Synapses( bn );
}
/* Phase 5. - Complete the construction of LHS and RHS matrices */
for ( k=0 ; k<3*nodes-2 ; k++ ) {
lhs.a[k] += StoredLHS[k];
rhs.a[k] += StoredRHS[k];
}
gs *= 0.5*dt;
lhs.a[3*nodes-3] += gs;
rhs.a[3*nodes-3] -= gs;
/* Phase 6. - Step potential forward */
Matrix_Vector_Multiply( &rhs, v, x);
x[nodes-1] += sc*dt;
for ( k=0 ; k<nodes ; k++ ) x[k] += SynCurrent[k];
cgs( 1, &lhs, x, v, v, CGS);
/* Phase 7. - Test for spikes */
if ( nstep == 1 ) {
vm2 = 0.0;
vm1 = v[nodes-1];
} else {
vm0 = v[nodes-1];
if ( !spk ) {
spk = ( vm0 > 50.0 && vm1 > vm2 && vm1 > vm0 );
if ( nstep >= 1000*NT && spk ) {
tnow = dt*((double) nstep);
tmp = tnow+0.5*dt*(vm2+3.0*vm0-4.0*vm1)/(vm0-2.0*vm1+vm2);
nn = ((int) floor(tmp))-1000*NT;
if ( fmod(tmp,1.0)>0.5 ) nn++;
fp = fopen(OUTPUT,"a");
fprintf(fp,"%d\n",nn);
fclose(fp);
}
}
vm2 = vm1;
vm1 = vm0;
}
/* Phase 8. - Reset spike flag */
if ( vs < 0.0 && spk == 1 ) {
spk = 0;
nspk++;
}
if ( nstep%(500*NT) == 0 ) {
tnow = dt*((double) nstep/NT);
printf("\rReached time %5.1lf ms \t Spikes so far %d", tnow, nspk);
}
}
return 0;
}
/******************************************************
Function to build a test dendrite from its root
******************************************************/
void Build_Test_Dendrite( branch **head, branch *root)
{
double tmp;
branch *bnow, *bnext, *btmp;
bnow = *head;
while ( bnow != NULL ) {
/* Store bnow's child in case it's corrupted */
bnext = bnow->child;
/* Decide if proximal end of bnow is connected to distal end of root */
tmp = pow(bnow->xl-root->xr,2)+
pow(bnow->yl-root->yr,2)+
pow(bnow->zl-root->zr,2);
if ( tmp <= 0.01 ) {
/* Remove bnow from the branch list */
Remove_Branch( head, bnow);
/* Connect bnow to the root as the child or a peer of the child.
Initialise childs' children and peers to NULL as default */
bnow->child = NULL;
bnow->peer = NULL;
bnow->parent = root;
/* Inform root about its child if it's the first child, or add
new child to first child's peer list */
if ( root->child != NULL ) {
btmp = root->child;
while ( btmp->peer != NULL ) btmp = btmp->peer;
btmp->peer = bnow;
} else {
root->child = bnow;
}
}
/* Initialise bnow to next branch in list */
bnow = bnext;
}
/* Iterate through remaining tree */
if ( root->child ) Build_Test_Dendrite( head, root->child);
if ( root->peer ) Build_Test_Dendrite( head, root->peer);
return;
}
/*********************************************************
Function to remove a branch from a branch list
*********************************************************/
void Remove_Branch(branch **head, branch *b)
{
if ( *head == NULL || b == NULL ) return;
if ( *head == b ) {
*head = b->child;
if ( *head != NULL ) (*head)->parent = NULL;
} else {
b->parent->child = b->child;
if ( b->child != NULL ) b->child->parent = b->parent;
}
b->parent = NULL;
b->child = NULL;
return;
}
/*********************************************
Function to count synapses on a branch
*********************************************/
int Count_Synapses( branch *bstart, branch *bnow)
{
static int n;
synapse *syn;
if ( bstart == bnow ) n = 0;
if ( bnow != NULL ) {
if ( bnow->child ) Count_Synapses(bstart, bnow->child);
if ( bnow->peer ) Count_Synapses(bstart, bnow->peer);
syn = bnow->synlist;
while ( syn ) {
n++;
syn = syn->next;
}
}
return n;
}
/**********************************************
Function to count number of branches
**********************************************/
int Count_Branches( branch *bstart, branch *bnow)
{
static int n;
if ( bstart == bnow ) n = 0;
if ( bnow != NULL ) {
