Field Secretion | Interacting with PDE Solver Fields

Related:

Methods

1. fieldSecretor.``secreteInsideCellTotalCount`` – returns a FieldSecretorResult` object that contains the summary of the secretion/uptake operation. Most importantly, when we access ``total_amount member of the res object we get the total amount that was added/uptaken from the chemical field e.g. :

cell.lambdaVolume –

Every field declared in a PDE solver is accessible by name in Python from every registered steppable using the property field, which allows us to retrieve and change the value of a field at a particular point by using the coordinates of the point as indices of the field. For example, if we have a PDE solver running with a field named ATTR and we would like to increment the value of ATTR at a point (10, 20, 30), we could write in a steppable,

self.field.ATTR[10, 20, 30] += 1

Likewise, we can manipulate a field using slicing operators, such as setting the value of our ATTR field to a value of 1.0 along a line,

self.field.ATTR[0:11, 20, 0] = 1.0

Note

The functionality described up to this point is also applicable for extra scalar and vector fields. They can also be accessed and manipulated using the field property of a steppable. For more on extra fields, see Adding and managing extra fields for visualization purposes.

Field Secretion

PDE solvers in CC3D allow you to specify secretion properties individually for each cell type. However, there are situations where you want only a single cell to secrete the chemical. In this case, you have to use Secretor objects. In Twedit++, go to the CC3D Python->Secretion menu to see what options are available. Let us look at the example code to understand what kind of capabilities CC3D offers in this regard (see Demos/SteppableDemos/Secretion):

class SecretionSteppable(SecretionBasePy):
    def __init__(self, frequency=1):
        SecretionBasePy.__init__(self, frequency)

    def step(self, mcs):
        attr_secretor = self.get_field_secretor("ATTR")
        for cell in self.cell_list:
            if cell.type == self.WALL:
                # Choose one of the secretion methods according to your use case
                attr_secretor.secreteInsideCellAtBoundaryOnContactWith(cell, 300, [self.WALL])
                attr_secretor.secreteOutsideCellAtBoundaryOnContactWith(cell, 300, [self.MEDIUM])
                attr_secretor.secreteInsideCell(cell, 300)
                attr_secretor.secreteInsideCellAtBoundary(cell, 300)
                attr_secretor.secreteOutsideCellAtBoundary(cell, 500)
                attr_secretor.secreteInsideCellAtCOM(cell, 300)

Note

[History] As we mentioned in the introductory section, we switched capitalization conventions for Python functions. For example, we use get_field_secretor and not getFieldSecretor. However, there are function calls in the above snippet that do not follow this convention - e.g. secreteInsideCell. This is because those functions belong to a C++ object (here, attr_secretor) that is accessed through Python. We decided to keep those two conventions (snake-case for pure Python functions) and Pascal-case for C++ functions. It provides a clue for where various functions come from.

In the step function, we obtain a handle to field secretor object that operates on diffusing field ATTR. In the for loop where we go over all cells in the simulation we pick cells that are of type 3 (notice we use a numeric value here instead of an alias). Inside the loop, we use secreteInsideCell, secreteInsideCellAtBoundary, secreteOutsideCellAtBoundary, and secreteInsideCellAtCOM member functions of the secretor object to carry out secretion in the region occupied by a given cell. See the secretion reference guide for more details.

secreteInsideCell: increases concentration by a given amount (here 300) in every pixel occupied by a cell.

secreteInsideCellAtBoundary and secreteOutsideCellAtBoundary: increases concentration but only in pixels at the cell’s boundary. The “inside” version chooses the cell’s pixels (recommended) whereas the “outside” version chooses pixels touching the cell’s boundary.

secreteInsideCellAtCOM: increases concentration for the single pixel that is closest to the cell’s center of mass.

Notice that SecretionSteppable inherits from SecretionBasePy. We do this to ensure that Python-based secretion plays nicely with PDE solvers. This requires that such steppable must be called before MCS, or rather before the PDE solvers start evolving the field. If we look at the definition of SecretionBasePy, we will see that it inherits from SteppableBasePy. In the __init__ function, it sets the self.runBeforeMCS flag to 1:

class SecretionBasePy(SteppableBasePy):
    def __init__(self, frequency=1):
        SteppableBasePy.__init__(self, frequency)
        self.runBeforeMCS = 1

Direct (but somewhat naive) Implementation

Now, for the sake of completeness, let us implement cell secretion at the COM using alternative code:

field = self.field.ATTR
lmf_length = 1.0;
x_scale = 1.0
y_scale = 1.0
z_scale = 1.0
# FOR HEX LATTICE IN 2D
#         lmf_length = sqrt(2.0/(3.0*sqrt(3.0)))*sqrt(3.0)
#         x_scale = 1.0
#         y_scale = sqrt(3.0)/2.0
#         z_scale = sqrt(6.0)/3.0

for cell in self.cell_list:
    # converting from real coordinates to pixels
    x_cm = int(cell.xCOM / (lmf_length * x_scale))
    y_cm = int(cell.yCOM / (lmf_length * y_scale))

    if cell.type == 3:
        field[x_cm, y_cm, 0] = field[x_cm, y_cm, 0] + 10.0

As you can tell, it is significantly more work than our original solution.

