/*
This file is the source for a construal of Plasmodium Vivax Malarial Infection ('the PVMI construal')
generated for illustrative purposes in connection with the abstract:
'A conception of computing with promise for medical education'
by Meurig Beynon and Will Beynon, as presented at the 5th International Online Medical Conference (IOMC 2012).
To execute the construal, direct an up-to-date version of the Firefox browser at the url:
http://www.dcs.warwick.ac.uk/~wmb/JsEden/js-eden
paste the contents of the file into the Eden Interpreter Window, and press 'Submit'.
(It may be necessary to instruct the browser to 'Continue' the loading of the script, should it report
an 'Unresponsive script'.)
When the file is loaded, a visualisation will be displayed on the Canvas and accompanying documentation
will be accessible via the 'HTML Output' tab.
*/
liver is Rectangle(25,215,70,70,"brown");
## blood is Rectangle(40,40,580,100,"red");
blood is Circle(250,250,200,"red", "red");
organs is Circle(250,250,180,"white", "white");
sporozoites is Circle(600,90, 5,"green","white");
livercentre is [60, 250];
livercell is Circle(livercentre[1],livercentre[2], 15, "yellow", "black");
## library functions ...
PI = 3.14159265358979;
func sin {
${{
var x1 = arguments[0];
return Math.sin(x1);
}}$;
};
func cos {
${{
var x1 = arguments[0];
return Math.cos(x1);
}}$;
};
## picture is [blood, liver, sporozoites, livercell];
## get sporozoites to migrate
loc0 = [460,250];
sporolocx is loc0[1]; sporolocy is loc0[2]; spororad = 5;
sporozoites is Circle(sporolocx, sporolocy, spororad, (spororad<15) ? "green" : "brown", (spororad<15) ? "white" : "brown");
/*
## when sporozoites are in circulation ...
phi is theta - ... ;
loc0 is [centtarget[1]+ 190*cos(phi), centtarget[2]- 190*sin(phi)];
*/
## sporozoites circulate in the blood
centtarget = [250,250];
theta = 0;
cyclepoint is Text(".", centtarget[1]+ 150*cos(15*PI/15+theta), centtarget[2]- 150*sin(15*PI/15+theta), "black");
loc1 is [centtarget[1]+ 190*cos(2*PI/15+theta), centtarget[2]- 190*sin(2*PI/15+theta)];
loc2 is [centtarget[1]+ 190*cos(4*PI/15+theta), centtarget[2]- 190*sin(4*PI/15+theta)];
loc3 is [centtarget[1]+ 190*cos(6*PI/15+theta), centtarget[2]- 190*sin(6*PI/15+theta)];
loc4 is [centtarget[1]+ 190*cos(8*PI/15+theta), centtarget[2]- 190*sin(8*PI/15+theta)];
loc5 is [centtarget[1]+ 190*cos(10*PI/15+theta), centtarget[2]- 190*sin(10*PI/15+theta)];
loc6 is [centtarget[1]+ 190*cos(12*PI/15+theta), centtarget[2]- 190*sin(12*PI/15+theta)];
loc7 is [centtarget[1]+ 190*cos(14*PI/15+theta), centtarget[2]- 190*sin(14*PI/15+theta)];
loc8 is [centtarget[1]+ 190*cos(16*PI/15+theta), centtarget[2]- 190*sin(16*PI/15+theta)];
loc9 is [centtarget[1]+ 190*cos(18*PI/15+theta), centtarget[2]- 190*sin(18*PI/15+theta)];
loc10 is [centtarget[1]+ 190*cos(20*PI/15+theta), centtarget[2]- 190*sin(20*PI/15+theta)];
loc11 is [centtarget[1]+ 190*cos(22*PI/15+theta), centtarget[2]- 190*sin(22*PI/15+theta)];
loc12 is [centtarget[1]+ 190*cos(24*PI/15+theta), centtarget[2]- 190*sin(24*PI/15+theta)];
loc13 is [centtarget[1]+ 190*cos(26*PI/15+theta), centtarget[2]- 190*sin(26*PI/15+theta)];
loc14 is [centtarget[1]+ 190*cos(28*PI/15+theta), centtarget[2]- 190*sin(28*PI/15+theta)];
loc15 is [centtarget[1]+ 190*cos(30*PI/15+theta), centtarget[2]- 190*sin(30*PI/15+theta)];
bcrad = 6;
bloodcorp1 is Circle(loc1[1], loc1[2], bcrad, "pink", "grey");
bloodcorp2 is Circle(loc2[1], loc2[2], bcrad, "pink", "grey");
bloodcorp3 is Circle(loc3[1], loc3[2], bcrad, "pink", "grey");
bloodcorp4 is Circle(loc4[1], loc4[2], bcrad, "pink", "grey");
bloodcorp5 is Circle(loc5[1], loc5[2], bcrad, "pink", "grey");