if ( bnow->child ) Count_Branches(bstart, bnow->child);
if ( bnow->peer ) Count_Branches(bstart, bnow->peer);
n++;
}
return n;
}
/*******************************************************
Function to enumerate the nodes on a dendrite
*******************************************************/
void Enumerate_Nodes(branch *bnow, int *FirstNode )
{
branch *btmp;
if ( bnow->child ) Enumerate_Nodes( bnow->child, FirstNode );
if ( bnow->peer ) Enumerate_Nodes( bnow->peer, FirstNode );
if ( bnow->child ) {
btmp = bnow->child;
while ( btmp ) {
btmp->junct = *FirstNode;
btmp = btmp->peer;
}
}
*FirstNode += bnow->nc;
bnow->first = *FirstNode-1;
return;
}
/***************************************************
Function to constuct sparse matrices
***************************************************/
void Generate_Dendrite( branch *b, int *counter)
{
int k, CurrentNode, nc;
extern double pi;
extern SparseMatrix lhs, rhs;
branch *btmp;
double SumL, SumR;
/* Step 1 - Recurse to the end of the dendrite */
if ( b->child ) Generate_Dendrite( b->child, counter);
if ( b->peer ) Generate_Dendrite( b->peer, counter);
/* Step 2 - Build matrix entries for distal node of branch */
nc = b->nc;
CurrentNode = (b->first)-(nc-1);
if ( b->child ) {
btmp = b->child;
SumR = SumL = 0.0;
while ( btmp ) {
lhs.a[*counter] = pi*(btmp->diam)*(btmp->hseg)/6.0;
rhs.a[*counter] = -0.25*pi*pow(btmp->diam,2)/(btmp->hseg);
SumL += 2.0*pi*(btmp->diam)*(btmp->hseg)/6.0;
SumR += 0.25*pi*pow(btmp->diam,2)/(btmp->hseg);
lhs.col[*counter] = rhs.col[*counter] = btmp->first;
(*counter)++;
btmp = btmp->peer;
}
lhs.a[*counter] = SumL+2.0*pi*(b->diam)*(b->hseg)/6.0;
rhs.a[*counter] = SumR+0.25*pi*pow(b->diam,2)/(b->hseg);
lhs.col[*counter] = rhs.col[*counter] = CurrentNode;
(*counter)++;
lhs.a[*counter] = pi*(b->diam)*(b->hseg)/6.0;
rhs.a[*counter] = -0.25*pi*pow(b->diam,2)/(b->hseg);
if ( CurrentNode == b->first ) {
lhs.col[*counter] = rhs.col[*counter] = b->junct;
} else {
lhs.col[*counter] = rhs.col[*counter] = CurrentNode+1;
}
(*counter)++;
lhs.StartRow[CurrentNode+1] = rhs.StartRow[CurrentNode+1] = *counter;
} else {
lhs.a[*counter] = 2.0*pi*(b->diam)*(b->hseg)/6.0;
rhs.a[*counter] = 0.25*pi*pow(b->diam,2)/(b->hseg);
lhs.col[*counter] = rhs.col[*counter] = CurrentNode;
(*counter)++;
lhs.a[*counter] = pi*(b->diam)*(b->hseg)/6.0;
rhs.a[*counter] = -0.25*pi*pow(b->diam,2)/(b->hseg);
if ( CurrentNode == b->first ) {
lhs.col[*counter] = rhs.col[*counter] = b->junct;
} else {
lhs.col[*counter] = rhs.col[*counter] = CurrentNode+1;
}
(*counter)++;
lhs.StartRow[CurrentNode+1] = rhs.StartRow[CurrentNode+1] = *counter;
}
/* Step 3 - Build matrix entries for internal nodes of branch */
for ( k=nc-1 ; k>0 ; k-- ) {
CurrentNode++;
lhs.a[*counter] = pi*(b->diam)*(b->hseg)/6.0;
rhs.a[*counter] = -0.25*pi*pow(b->diam,2)/(b->hseg);
lhs.col[*counter] = rhs.col[*counter] = CurrentNode-1;
(*counter)++;
lhs.a[*counter] = 4.0*pi*(b->diam)*(b->hseg)/6.0;
rhs.a[*counter] = 0.5*pi*pow(b->diam,2)/(b->hseg);
lhs.col[*counter] = rhs.col[*counter] = CurrentNode;
(*counter)++;
lhs.a[*counter] = pi*(b->diam)*(b->hseg)/6.0;
rhs.a[*counter] = -0.25*pi*pow(b->diam,2)/(b->hseg);
if ( CurrentNode == b->first ) {
lhs.col[*counter] = rhs.col[*counter] = b->junct;
} else {
lhs.col[*counter] = rhs.col[*counter] = CurrentNode+1;
}
(*counter)++;
lhs.StartRow[CurrentNode+1] = rhs.StartRow[CurrentNode+1] = *counter;
}
return;
}
/***********************************************
Function to assign synaptic weights
