diff --git a/Sofa/Component/Topology/Container/Constant/src/sofa/component/topology/container/constant/MeshTopology.cpp b/Sofa/Component/Topology/Container/Constant/src/sofa/component/topology/container/constant/MeshTopology.cpp
index 5ae461075e0..d41efbaed97 100644
--- a/Sofa/Component/Topology/Container/Constant/src/sofa/component/topology/container/constant/MeshTopology.cpp
+++ b/Sofa/Component/Topology/Container/Constant/src/sofa/component/topology/container/constant/MeshTopology.cpp
@@ -492,6 +492,7 @@ MeshTopology::MeshTopology()
     , d_seqTetrahedra(initData(&d_seqTetrahedra, "tetrahedra", "List of tetrahedron indices"))
     , d_seqHexahedra(initData(&d_seqHexahedra, "hexahedra", "List of hexahedron indices"))
     , d_seqUVs(initData(&d_seqUVs, "uv", "List of uv coordinates"))
+    , d_computeAllBuffers(initData(&d_computeAllBuffers, false, "computeAllBuffers", "Option to compute all crossed topology buffers at init. False by default"))
     , nbPoints(0)
     , validTetrahedra(false), validHexahedra(false)
     , revision(0)
@@ -524,7 +525,6 @@ MeshTopology::MeshTopology()
 
 void MeshTopology::init()
 {
-
     BaseMeshTopology::init();
 
     const auto hexahedra = sofa::helper::getReadAccessor(d_seqHexahedra);
@@ -533,7 +533,6 @@ void MeshTopology::init()
     const auto triangles = sofa::helper::getReadAccessor(d_seqTriangles);
     const auto edges = sofa::helper::getReadAccessor(d_seqEdges);
 
-
     // looking for upper topology
     if (!hexahedra.empty())
         m_upperElementType = geometry::ElementType::HEXAHEDRON;
@@ -548,6 +547,11 @@ void MeshTopology::init()
     else
         m_upperElementType = sofa::geometry::ElementType::POINT;
 
+    // If true, will compute all crossed element buffers such as triangleAroundEdges, EdgesIntriangle, etc.
+    if (d_computeAllBuffers.getValue())
+    {
+        computeCrossElementBuffers();
+    }
 
     // compute the number of points, if the topology is charged from the scene or if it was loaded from a MeshLoader without any points data.
     if (nbPoints==0)
@@ -576,6 +580,7 @@ void MeshTopology::init()
         nbPoints = n;
     }
 
+
     if(edges.empty() )
     {
         if(d_seqEdges.getParent() != nullptr )
@@ -608,6 +613,72 @@ void MeshTopology::init()
     }
 }
 
+void MeshTopology::computeCrossElementBuffers()
+{
+    const auto hexahedra = sofa::helper::getReadAccessor(d_seqHexahedra);
+    const auto tetrahedra = sofa::helper::getReadAccessor(d_seqTetrahedra);
+    const auto quads = sofa::helper::getReadAccessor(d_seqQuads);
+    const auto triangles = sofa::helper::getReadAccessor(d_seqTriangles);
+    const auto edges = sofa::helper::getReadAccessor(d_seqEdges);
+
+    if (!hexahedra.empty()) // Create hexahedron cross element buffers.
+    {
+        createHexahedraAroundVertexArray();
+
+        if (!quads.empty())
+        {
+            createQuadsInHexahedronArray();
+            createHexahedraAroundQuadArray();
+        }
+
+        if (!edges.empty())
+        {
+            createEdgesInHexahedronArray();
+            createHexahedraAroundEdgeArray();
+        }
+    }
+    if (!tetrahedra.empty()) // Create tetrahedron cross element buffers.
+    {
+        createTetrahedraAroundVertexArray();
+
+        if (!triangles.empty())
+        {
+            createTrianglesInTetrahedronArray();
+            createTetrahedraAroundTriangleArray();
+        }
+
+        if (!edges.empty())
+        {
+            createEdgesInTetrahedronArray();
+            createTetrahedraAroundEdgeArray();
+        }
+    }
+    if (!quads.empty()) // Create triangle cross element buffers.
+    {
+        createQuadsAroundVertexArray();
+
+        if (!edges.empty())
+        {
+            createEdgesInQuadArray();
+            createQuadsAroundEdgeArray();
+        }
+    }
+    if (!triangles.empty()) // Create triangle cross element buffers.
+    {
+        createTrianglesAroundVertexArray();
+
+        if (!edges.empty())
+        {
+            createEdgesInTriangleArray();
+            createTrianglesAroundEdgeArray();
+        }
+    }
+    if (!edges.empty())
+    {
+        createEdgesAroundVertexArray();
+    }
+}
+
 void MeshTopology::clear()
 {
     nbPoints = 0;
diff --git a/Sofa/Component/Topology/Container/Constant/src/sofa/component/topology/container/constant/MeshTopology.h b/Sofa/Component/Topology/Container/Constant/src/sofa/component/topology/container/constant/MeshTopology.h
index d4b0d37e717..4d79f8cff17 100644
--- a/Sofa/Component/Topology/Container/Constant/src/sofa/component/topology/container/constant/MeshTopology.h
+++ b/Sofa/Component/Topology/Container/Constant/src/sofa/component/topology/container/constant/MeshTopology.h
@@ -86,6 +86,9 @@ class SOFA_COMPONENT_TOPOLOGY_CONTAINER_CONSTANT_API MeshTopology : public core:
 public:
     void init() override;
 
