public string SpatialRelationshipDescription {get; set;}

{
  // Must be called within QueuedTask.Run
  void FindSpatiallyRelatedFeaturesUsingDE9IMPredicate(Geodatabase geodatabase, FeatureClass polygonFeatureClass, FeatureClass polylineFeatureClass)
  {
    using (RowCursor polygonRowCursor = polygonFeatureClass.Search(new QueryFilter()))
    {
      if (polygonRowCursor.MoveNext())
      {
        using (Feature polygonFeature = polygonRowCursor.Current as Feature)
        {
          // DE9IM predicate string to find overlapping features
          string overlappingDE9IM = "1*T***T**";

          SpatialQueryFilter spatialQueryFilter = new SpatialQueryFilter()
          {
            FilterGeometry = polygonFeature.GetShape(),
            SpatialRelationship = SpatialRelationship.Relation,
            SpatialRelationshipDescription = overlappingDE9IM
          };

          using (RowCursor overlappingPolyline = polylineFeatureClass.Search(spatialQueryFilter))
          {
            while (overlappingPolyline.MoveNext())
            {
              // Overlapping polylines on the polygon
            }
          }
        }
      }
    }
  }
}