***********************************************/
void Initialise_Synapses( branch *b )
{
extern SparseMatrix lhs, rhs;
int k;
double rat, interval;
synapse *syn;
if ( b->child ) Initialise_Synapses( b->child );
if ( b->peer ) Initialise_Synapses( b->peer );
syn = b->synlist;
while ( syn ) {
rat = (syn->xp)/(b->hseg);
k = ((int) floor(rat));
rat = fmod(rat,1.0);
/* Phase 1. - Set up matrix nodes */
if ( k == 0 ) {
syn->np = b->junct;
syn->nd = b->first;
} else {
syn->np = b->first-k+1;
syn->nd = b->first-k;
}
/* Phase 2. - Set up weights */
syn->wpp = (1.0-rat)*(1.0-rat); /* Weight of proximal potential in proximal current */
syn->wdp = rat*(1.0-rat); /* Weight of distal potential in proximal current */
syn->wpd = rat*(1.0-rat); /* Weight of proximal potential in distal current */
syn->wdd = rat*rat; /* Weight of distal potential in distal current */
syn->wp = (1.0-rat)*(syn->vsyn); /* Weight of input at proximal node */
syn->wd = rat*(syn->vsyn); /* Weight of input at distal node */
/* Phase 3. - Location of sparse entries in equation arising from distal neighbour */
k = lhs.StartRow[syn->nd];
while ( syn->nd != lhs.col[k] ) k++;
syn->ndd = k;
while ( syn->np != lhs.col[k] ) k++;
syn->npd = k;
/* Phase 4. - Location of sparse entries in equation arising from proximal neighbour */
k = lhs.StartRow[syn->np];
while ( syn->nd != lhs.col[k] ) k++;
syn->ndp = k;
while ( syn->np != lhs.col[k] ) k++;
syn->npp = k;
/* Phase 5. - Set initial conductances and firing times */
syn->gold = syn->gnew = 0.0;
interval = -(((double) NT*1000)/RATE)*log(ran(&ix, &iy, &iz));
if ( fmod(interval,1.0) <= 0.5 ) {
syn->LocalSynTime = -((int) floor(interval));
} else {
syn->LocalSynTime = -((int) ceil(interval));
}
syn = syn->next;
}
return;
}
/***********************************************
Function to update status of synapses
***********************************************/
void Update_Synapses( branch *b )
{
extern SparseMatrix lhs, rhs;
extern double *SynCurrent;
double interval, gold, gnew, tmp;
synapse *syn;
if ( b->child ) Update_Synapses( b->child );
if ( b->peer ) Update_Synapses( b->peer );
syn = b->synlist;
while ( syn ) {
gold = syn->gold = syn->gnew;
(syn->LocalSynTime)++;
if ( syn->LocalSynTime < 1 ) {
gnew = syn->gnew = 0.0;
} else if ( syn->LocalSynTime < syn->MaxLocalSynTime ) {
gnew = syn->gnew = syn->SynCond->g[syn->LocalSynTime];
} else {
gnew = syn->gnew = 0.0;
interval = -(((double) NT*1000)/RATE)*log(ran(&ix, &iy, &iz));
if ( fmod(interval,1.0) <= 0.5 ) {
syn->LocalSynTime = -((int) floor(interval));
} else {
syn->LocalSynTime = -((int) ceil(interval));
}
}
if ( gold != 0.0 || gnew != 0.0 ) {
tmp = 0.5*(syn->SynCond->dt);
SynCurrent[syn->nd] += (syn->wd)*tmp*(gold+gnew);
SynCurrent[syn->np] += (syn->wp)*tmp*(gold+gnew);
lhs.a[syn->ndd] += (syn->wdd)*tmp*gnew;
rhs.a[syn->ndd] -= (syn->wdd)*tmp*gold;
lhs.a[syn->npd] += (syn->wpd)*tmp*gnew;
rhs.a[syn->npd] -= (syn->wpd)*tmp*gold;
lhs.a[syn->ndp] += (syn->wdp)*tmp*gnew;
rhs.a[syn->ndp] -= (syn->wdp)*tmp*gold;
lhs.a[syn->npp] += (syn->wpp)*tmp*gnew;
rhs.a[syn->npp] -= (syn->wpp)*tmp*gold;
}
syn = syn->next;
}
return;
}
/**********************************************************
Multiplies sparse matrix a[ ][ ] with vector v[ ]
**********************************************************/
void Matrix_Vector_Multiply( SparseMatrix *a, double *v , double *b)
{
int i, j, k, n;
n = a->n;
for ( j=0 ; j<n ; j++) {
k = a->StartRow[j+1];
for( b[j]=0.0,i=(a->StartRow[j]) ; i<k ; i++ ) {
b[j] += (a->a[i])*v[a->col[i]];
}
}
return;
}
/***********************************************