+    /// Method called by component Init method. Will create all the topology buffers
+    void computeCrossElementBuffers() override;
+
     Size getNbPoints() const override;
 
     void setNbPoints(Size  n) override;
@@ -348,6 +351,7 @@ class SOFA_COMPONENT_TOPOLOGY_CONTAINER_CONSTANT_API MeshTopology : public core:
     Data<SeqTetrahedra>      d_seqTetrahedra; ///< List of tetrahedron indices
     Data<SeqHexahedra>	   d_seqHexahedra; ///< List of hexahedron indices
     Data<SeqUV>	d_seqUVs; ///< List of uv coordinates
+    Data<bool> d_computeAllBuffers; ///< Option to call method computeCrossElementBuffers. False by default
 
 protected:
     Size  nbPoints;
diff --git a/Sofa/Component/Topology/Container/Dynamic/src/sofa/component/topology/container/dynamic/EdgeSetTopologyContainer.cpp b/Sofa/Component/Topology/Container/Dynamic/src/sofa/component/topology/container/dynamic/EdgeSetTopologyContainer.cpp
index 15ddadbc529..4e212ff7696 100644
--- a/Sofa/Component/Topology/Container/Dynamic/src/sofa/component/topology/container/dynamic/EdgeSetTopologyContainer.cpp
+++ b/Sofa/Component/Topology/Container/Dynamic/src/sofa/component/topology/container/dynamic/EdgeSetTopologyContainer.cpp
@@ -77,10 +77,10 @@ void EdgeSetTopologyContainer::init()
 
     // only init if edges are present at init.
     if (!m_edge.empty())
-        initTopology();
+        computeCrossElementBuffers();
 }
 
-void EdgeSetTopologyContainer::initTopology()
+void EdgeSetTopologyContainer::computeCrossElementBuffers()
 {
     // force computation of neighborhood elements
     createEdgesAroundVertexArray();
diff --git a/Sofa/Component/Topology/Container/Dynamic/src/sofa/component/topology/container/dynamic/EdgeSetTopologyContainer.h b/Sofa/Component/Topology/Container/Dynamic/src/sofa/component/topology/container/dynamic/EdgeSetTopologyContainer.h
index 2cf809bbe3a..ee9d4404c18 100644
--- a/Sofa/Component/Topology/Container/Dynamic/src/sofa/component/topology/container/dynamic/EdgeSetTopologyContainer.h
+++ b/Sofa/Component/Topology/Container/Dynamic/src/sofa/component/topology/container/dynamic/EdgeSetTopologyContainer.h
@@ -100,7 +100,7 @@ class SOFA_COMPONENT_TOPOLOGY_CONTAINER_DYNAMIC_API EdgeSetTopologyContainer : p
     /// Dynamic Topology API
     /// @{
     /// Method called by component Init method. Will create all the topology neighborhood buffers.
-    void initTopology();
+    void computeCrossElementBuffers() override;
 
     /** \brief Checks if the topology is coherent
      *
diff --git a/Sofa/Component/Topology/Container/Dynamic/src/sofa/component/topology/container/dynamic/HexahedronSetTopologyContainer.cpp b/Sofa/Component/Topology/Container/Dynamic/src/sofa/component/topology/container/dynamic/HexahedronSetTopologyContainer.cpp
index b8fb2b1c268..554a87f9352 100644
--- a/Sofa/Component/Topology/Container/Dynamic/src/sofa/component/topology/container/dynamic/HexahedronSetTopologyContainer.cpp
+++ b/Sofa/Component/Topology/Container/Dynamic/src/sofa/component/topology/container/dynamic/HexahedronSetTopologyContainer.cpp
@@ -83,12 +83,12 @@ void HexahedronSetTopologyContainer::init()
     }
 
     if (!m_hexahedron.empty())
-        initTopology();
+        computeCrossElementBuffers();
 }
 
