I have two solutions:
A) Uses the visual tree
TreeViewItem selected = (TreeViewItem)dataSourceTreeView.SelectedItem;
double textWidth = 0;
double expanderWidth = 0;
Grid grid = (Grid)VisualTreeHelper.GetChild(selected, 0);
ToggleButton toggleButton = (ToggleButton)VisualTreeHelper.GetChild(grid, 0);
expanderWidth = toggleButton.ActualWidth;
Border bd = (Border)VisualTreeHelper.GetChild(grid, 1);
textWidth = bd.ActualWidth;
B) If you don't want to use the visual tree
TreeViewItem selected = (TreeViewItem)dataSourceTreeView.SelectedItem;
double textWidth = 0;
Typeface typeface = new Typeface(selected.FontFamily,
selected.FontStyle, selected.FontWeight, selected.FontStretch);
GlyphTypeface glyphTypeface;
if (!typeface.TryGetGlyphTypeface(out glyphTypeface))
throw new InvalidOperationException("No glyphtypeface found");
string headerText = (string)selected.Header;
double size = selected.FontSize;
ushort[] glyphIndexes = new ushort[headerText.Length];
double[] advanceWidths = new double[headerText.Length];
for (int n = 0; n < headerText.Length; n++)
{
ushort glyphIndex = glyphTypeface.CharacterToGlyphMap[headerText[n]];
glyphIndexes[n] = glyphIndex;
double width = glyphTypeface.AdvanceWidths[glyphIndex] * size;
advanceWidths[n] = width;
textWidth += width;
}