bloodcorp6 is Circle(loc6[1], loc6[2], bcrad, "pink", "grey");
bloodcorp7 is Circle(loc7[1], loc7[2], bcrad, "pink", "grey");
bloodcorp8 is Circle(loc8[1], loc8[2], bcrad, "pink", "grey");
bloodcorp9 is Circle(loc9[1], loc9[2], bcrad, "pink", "grey");
bloodcorp10 is Circle(loc10[1], loc10[2], bcrad, "pink", "grey");
bloodcorp11 is Circle(loc11[1], loc11[2], bcrad, "pink", "grey");
bloodcorp12 is Circle(loc12[1], loc12[2], bcrad, "pink", "grey");
bloodcorp13 is Circle(loc13[1], loc13[2], bcrad, "pink", "grey");
bloodcorp14 is Circle(loc14[1], loc14[2], bcrad, "pink", "grey");
bloodcorp15 is Circle(loc15[1], loc15[2], bcrad, "pink", "grey");
picture is [blood, organs, liver, livercell, sporozoites, bloodcorp1, bloodcorp2, bloodcorp3, bloodcorp4, bloodcorp5, bloodcorp6, bloodcorp7, bloodcorp8, bloodcorp9, bloodcorp10, bloodcorp11, bloodcorp12, bloodcorp13, bloodcorp14, bloodcorp15];
bloodspeed = 10;
## higher value means slower circulation rate
bloodspeed = 100;
steps = 0;
proc bloodcirc {
after (bloodspeed) {
steps++;
bloodcirc();
}
}
theta is (steps % 300) * 2 * PI/300;
bloodcirc();
mosquitobite is Button("bite", ((loc0[1] == 460) ? "Start Stage 1: Inoculation" : "Mosquito has bitten"), 480, 250, loc0[1]==460);
picture is (spororad < 15) ? [explanation, mosquitobite, blood, organs, cyclepoint, sporesgrow, liver, livercell, sporozoites, bloodcorp1, bloodcorp2, bloodcorp3, bloodcorp4, bloodcorp5, bloodcorp6, bloodcorp7, bloodcorp8, bloodcorp9, bloodcorp10, bloodcorp11, bloodcorp12, bloodcorp13, bloodcorp14, bloodcorp15] : [explanation, mosquitobite, blood, organs, cyclepoint, sporesgrow, liver, livercell, sporozoites, bloodcorp1, bloodcorp2, bloodcorp3, bloodcorp4, bloodcorp5, bloodcorp6, bloodcorp7, bloodcorp8, bloodcorp9, bloodcorp10, bloodcorp11, bloodcorp12, bloodcorp13, bloodcorp14, bloodcorp15, merozoite1, merozoite2, merozoite3, merozoite4];
proc bitten : bite_clicked {
auto theta0;
if (bite_clicked) {
theta0 = theta;
phi is theta - theta0;
loc0 is [centtarget[1]+ 190*cos(phi), centtarget[2]- 190*sin(phi)];
}
}
func ptsnear {
para p, q, near;
auto result;
result = (((p[1]-q[1])*(p[1]-q[1])+(p[2]-q[2])*(p[2]-q[2]))<(near*near));
return result;
}
sporoinliver is ptsnear(livercentre,loc0,10);
proc mksporogrow : sporoinliver {
if (sporoinliver&&(loc0!=livercentre)) {
loc0 = livercentre;
}
}
sporesgrow is Button("sporesgrow", ((spororad == 5) ? (((spororad== 5)&&(loc0==livercentre)) ? "Start Stage 3: Schizogony" : "Patient well"): (spororad <=15 && freeinblood==0) ? "Liver Stage" : "Blood Stage"), 130, 250, (spororad== 5)&&(loc0==livercentre));
proc sporogrow : sporesgrow_clicked {
if (loc0 == livercentre) {
after (3000) {
if (spororad < 15) {
spororad++;
sporogrow();
}
}
}
}
currentstate is (sporolocx == 460) ? "Stage 0. Body is free of infection" : (!sporoinliver) ? "Stage 2. Sporozoites enter hepatocytes" :
((sporoinliver && (spororad<15)) ? (( spororad>5) ? "Stage 3: Schizogony": "") : ((circuits==0) ? "Stage 4: Merozoites exit the liver calls and invade red blood cells" : bloodstagephase ));
bloodstagephase is "Stage 5: Erythrocytic Cycle:" // ((theta < 1.5) ? " Cell rupture, merozoite release and further RBC invasion" : " Asexual (and sexual) reproduction");
/*
*/
explanation is Text(currentstate, 20, 30, "black");
merodisp = 3;
merorad = 2;
mero1x is livercentre[1]+merodisp-25;
mero1y is livercentre[2]+merodisp-25;
mero2x is livercentre[1]-merodisp-25;
mero2y is livercentre[2]+merodisp-25;
mero3x is livercentre[1]-merodisp-25;
mero3y is livercentre[2]-merodisp-25;
mero4x is livercentre[1]+merodisp-25;
mero4y is livercentre[2]-merodisp-25;
merozoites is [merozoite1, merozoite2, merozoite3, merozoite4];