Allocate memory to a sparse matrix
***********************************************/
void Matrix_Malloc( SparseMatrix *a, int n, int w)
{
a->a = (double *) malloc( w*sizeof(double) );
a->col = (int *) malloc( w*sizeof(int) );
a->StartRow = (int *) malloc( (n+1)*sizeof(int) );
a->n = n;
a->l = malloc(sizeof(SparseMatrix));
a->u = malloc(sizeof(SparseMatrix));
a->l->a = (double *) malloc( (2*n-1)*sizeof(double) );
a->l->col = (int *) malloc( (2*n-1)*sizeof(int) );
a->l->StartRow = (int *) malloc( (n+1)*sizeof(int) );
a->l->n = n;
a->u->a = (double *) malloc( (2*n-1)*sizeof(double) );
a->u->col = (int *) malloc( (2*n-1)*sizeof(int) );
a->u->StartRow = (int *) malloc( (n+1)*sizeof(int) );
a->u->n = n;
return;
}
/**********************************************
De-allocates memory of a sparse matrix
**********************************************/
void Matrix_Free( SparseMatrix *a)
{
free(a->a);
free(a->col);
free(a->StartRow);
free(a);
}
/**************************************************
Function to assign branch nodes
**************************************************/
void Assign_Branch_Nodes( branch *b, double *h )
{
int k;
double hseg;
b->nc = ((int) ceil((b->plen)/(*h)));
b->hseg = (b->plen)/((double) b->nc);
if ( b->child ) Assign_Branch_Nodes( b->child, h);
if ( b->peer ) Assign_Branch_Nodes( b->peer, h);
return;
}
/************************************************************
Function returns primitive uniform random number.
************************************************************/
double ran(unsigned int *ix, unsigned int *iy, unsigned int *iz)
{
double tmp;
/* 1st item of modular arithmetic */
*ix = (171*(*ix))%30269;
/* 2nd item of modular arithmetic */
*iy = (172*(*iy))%30307;
/* 3rd item of modular arithmetic */
*iz = (170*(*iz))%30323;
/* Generate random number in (0,1) */
tmp = ((double) (*ix))/30269.0+((double) (*iy))/30307.0
+((double) (*iz))/30323.0;
return fmod(tmp,1.0);
}
/********************************************************************
ALPHA for ACTIVATION OF SODIUM
*******************************************************************/
double alfa_m( double volt )
{
double tmp;
static double fac;
static int start=1;
if ( start ) {
fac = pow(3.0,0.1*CELSIUS-0.63);
start = !start;
}
tmp = -0.1*(volt-25.0);
if ( fabs(tmp)<0.001 ) {
tmp = 1.0/(((tmp/24.0+1.0/6.0)*tmp+0.5)*tmp+1.0);
} else {
tmp = tmp/(exp(tmp)-1.0);
}
return tmp*fac;
}
/********************************************************************
BETA for ACTIVATION OF SODIUM
********************************************************************/
double beta_m( double volt )
{
double tmp;
static double fac;
static int start=1;
if ( start ) {
fac = pow(3.0,0.1*CELSIUS-0.63);
start = !start;
}
tmp = volt/18.0;
return 4.0*fac*exp(-tmp);
}
/********************************************************************
ALPHA for INACTIVATION OF SODIUM
********************************************************************/
double alfa_h( double volt )
{
double tmp;
static double fac;
static int start=1;
if ( start ) {
fac = pow(3.0,0.1*CELSIUS-0.63);
start = !start;
}
tmp = 0.05*volt;
return 0.07*fac*exp(-tmp);
}
/********************************************************************
BETA for INACTIVATION OF SODIUM
********************************************************************/
double beta_h( double volt )
{
double tmp;
static double fac;
static int start=1;
if ( start ) {
fac = pow(3.0,0.1*CELSIUS-0.63);
start = !start;
}
tmp = -0.1*(volt-30.0);
return fac/(exp(tmp)+1.0);
}
