Retrieving elements from a Grid in C#?

Let's say I have a grid defined in XAML with 2 rows and 2 columns, with
a button in each cell defined by the grid:

<Grid x:Name="myGrid" >
<Grid.ColumnDefinitions>
<ColumnDefinition />
<ColumnDefinition />
</Grid.ColumnDefinitions>
<Grid.RowDefinitions>
<RowDefinition />
<RowDefinition />
</Grid.RowDefinitions>
<Button Grid.Row="0" Grid.Column="0" />
<Button Grid.Row="0" Grid.Column="1" />
<Button Grid.Row="1" Grid.Column="0" />
<Button Grid.Row="1" Grid.Column="1" />
</Grid>


My question is, can I programmatically get a reference to a particular
button object, given the row and column coordinates?

For example, I'd love to be able to do this:

Button buttonReference = myGrid.Children.get(0, 0);

and have it return the button at 0,0 in the grid. While inspecting the
API I can't seem to find something that would give me this desired
functionality. System.Windows.Controls.Grid has a property Children
(inherited from Panel) which returns a UIElementCollection. From there,
the best you can do it get an Enumerator and loop through the children.
There must be a way to pick out a single one, right? I'm going for
performance as I will be updating the content of each grid child quite
frequently, and I simply can't afford to enumerate the entire Children
collection each time.

Anyone found anything that may help?

Regards,
Jason