merozoite1 is Circle(mero1x, mero1y, merorad, "brown", "brown");
merozoite2 is Circle(mero2x, mero2y, merorad, "blue", "blue");
merozoite3 is Circle(mero3x, mero3y, merorad, "blue", "blue");
merozoite4 is Circle(mero4x, mero4y, merorad, "blue", "blue");
##############################################
totalnumrbcs = 30000000000000;
noofinfectablebcs0 = 900000000000;
noofinfectablebcs = noofinfectablebcs0;
propinfbcs is bcinfnum / totalnumrbcs;
freeinblood is (spororad==15) ? 2000 : 0;
bcinfnum = 0.0;
bcsinfpercluster is int(bcinfnum/15);
bcinfection is [bcsinfpercluster,bcsinfpercluster,bcsinfpercluster,bcsinfpercluster,bcsinfpercluster,bcsinfpercluster,bcsinfpercluster,bcsinfpercluster,bcsinfpercluster,bcsinfpercluster,bcsinfpercluster,bcsinfpercluster,bcsinfpercluster,bcsinfpercluster,bcsinfpercluster];
merocount is freeinblood + bcinfnum;
circuits = 0;
func powerof2 {
para n;
auto result;
result = 1;
while (n>0) {
result = 2 * result;
n--;
}
return result;
}
alpha = 0.930;
beta = 0.5;
gamma = 0.2;
divisionstage = -1;
nohostcellsfordiv = 0;
merotobekilled = false;
onetoabc is int(bcinfnum * alpha);
dividing is (divisionstage>=0) ? int(bcinfnum * (1-alpha) * powerof2(divisionstage)) : 0;
textnumofinfectablerbcs is Text("Number of infectable RBCs: " // str(noofinfectablebcs),20,20, "red");
textfreeinblood is Text("Number of merozoites free in blood: " // str(freeinblood), 20,40, "blue");
textinbcs is Text("Number of merozoites sited one to a blood cell: " // str(onetoabc), 20,60, "blue");
textdividing is Text("Number of merozoites generated by division in " // str(nohostcellsfordiv) // " blood cells: " // str(dividing), 20, 80, "blue");
buttenterbc is Button("RBCEntry", "Proportion " // str(beta) // " of free merozoites enter bcs", 20, 120, divisionstage==-1);
buttkillinf is Button("MeroKill", "Proportion " // str(1.00-gamma) // " of free merozoites killed", 20, 150, merotobekilled);
buttmerodiv is Button("MeroDiv", "Proportion " // str((100 - 100*alpha)/100) // " of embedded merozoites divide stage-by-stage", 20, 180, divisionstage>=0);
## buttnewbcsgen is Button("GenBCs", "Introduce " // str(noofinfectablebcs0) // " new blood cells, together with " // str(int((1.000-alpha)*bcinfnum)) // " to replace the exploded cells, that can be infected", 20, 210, divisionstage==-1);
## picture is [textnumofinfectablerbcs, textfreeinblood, textinbcs, textdividing, buttenterbc, buttkillinf, buttmerodiv, buttnewbcsgen];
## picture is [textnumofinfectablerbcs, textfreeinblood, textinbcs, textdividing, buttenterbc, buttkillinf, buttmerodiv];
proc infectRBCs : RBCEntry_clicked {
if (RBCEntry_clicked) {
bcinfnum = bcinfnum + int(beta * freeinblood);
freeinblood = int((1-beta) * freeinblood);
divisionstage = 0;
nohostcellsfordiv = dividing;
merotobekilled = true;
}
}
proc killmeros : MeroKill_clicked {
if (MeroKill_clicked) {
freeinblood = int(gamma * freeinblood);
merotobekilled = false;
}
}
proc merosdivide : MeroDiv_clicked {
if (MeroDiv_clicked) {
if ((divisionstage>=0) && (divisionstage < 4)) divisionstage++;
else
if (divisionstage == 4){
bcinfnum = onetoabc;
freeinblood = freeinblood + dividing;
divisionstage = -1;
noofinfectablebcs = noofinfectablebcs0 + nohostcellsfordiv;
nohostcellsfordiv = 0;
}
}
}
circuits = 0;
proc simulatestep {
RBCEntry_clicked = true;
MeroKill_clicked = true;
merodivide();
circuits++;
}
proc merodivide {
if (divisionstage != -1) {
MeroDiv_clicked = true;
merodivide();
}
}
proc simulateproc {
after (100) {
simulatestep();
if (freeinblood < noofinfectablebcs) simulateproc();
}
}
################################
proc onecircuit : steps {
if ((spororad==15)&&(steps == (int(steps/300)*300)) && (infpercentage<3)) simulatestep();