Lattice Conversion Factors

In the code where we manually implement secretion at the cell’s COM, we use strange-looking variables like lmf_length, x_scale and y_scale. CC3D allows users to run simulations on square (Cartesian) or hexagonal lattices. Under the hood, these two lattices rely on the Cartesian lattice. However, distances between neighboring pixels are different on Cartesian and hex lattices. This is what those 3 variables accomplish. The take-home message is that to convert COM coordinates on hex lattice to Cartesian lattice coordinates, we need to use converting factors. Please see writeup “Hexagonal Lattices in CompuCell3D” (http://www.compucell3d.org/BinDoc/cc3d_binaries/Manuals/HexagonalLattice.pdf) for more information. To convert between hex and Cartesian lattice coordinates we can use SteppableBasePy built-in functions (self.cartesian_2_hex, and self.hex_2_cartesian). You can use Twedit++’s Python snippets menu: Distances → Vectors → Transformations to get code like this:

hex_coords = self.cartesian_2_hex(coords=[10, 20, 11])
pt = self.hex_2_cartesian(coords=[11.2, 13.1, 21.123])

Tracking Amount of Secreted (Uptaken) Chemical

While the ability to have fine control over how the chemicals get secreted/uptaken is a useful feature, quite often we would like to know the total amount of the chemical that was added to the simulation as a result of the call to one of the secrete or uptake functions from the secretor object.

Let us rewrite the previous example using the API that facilitates tracking the amount of chemical that was added:

class SecretionSteppable(SecretionBasePy):
    def __init__(self, frequency=1):
        SecretionBasePy.__init__(self, frequency)

    def step(self, mcs):
        attr_secretor = self.get_field_secretor("ATTR")
        for cell in self.cell_list:
            if cell.type == 3:

                res = attr_secretor.secreteInsideCellTotalCount(cell, 300)
                print('secreted  ', res.tot_amount, ' inside cell')
                res = attr_secretor.secreteInsideCellAtBoundaryTotalCount(cell, 300)
                print('secreted  ', res.tot_amount, ' inside cell at the boundary')
                res = attr_secretor.secreteOutsideCellAtBoundaryTotalCount(cell, 500)
                print('secreted  ', res.tot_amount, ' outside the cell at the boundary')
                res = attr_secretor.secreteInsideCellAtCOMTotalCount(cell, 300)
                print('secreted  ', res.tot_amount, ' inside the cell at the COM')

As you can see, the calls that return the total amount of chemical added/uptaked are the same calls as we used in our previous example except we add TotalCount to the name of the function. The new function, secreteInsideCellTotalCount, returns an object called res that is an instance of the FieldSecretorResult class that contains the summary of the secretion/uptake operation. Most importantly, when we access total_amount member of the res object we get the total amount that was added/uptaken from the chemical field e.g. :

res = attr_secretor.secreteInsideCellTotalCount(cell, 300)
print('secreted  ', res.tot_amount, ' inside cell')

Volume Integrals

FieldSecretor objects also provide convenience methods to easily and quickly compute a volume integral of a PDE solver field over a particular cell or the entire simulation domain. Say we would like to construct another steppable to be also simulated with the previously described SecretionSteppable, and say this additional steppable computes the volume integral of the diffusing field ATTR everywhere for each cell. Such a steppable could look like the following…

Obtaining how much chemical the cell is exposed to (sampling)

To fetch the total amount of chemical a cell is exposed to we can simpli call secretor_object.amountSeenByCell(cell). In more detail

class SecretionSteppable(SecretionBasePy):
    def __init__(self,frequency=1):
        SecretionBasePy.__init__(self,frequency)

    def step(self,mcs):
        attr_secretor = self.get_field_secretor("ATTR")
        for cell in self.cell_list:
            print('Cell exposed to  ', attr_secretor.amountSeenByCell(cell), 'units of ATTR')

class IntegralSteppable(SteppableBasePy):
    def __init__(self, frequency=1):
        SteppableBasePy.__init__(self, frequency)

    def step(self, mcs):
        attr_secretor = self.get_field_secretor("ATTR")
        total_attr = attr_secretor.totalFieldIntegral()
        for cell in self.cell_list:
            cell_total_attr = attr_secretor.amountSeenByCell(cell)

Like in SecretionSteppable, a field secretor object is obtained for the diffusing field ATTR. However, IntegralSteppable computes the volume integral of the ATTR field over the simulation domain using the field secretor method totalFieldIntegral (and stores it in total_attr). Likewise, in a loop over every cell, IntegralSteppable then computes the volume integral of the ATTR field over the domain of each cell using the field secretor method amountSeenByCell by simply passing as argument a cell of interest (and stores it in cell_total_attr).

Algorithmic Considerations

Note that, in the previous example, IntegralSteppable inherits from SteppableBasePy instead of from SecretionBasePy. This distinction is important because CC3D calls step on all steppables that inherit from SteppableBasePy after executing diffusion by the PDE solvers. In our case, we are then enforcing that computing volume integrals occurs after diffusion and secretion have been implemented for a simulation step. If we were to simulate SecretionSteppable and IntegralSteppable with a PDE solver, then the order of calls to step would be executed as follows,

SecretionSteppable instance performs cell-based secretion for ATTR field
PDE solver performs diffusion of ATTR field
IntegralSteppable instance computes volume integrals of ATTR field