/********************************************************************
ALPHA for ACTIVATION OF POTASSIUM
********************************************************************/
double alfa_n( double volt )
{
double tmp;
static double fac;
static int start=1;
if ( start ) {
fac = pow(3.0,0.1*CELSIUS-0.63);
start = !start;
}
tmp = -0.1*(volt-10.0);
if ( fabs(tmp)<0.001 ) {
tmp = 0.1/(((tmp/24.0+1.0/6.0)*tmp+0.5)*tmp+1.0);
} else {
tmp = 0.1*tmp/(exp(tmp)-1.0);
}
return tmp*fac;
}
/********************************************************************
BETA for ACTIVATION OF POTASSIUM
********************************************************************/
double beta_n( double volt )
{
double tmp;
static double fac;
static int start=1;
if ( start ) {
fac = pow(3.0,0.1*CELSIUS-0.63);
start = !start;
}
tmp = 0.0125*volt;
return 0.125*fac*exp(-tmp);
}
/********************************************
Computes a conductance profile
********************************************/
cond *ConductanceProfile( double dt, /* Integration time step */
double tau, /* Synaptic time constant */
double tol, /* Determines off-threshold for synapse */
double gmax /* Maximum conductance (mS) */ )
{
int k;
cond *out;
double tmp, told, tnew;
out = (cond *) malloc( sizeof(cond) );
out->dt = dt;
out->tau = tau;
out->tol = tol;
out->gmax = gmax;
/* Iterate to find duration of pulse */
tmp = 1.0-log(tol);
tnew = tmp;
do {
told = tnew;
tnew = tmp+log(told);
} while ( fabs(tnew-told)>5.e-11 );
out->n = ((int) ceil(tau*tnew/dt));
out->g = (double *) malloc( (out->n)*sizeof(double) );
out->g[0] = 0.0;
for ( k=1 ; k<(out->n) ; k++ ) {
tmp = dt*((double) k)/tau;
out->g[k] = gmax*tmp*exp(1.0-tmp);
}
return out;
}
void cgs(int getmem, SparseMatrix *a, double *b, double *x0, double *x, double tol)
{
long int i, k, n, finish;
static int start=1;
double rho_old, rho_new, alpha, beta, sigma, err;
static double *p, *q, *u, *v, *r, *rb, *y;
/* Step 1 - Check memory status */
n = a->n;
if ( start ) {
r = (double *) malloc( n*sizeof(double) );
rb = (double *) malloc( n*sizeof(double) );
p = (double *) malloc( n*sizeof(double) );
q = (double *) malloc( n*sizeof(double) );
u = (double *) malloc( n*sizeof(double) );
v = (double *) malloc( n*sizeof(double) );
y = (double *) malloc( n*sizeof(double) );
start = 0;
}
/* Step 2 - Initialise residual, p[ ] and q[ ] */
Matrix_Vector_Multiply( a, x0, r);
for ( rho_old=0.0,i=0 ; i<n ; i++ ) {
r[i] = b[i]-r[i];
rho_old += r[i]*r[i];
rb[i] = r[i];
p[i] = 0.0;
q[i] = 0.0;
}
if ( rho_old<tol*((double) n) ) {
for ( i=0 ; i<n ; i++ ) x[i] = x0[i];
return;
}
rho_old = 1.0;
finish = 0;
/* The main loop */
while ( !finish ) {
/* Compute scale parameter for solution update */
for ( rho_new=0.0,i=0 ; i<n ; i++ ) rho_new += r[i]*rb[i];
beta = rho_new/rho_old;
/* Update u[ ] and p[ ] */
for ( i=0 ; i<n ; i++ ) {
u[i] = r[i]+beta*q[i];
p[i] = u[i]+beta*(q[i]+beta*p[i]);
}
/* Update v[ ] and compute sigma */
Matrix_Vector_Multiply( a, p, v);
for ( sigma=0.0,i=0 ; i<n ; i++ ) sigma += rb[i]*v[i];
/* Compute alpha and update q[ ], v[ ] and x[ ] */
alpha = rho_new/sigma;
for ( i=0 ; i<n ; i++ ) {
q[i] = u[i]-alpha*v[i];
v[i] = alpha*(u[i]+q[i]);
x[i] += v[i];
}
/* Update r[ ] and estimate error */
Matrix_Vector_Multiply( a, v, y);
for ( err=0.0,i=0 ; i<n ; i++ ) {
r[i] -= y[i];
err += r[i]*r[i];
}
rho_old = rho_new;
if ( err<tol*((double) n) ) finish = 1;
}
/* Check memory status */
if ( getmem<=0 ) start = 1;
if ( start ) {
free(r);
free(rb);
free(p);
free(q);
free(u);
free(v);
free(y);
}
return;
}