};
## visualise according to number of decimal digits in the merozoite count
func ntodecls {
para n;
auto result;
result = [];
while (n>0) {
result = result // [int(n%10)];
n = int(n/10);
}
return result;
}
bcsinfdiglen is ntodecls(bcsinfpercluster);
bloodcorpinf1 is Circle(loc1[1], loc1[2], bcsinfdiglen#, "blue", "blue");
bloodcorpinf2 is Circle(loc2[1], loc2[2], bcsinfdiglen#, "blue", "blue");
bloodcorpinf3 is Circle(loc3[1], loc3[2], bcsinfdiglen#, "blue", "blue");
bloodcorpinf4 is Circle(loc4[1], loc4[2], bcsinfdiglen#, "blue", "blue");
bloodcorpinf5 is Circle(loc5[1], loc5[2], bcsinfdiglen#, "blue", "blue");
bloodcorpinf6 is Circle(loc6[1], loc6[2], bcsinfdiglen#, "blue", "blue");
bloodcorpinf7 is Circle(loc7[1], loc7[2], bcsinfdiglen#, "blue", "blue");
bloodcorpinf8 is Circle(loc8[1], loc8[2], bcsinfdiglen#, "blue", "blue");
bloodcorpinf9 is Circle(loc9[1], loc9[2], bcsinfdiglen#, "blue", "blue");
bloodcorpinf10 is Circle(loc10[1], loc10[2], bcsinfdiglen#, "blue", "blue");
bloodcorpinf11 is Circle(loc11[1], loc11[2], bcsinfdiglen#, "blue", "blue");
bloodcorpinf12 is Circle(loc12[1], loc12[2], bcsinfdiglen#, "blue", "blue");
bloodcorpinf13 is Circle(loc13[1], loc13[2], bcsinfdiglen#, "blue", "blue");
bloodcorpinf14 is Circle(loc14[1], loc14[2], bcsinfdiglen#, "blue", "blue");
bloodcorpinf15 is Circle(loc15[1], loc15[2], bcsinfdiglen#, "blue", "blue");
rbccount = totalnumrbcs;
unitrbc is rbccount / 15; ## have visualised 15 groups of rbc's
## for P. Vivax a high level of infection would be 3% - say 1 trillion rbc infected
## 2 to the power 40 is around a trillion
infpercentage is (merocount * 100)/rbccount;
picture is (spororad < 15) ? [cyclepoint, explanation, mosquitobite, blood, organs, cyclepoint, sporesgrow, liver, livercell, sporozoites, bloodcorp1, bloodcorp2, bloodcorp3, bloodcorp4, bloodcorp5, bloodcorp6, bloodcorp7, bloodcorp8, bloodcorp9, bloodcorp10, bloodcorp11, bloodcorp12, bloodcorp13, bloodcorp14, bloodcorp15] : [cyclepoint, explanation, mosquitobite, blood, organs, cyclepoint, sporesgrow, liver, livercell, sporozoites, bloodcorp1, bloodcorp2, bloodcorp3, bloodcorp4, bloodcorp5, bloodcorp6, bloodcorp7, bloodcorp8, bloodcorp9, bloodcorp10, bloodcorp11, bloodcorp12, bloodcorp13, bloodcorp14, bloodcorp15, bloodcorpinf1, bloodcorpinf2, bloodcorpinf3, bloodcorpinf4, bloodcorpinf5, bloodcorpinf6, bloodcorpinf7, bloodcorpinf8, bloodcorpinf9, bloodcorpinf10, bloodcorpinf11, bloodcorpinf12, bloodcorpinf13, bloodcorpinf14, bloodcorpinf15, merozoite1, merozoite2, merozoite3, merozoite4];
## additions 29/12/2011
blood is Circle(250,250,205,"red", "red");
organs is Circle(250,250,175,"white", "red");
## makes blood band 30 pixels wide, and makes inner rim of blood band red
bcrad = 11;
## this radius gives room to visualise the biggest levels of infection that make sense
## if we visualise only the vulnerable RBCs, then this number may increase as the simulation goes on
## - proportion of young RBCs increases
func char {
${{
var x1 = arguments[0];
s = "%" + (Number(x1).toString(16));
return unescape(s);
}}$;
};
func octaltr {
para n;
if (n<10) return(str(n));
else return char(97 + n - 10);
}
## function round() doesn't exist in JS-Eden
func round {
para x;
return ((x - int(x))>=0.5) ? int(x)+1 : int(x);
}
func rgb2color {
para redval, greenval, blueval;
auto s, i;
## check values are in allowable 0-255 range
if ((redval<0)||(greenval<0)||(blueval<0)||
(redval>255)||(greenval>255)||(blueval>255))
error("colour out of range");
## round to nearest integer - need to have each component as a strict 2 + character length hex number - can't deal with real numbers directly, and don't need to?