-void HexahedronSetTopologyContainer::initTopology()
+void HexahedronSetTopologyContainer::computeCrossElementBuffers()
 {
-    QuadSetTopologyContainer::initTopology();
+    QuadSetTopologyContainer::computeCrossElementBuffers();
 
     // Create tetrahedron cross element buffers.
     createQuadsInHexahedronArray();
diff --git a/Sofa/Component/Topology/Container/Dynamic/src/sofa/component/topology/container/dynamic/HexahedronSetTopologyContainer.h b/Sofa/Component/Topology/Container/Dynamic/src/sofa/component/topology/container/dynamic/HexahedronSetTopologyContainer.h
index 65238e957a2..9bb8f012910 100644
--- a/Sofa/Component/Topology/Container/Dynamic/src/sofa/component/topology/container/dynamic/HexahedronSetTopologyContainer.h
+++ b/Sofa/Component/Topology/Container/Dynamic/src/sofa/component/topology/container/dynamic/HexahedronSetTopologyContainer.h
@@ -222,8 +222,8 @@ class SOFA_COMPONENT_TOPOLOGY_CONTAINER_DYNAMIC_API HexahedronSetTopologyContain
     /// Dynamic Topology API
     /// @{
 
-    /// Method called by component Init method. Will create all the topology neighborhood buffers and call @see TriangleSetTopologyContainer::initTopology()
-    void initTopology();
+    /// Method called by component Init method. Will create all the topology neighboorhood buffers and call @see QuadSetTopologyContainer::computeCrossElementBuffers()
+    void computeCrossElementBuffers() override;
 
     /** \brief Checks if the topology is coherent
      *
diff --git a/Sofa/Component/Topology/Container/Dynamic/src/sofa/component/topology/container/dynamic/QuadSetTopologyContainer.cpp b/Sofa/Component/Topology/Container/Dynamic/src/sofa/component/topology/container/dynamic/QuadSetTopologyContainer.cpp
index b9434772f7f..d861dfc5ea2 100644
--- a/Sofa/Component/Topology/Container/Dynamic/src/sofa/component/topology/container/dynamic/QuadSetTopologyContainer.cpp
+++ b/Sofa/Component/Topology/Container/Dynamic/src/sofa/component/topology/container/dynamic/QuadSetTopologyContainer.cpp
@@ -72,13 +72,13 @@ void QuadSetTopologyContainer::init()
 
     // only init if triangles are present at init.
     if (!m_quads.empty())
-        initTopology();
+        computeCrossElementBuffers();
 }
 
-void QuadSetTopologyContainer::initTopology()
+void QuadSetTopologyContainer::computeCrossElementBuffers()
 {
     // Force creation of Edge Neighborhood buffers.
-    EdgeSetTopologyContainer::initTopology();
+    EdgeSetTopologyContainer::computeCrossElementBuffers();
 
     // Create triangle cross element buffers.
     createEdgesInQuadArray();
diff --git a/Sofa/Component/Topology/Container/Dynamic/src/sofa/component/topology/container/dynamic/QuadSetTopologyContainer.h b/Sofa/Component/Topology/Container/Dynamic/src/sofa/component/topology/container/dynamic/QuadSetTopologyContainer.h
index 54a78981e3a..58efedcc105 100644
--- a/Sofa/Component/Topology/Container/Dynamic/src/sofa/component/topology/container/dynamic/QuadSetTopologyContainer.h
+++ b/Sofa/Component/Topology/Container/Dynamic/src/sofa/component/topology/container/dynamic/QuadSetTopologyContainer.h
@@ -144,8 +144,8 @@ class SOFA_COMPONENT_TOPOLOGY_CONTAINER_DYNAMIC_API QuadSetTopologyContainer : p
 
     /// Dynamic Topology API
     /// @{
-    /// Method called by component Init method. Will create all the topology neighborhood buffers and call @see EdgeSetTopologyContainer::initTopology()
-    void initTopology();
+    /// Method called by component Init method. Will create all the topology neighboorhood buffers and call @see EdgeSetTopologyContainer::computeCrossElementBuffers()
+    void computeCrossElementBuffers() override;
 
     /** \brief Checks if the topology is coherent
     *
diff --git a/Sofa/Component/Topology/Container/Dynamic/src/sofa/component/topology/container/dynamic/TetrahedronSetTopologyContainer.cpp b/Sofa/Component/Topology/Container/Dynamic/src/sofa/component/topology/container/dynamic/TetrahedronSetTopologyContainer.cpp
index d8fbe58adcd..5ad91e53519 100644
--- a/Sofa/Component/Topology/Container/Dynamic/src/sofa/component/topology/container/dynamic/TetrahedronSetTopologyContainer.cpp
+++ b/Sofa/Component/Topology/Container/Dynamic/src/sofa/component/topology/container/dynamic/TetrahedronSetTopologyContainer.cpp
@@ -79,12 +79,12 @@ void TetrahedronSetTopologyContainer::init()
     }
 
     if (!m_tetrahedron.empty())
-        initTopology();
+        computeCrossElementBuffers();
 }
 
