Discretization

Discretization#

A morphology is continuous cable, but a simulation works on a finite set of state variables. Discretization is the step that divides the continuous geometry into discrete control volumes (CVs), each treated as a single isopotential compartment. This concept applies only to multi-compartment Cell models.

Control volumes#

A braincell.CV is one isopotential chunk of cable. The collection of CVs for a cell forms a CVTree whose connectivity mirrors the morphology. Each CV holds the membrane voltage and the channel states for its patch of membrane; adjacent CVs exchange current through axial resistance.

   one branch                          discretized into 3 CVs
   ●━━━━━━━━━━━━━━━━━━━━━●     ──▶      ●━━━━●━━━━●━━━━●
                                        CV0  CV1  CV2

The finer the discretization (more, shorter CVs), the more accurately voltage gradients along a dendrite are resolved — at the cost of more state and computation. Choosing the resolution is the job of a CV policy.

CV policies#

A braincell.CVPolicy decides how many CVs each branch receives. braincell provides several, which you can mix:

Policy

Rule

CVPerBranch

a fixed number of CVs per branch (e.g. one).

MaxCVLen

cap each CV’s physical length; long branches get more CVs.

DLambda

the classic d-λ rule: size CVs as a fraction of the AC length constant, so electrically long cable is discretized more finely.

CVPolicyByTypeRule

apply different rules to different branch types (e.g. fine soma, coarse axon).

CompositeByTypePolicy

compose several by-type policies into one.

 
import brainunit as u
import braincell

# the d-lambda rule at 100 Hz
policy = braincell.DLambda(frequency=100. * u.Hz)

# or: no CV longer than 20 microns
policy = braincell.MaxCVLen(20. * u.um)

Tip

The d-λ rule (DLambda) is the standard default in detailed modeling: it puts compartments where the cable physics needs them and spares them where it doesn’t. Start there unless you have a reason not to.

From CVs to runtime#

Once the CVs are fixed, braincell’s runtime layer (braincell._compute) builds an execution graph over them — a Node/ NodeTree of compute points — and assembles the frozen, JAX-friendly state that the integrator advances. You do not interact with this layer directly; it is what paint/place + a CV policy compile into.

See also#