redval = round(redval);
greenval = round(greenval);
blueval = round(blueval);
## use the c func to get the string back
## s = "";
## sprintf(s,"#%02x%02x%02x",redval,greenval,blueval);
s = "#" // octaltr(int(redval/16)) // octaltr(int(redval - int(redval/16)*16))
// octaltr(int(greenval/16)) // octaltr(int(greenval - int(greenval/16)*16))
// octaltr(int(blueval/16)) // octaltr(int(blueval - int(blueval/16)*16));
return s;
}
## changing the colour of the blood ...
blood is Circle(250,250,205,rgb2color(255,255,0), "red");
rb = 255; gb = 0; bb = 0;
blood is Circle(250,250,205,rgb2color(rb,gb,bb), "red");
rb is 255 - 10 * ntodecls(freeinblood)#;
gb is 15 * ntodecls(freeinblood)#;
/*
${{
function log10(val) {
return Math.log(val) / Math.log(10);
};
$}};
rb is 255 - int(log10(freeinblood));
gb is 15 + int(log10(freeinblood));
*/
#################################
gametes = 0;
buttmerodiv is Button("MeroDiv", "Proportion " // str((100 - 100*alpha)/100) // " of embedded merozoites divide stage-by-stage and are released into the bloodstream; others mature and are released as gametocytes", 20, 180, divisionstage>=0);
proc merosdivide : MeroDiv_clicked {
if (MeroDiv_clicked) {
if ((divisionstage>=0) && (divisionstage < 4)) divisionstage++;
else
if (divisionstage == 4){
bcinfnum = onetoabc - int(nohostcellsfordiv/64 * 3);
freeinblood = freeinblood + dividing;
gametes = gametes + int(nohostcellsfordiv/64 * 3);
divisionstage = -1;
noofinfectablebcs = noofinfectablebcs0 + int(nohostcellsfordiv * (1 + 3/64));
nohostcellsfordiv = 0;
}
}
}
textgametesinblood is Text("Number of gametes free in blood: " // str(gametes), 20,100, "blue");
ratiogammero is gametes / freeinblood;
picture is [textnumofinfectablerbcs, textfreeinblood, textinbcs, textdividing, textgametesinblood, buttenterbc, buttkillinf, buttmerodiv];
###################################################
gametespercluster is int(gametes/15);
mgametecol is "black";
fgametecol is "white";
gametediglen is ntodecls(gametespercluster);
gamete1 is Circle((loc1[1]+loc2[1])/2, (loc1[2]+loc2[2])/2, gametediglen#, mgametecol, mgametecol);
gamete2 is Circle((loc2[1]+loc3[1])/2, (loc2[2]+loc3[2])/2, gametediglen#, fgametecol,fgametecol);
gamete3 is Circle((loc3[1]+loc4[1])/2, (loc3[2]+loc4[2])/2, gametediglen#, mgametecol, mgametecol);
gamete4 is Circle((loc4[1]+loc5[1])/2, (loc4[2]+loc5[2])/2, gametediglen#, fgametecol, fgametecol);
gamete5 is Circle((loc5[1]+loc6[1])/2, (loc5[2]+loc6[2])/2, gametediglen#, mgametecol, mgametecol);
gamete6 is Circle((loc6[1]+loc7[1])/2, (loc6[2]+loc7[2])/2, gametediglen#, fgametecol, fgametecol);
gamete7 is Circle((loc7[1]+loc8[1])/2, (loc7[2]+loc8[2])/2, gametediglen#, mgametecol, mgametecol);
gamete8 is Circle((loc8[1]+loc9[1])/2, (loc8[2]+loc9[2])/2, gametediglen#, fgametecol, fgametecol);
gamete9 is Circle((loc9[1]+loc10[1])/2, (loc9[2]+loc10[2])/2, gametediglen#, mgametecol, mgametecol);
gamete10 is Circle((loc10[1]+loc11[1])/2, (loc10[2]+loc11[2])/2, gametediglen#, fgametecol, fgametecol);
gamete11 is Circle((loc11[1]+loc12[1])/2, (loc11[2]+loc12[2])/2, gametediglen#, mgametecol, mgametecol);
gamete12 is Circle((loc12[1]+loc13[1])/2, (loc12[2]+loc13[2])/2, gametediglen#, fgametecol, fgametecol);
gamete13 is Circle((loc13[1]+loc14[1])/2, (loc13[2]+loc14[2])/2, gametediglen#, mgametecol, mgametecol);
