Blur flowdocument in WPF

Question

I'm looking a way to blur FlowDocument like this:

 FlowDocument doc = new FlowDocument();
 BlurEffect blur = new BlurEffect();
 blur.Radius = 10;
 doc.Effect = blur; // it doesn't work! (FlowDocument doesn't have Effect property)

Update:

Above code is a part of a Converter which return FlowDocument for using in a FlowDocumentScrollViewer. Some items (returned flow documents) have specific conditions which should be blurred.

<DataGrid ItemsSource="{Binding Items}">
  <DataGrid.Columns>
     <DataGridTemplateColumn>  
         <DataGridTemplateColumn.CellTemplate>          
           <DataTemplate>
              <FlowDocumentScrollViewer 
                Document="{Binding ., Converter={StaticResource ItemToFlowDocConverter}}"/>                
           </DataTemplate>  
         <DataGridTemplateColumn.CellTemplate>       
    </DataGridTemplateColumn>
</DataGrid.Columns>