gamete14 is Circle((loc14[1]+loc15[1])/2, (loc14[2]+loc15[2])/2, gametediglen#, fgametecol, fgametecol);
gamete15 is Circle((loc15[1]+loc1[1])/2, (loc15[2]+loc1[2])/2, gametediglen#, mgametecol, mgametecol);
picture is (spororad < 15) ? [cyclepoint, explanation, mosquitobite, blood, organs, cyclepoint, sporesgrow, liver, livercell, sporozoites, bloodcorp1, bloodcorp2, bloodcorp3, bloodcorp4, bloodcorp5, bloodcorp6, bloodcorp7, bloodcorp8, bloodcorp9, bloodcorp10, bloodcorp11, bloodcorp12, bloodcorp13, bloodcorp14, bloodcorp15] : [cyclepoint, explanation, mosquitobite, blood, organs, cyclepoint, sporesgrow, liver, sporozoites, bloodcorp1, bloodcorp2, bloodcorp3, bloodcorp4, bloodcorp5, bloodcorp6, bloodcorp7, bloodcorp8, bloodcorp9, bloodcorp10, bloodcorp11, bloodcorp12, bloodcorp13, bloodcorp14, bloodcorp15, bloodcorpinf1, bloodcorpinf2, bloodcorpinf3, bloodcorpinf4, bloodcorpinf5, bloodcorpinf6, bloodcorpinf7, bloodcorpinf8, bloodcorpinf9, bloodcorpinf10, bloodcorpinf11, bloodcorpinf12, bloodcorpinf13, bloodcorpinf14, bloodcorpinf15, gamete1, gamete2, gamete3, gamete4, gamete5, gamete6, gamete7, gamete8, gamete9, gamete10, gamete11, gamete12, gamete13, gamete14, gamete15, merozoite1, merozoite2, merozoite3, merozoite4];
html("
An EM construal of Plasmodium Vivax malarial infection
The associated construal ('the PVMI construal') is intended to trace the stages in the development of a P. Vivax malarial infection from the point at which the sporozoites first enter the body to the point where the infection takes full hold over it. At this preliminary stage, the construal is still only provisonal and incomplete - there are many ways in which it may be developed to add details and address limitations (cf. the Malaria-ITS project at http://www.dcs.warwick.ac.uk/~empublic/js-eden2/). Only very basic medical science and an easily accessible understanding of vivax malaria has so far been taken into account and applied. The aspiration for construals such as this - as is characteristic of Empirical Modelling (EM) - is that they may be extended and refined in an open-ended manner by interested participants. These might include medical students and educators, researchers with an interest in more in-depth modelling of malaria, and computer scientists able to enhance the construal in technical respects. By way of useful orientation, and potential justification for the imperfect nature of any initial construal, see F.E. McKenzie's paper Why Model Malaria? at the url: http://www.sciencedirect.com/science/article/pii/S0169475800017890.
Principles of EM applied to modelling malaria
Malaria is caused by one of four species of protozoan Plasmodium that can infect humans. The generic stages of the lifecycle of the malaria parasite in the vertebral host to which the construal relates are as follows:
- An infected female Anopheles mosquito introduces sporozoites of the plasmodium parasite into the human bloodstream through a simple bite.
- Sporozoites travel to liver and enter hepatocytes.
- In the liver, sporozoites undergo asexual reproduction when activated to produce tens of thousands of merozoites contained in a schizont. This process is called schizogony. The duration of the liver stage depends on the species of Plasmodium infecting the host and can last between 6 - 14 days.
- The schizont ruptures, merozoites enter the bloodstream and rapidly invade red blood cells.
- Now in a erythrocytic or blood cycle, repeated asexual reproduction and merozoite proliferation, cell rupture and invasion of further red blood cells leads to significant parasitaemia and to clinical illness.
Some merozoites in red blood cells undergo sexual reproduction instead of further schizogomy leading to the production of gametocytes which are transmitted to a new vector mosquito in a blood meal to continue the plasmodium life cycle.
At Stage 3, Plasmodium Vivax or Plasmodium Ovale parasites may lie dormant in a hypnozoite stage instead of maturing in schizogony and immediately causing disease. Hypnozoites may be reactivated weeks or months later, relating to a relapsing course of infection.
In making the PVMI construal, we have focussed on the P. Vivax species, and elaborated the generic account of infection above accordingly. This higher level of specificity is desirable in making an EM construal, as the idea is that the current state of the construal should at all times reflect the current 'actual situation' to which it refers, and greater specificity gives wider scope for elaboration and refinement. (A variant of the construal directed at a generic malarial infection can be derived by pasting in the contents of the extension file 'extmalaria10.jse' from the same online directory.) From the point of the model-builder, this means that - in looking at the construal - it makes sense at all times to make present-tense assertions about what is happening in the actual situation. So, for instance, the construal is first presented in a state where we can say 'at this moment the human victim has not yet been infected', and in a subsequent state we may be able to say 'this is the moment at which the first gametocyte enters the bloodstream'. Contrast this with a conventional diagram depicting the parasite lifecycle, such as can be found at [1], where the dynamically changing correspondence between the static image and stages in the progress of an infection would be associated with pointing at different visual elements of the image. The 'present-tense' correspondence between a construal and its referent gives EM a distinctive character as a mode of 'live modelling'. As in all live encounters, meaning is latent in the possible sensible interactions with which we become familiar. This allows the modeller to return to states of the construal at any point and revise the construal to take fuller account of the situation to which it refers e.g. by refining the visualisation or the interface for interaction, or by exploring new avenues for interaction and interpretation that can be incorporated into the repertoire of sense-making activities associated with the construal.
In accordance with EM principles, the construal is developed by identifying observables in the referent and finding ways to give these counterparts in the construal. For the PVMI construal, examples of observables are: whether or not the human subject has been bitten, the location of the sporozoites in the body, the number of merozoites in the bloodstream, the number of infected red blood cells, the number of gametes present in the blood. The observables in the model can be listed by opening the 'Observables' tab on the left of this webpage. Specific subsets of observables can be selected by typing a 'regular expression' that pattern matches with specific observables into the search box at the top of the Observables panel.
Observables are subject to dependency relations - resembling the relationships between cells in a spreadsheet - that are also to be identified in the referent and reflected in the construal. In effect, changing the value of an observable in a 'live' interaction with the construal will automatically change the values of all observables that are dependent upon it. You can inspect the dependencies in the model by hovering over observables whose names are highlighted in blue in the Observables panel, when the definitions of these observables are displayed. As examples of dependency relations in the PVMI construal: the ratio of gametes to merozoites in the bloodstream depends on the number of gametes and merozoites, and the stage of the infection depends upon the current status of the parasite.
An EM construal captures the characteristics of its referent through presenting the modeller with observables that directly express or 'mimic' the qualities of the observables in the referent and the dependencies to which they are subject. This mode of capturing qualities of a referent differs from a formal representation and takes an experiential form. What is currently presented in the construal is experienced as 'metaphorically' representing what is experienced in the referent. In the PVMI construal, the process of developing suitable metaphors is exceptionally challenging. There are 30 trillion red blood cells for instance [2] and at most a few million pixels on a standard computer screen. The timescale on which blood circulates round the body - once every 20 seconds - is quite different from the scale on which the P. Vivax parasite
multiplies - once about every 48 hours - and the construal has to present state-transitions at an acceptable rate for the human viewer. As P. Vivax parasites preferentially infect young red blood cells, of which there are about a trillion initially, there is merit in distinguishing these from the rest. Red blood cells are renewed over a period of 120 days in health, a much longer period than that for which the infection is being tracked in this construal, and so older cells have in the first instance been neglected in modelling infection.
Interpreting and using the PVMI construal
To interpret the construal, the viewer needs to appreciate the metaphors that have been used. The model has a dynamic circulatory behaviour to reflect the notion that the malarial infection is a cyclic and progressive activity. One cycle corresponds metaphorically to a period in the development of the P. Vivax parasite originating with the entry of merozoites into blood cells and terminating with the release of a cluster of merozoites from a schizont or the emergence of gametes. This leads to a dramatic increase in the number of merozoites in the bloodstream, which in turn initiates the next surge of infection of blood cells.
Although it does not represent the circulation itself, the red annulus in the construal metaphorically represents the blood within it; the pink circles populations of young red blood cells. Each of the fifteen circles represents a fifteenth part of the approximately one trillion cells that are most vulnerable to infection by merozoites in P. Vivax. There is no visual counterpart in the model for red blood cells that, because of their age, are not vulnerable within the period of the infection being simulated, nor of individual corpuscles. The presence of merozoites within each of the fifteen clusters of red blood cells is metaphorically represented by blue circles that are placed on top of these pink circles. Like the red blood cells, the merozoites are so numerous that they cannot be visually depicted in a strictly proportionate manner. To overcome this problem, a logarithmic scale is used in the display. Each pink circle has radius 11 to indicate that it contains of the order of 10 to the power 11 cells. The radius of the blue circle that is superimposed is similarly specified according to the number of merozoites embedded within that population of cells.
Another significant feature of the infection process is the presence of merozoites and gametes within the blood stream. The same logarithmic convention that is used to depict red blood cells and merozoites is adopted to display the male and female gametes that are produced as the infection develops: these appear as black and white circles within the red annulus. A different metaphor is used to reflect the density of the merozoites free within the blood stream. The colour of the 'blood' within the annulus is modified as the number of merozoites increases, so that when the number of free merozoites is an N digit decimal number the 'blood colour' has a red component of 255-N*10 and a green component of N*15. In P. Vivax, the number of gametes in the bloodstream has been found to be very much smaller than the number of merozoites. Empirical studies estimate the median ratio of sexual to asexual parasites as 0.3% (0.07-6.2%) [3].
The mechanism that is used to update the infection status is invoked at the end of each cycle of infection. Mature erythrocytic schizonts, which in P. Vivax contain on average 16 merozoites, rupture releasing their contents into the bloodstream. In the course of a cycle, it is assumed that a certain proportion (1-gamma) of the merozoites are eliminated by the immune system, and that of the remainder a proportion (beta) enter the blood cells. Of those that enter blood cells, a small proportion (1-alpha) subdivide to form schizonts and even fewer generate gametocytes. The supply of young blood cells is also replenished. The way in which this mechanism has been constructed and the specific parameters used (which have been chosen to reflect the authors' current knowledge of P. Vivax) can be inspected by redefining the screen display thus:
picture is [textnumofinfectablerbcs, textfreeinblood, textinbcs, textdividing, textgametesinblood, buttenterbc, buttkillinf, buttmerodiv];
To restore the original display, the following definition should be reintroduced:
picture is (spororad < 15) ? [cyclepoint, explanation, mosquitobite, blood, organs, cyclepoint, sporesgrow, liver, livercell, sporozoites, bloodcorp1, bloodcorp2, bloodcorp3, bloodcorp4, bloodcorp5, bloodcorp6, bloodcorp7, bloodcorp8, bloodcorp9, bloodcorp10, bloodcorp11, bloodcorp12, bloodcorp13, bloodcorp14, bloodcorp15] : [cyclepoint, explanation, mosquitobite, blood, organs, cyclepoint, sporesgrow, liver, sporozoites, bloodcorp1, bloodcorp2, bloodcorp3, bloodcorp4, bloodcorp5, bloodcorp6, bloodcorp7, bloodcorp8, bloodcorp9, bloodcorp10, bloodcorp11, bloodcorp12, bloodcorp13, bloodcorp14, bloodcorp15, bloodcorpinf1, bloodcorpinf2, bloodcorpinf3, bloodcorpinf4, bloodcorpinf5, bloodcorpinf6, bloodcorpinf7, bloodcorpinf8, bloodcorpinf9, bloodcorpinf10, bloodcorpinf11, bloodcorpinf12, bloodcorpinf13, bloodcorpinf14, bloodcorpinf15, gamete1, gamete2, gamete3, gamete4, gamete5, gamete6, gamete7, gamete8, gamete9, gamete10, gamete11, gamete12, gamete13, gamete14, gamete15, merozoite1, merozoite2, merozoite3, merozoite4];
References
- http://www.niaid.nih.gov/topics/Malaria/Pages/lifecycle.aspx
- Pierige, F et al (January 2008). Cell-based drug delivery. Advanced Drug Delivery Reviews 60 (2): 286.95
- Pukrittayakamee et al (Sept 2008). Effects of Different Antimalarial Drugs on Gametocyte Carriage in P. Vivax Malaria, Am J Trop Med Hyg, Vol 79
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