-void TetrahedronSetTopologyContainer::initTopology()
+void TetrahedronSetTopologyContainer::computeCrossElementBuffers()
 {
-    TriangleSetTopologyContainer::initTopology();
+    TriangleSetTopologyContainer::computeCrossElementBuffers();
 
     // Create tetrahedron cross element buffers.
     createTrianglesInTetrahedronArray();
diff --git a/Sofa/Component/Topology/Container/Dynamic/src/sofa/component/topology/container/dynamic/TetrahedronSetTopologyContainer.h b/Sofa/Component/Topology/Container/Dynamic/src/sofa/component/topology/container/dynamic/TetrahedronSetTopologyContainer.h
index 089d3e6f7f2..2376324fbb2 100644
--- a/Sofa/Component/Topology/Container/Dynamic/src/sofa/component/topology/container/dynamic/TetrahedronSetTopologyContainer.h
+++ b/Sofa/Component/Topology/Container/Dynamic/src/sofa/component/topology/container/dynamic/TetrahedronSetTopologyContainer.h
@@ -193,8 +193,8 @@ class SOFA_COMPONENT_TOPOLOGY_CONTAINER_DYNAMIC_API TetrahedronSetTopologyContai
     /// Dynamic Topology API
     /// @{
 
-    /// Method called by component Init method. Will create all the topology neighborhood buffers and call @see TriangleSetTopologyContainer::initTopology()
-    void initTopology();
+    /// Method called by component Init method. Will create all the topology neighboorhood buffers and call @see TriangleSetTopologyContainer::computeCrossElementBuffers()
+    void computeCrossElementBuffers() override;
 
     /** \brief Checks if the topology is coherent
      *
diff --git a/Sofa/Component/Topology/Container/Dynamic/src/sofa/component/topology/container/dynamic/TriangleSetTopologyContainer.cpp b/Sofa/Component/Topology/Container/Dynamic/src/sofa/component/topology/container/dynamic/TriangleSetTopologyContainer.cpp
index cfc69119e8c..577727a1c01 100644
--- a/Sofa/Component/Topology/Container/Dynamic/src/sofa/component/topology/container/dynamic/TriangleSetTopologyContainer.cpp
+++ b/Sofa/Component/Topology/Container/Dynamic/src/sofa/component/topology/container/dynamic/TriangleSetTopologyContainer.cpp
@@ -73,13 +73,13 @@ void TriangleSetTopologyContainer::init()
 
     // only init if triangles are present at init.
     if (!m_triangle.empty())
-        initTopology();
+        computeCrossElementBuffers();
 }
 
-void TriangleSetTopologyContainer::initTopology()
+void TriangleSetTopologyContainer::computeCrossElementBuffers()
 {
     // Force creation of Edge Neighborhood buffers.
-    EdgeSetTopologyContainer::initTopology();
+    EdgeSetTopologyContainer::computeCrossElementBuffers();
 
     // Create triangle cross element buffers.
     createEdgesInTriangleArray();
diff --git a/Sofa/Component/Topology/Container/Dynamic/src/sofa/component/topology/container/dynamic/TriangleSetTopologyContainer.h b/Sofa/Component/Topology/Container/Dynamic/src/sofa/component/topology/container/dynamic/TriangleSetTopologyContainer.h
index 8c41f4a5ecd..ba0bfa3c8f9 100644
--- a/Sofa/Component/Topology/Container/Dynamic/src/sofa/component/topology/container/dynamic/TriangleSetTopologyContainer.h
+++ b/Sofa/Component/Topology/Container/Dynamic/src/sofa/component/topology/container/dynamic/TriangleSetTopologyContainer.h
@@ -151,8 +151,8 @@ class SOFA_COMPONENT_TOPOLOGY_CONTAINER_DYNAMIC_API TriangleSetTopologyContainer
 
     /// Dynamic Topology API
     /// @{
-    /// Method called by component Init method. Will create all the topology neighborhood buffers and call @see EdgeSetTopologyContainer::initTopology()
-    void initTopology();
+    /// Method called by component Init method. Will create all the topology neighboorhood buffers and call @see EdgeSetTopologyContainer::computeCrossElementBuffers()
+    void computeCrossElementBuffers() override;
 
     /** \brief Checks if the topology is coherent
      *
diff --git a/Sofa/framework/Core/src/sofa/core/topology/BaseMeshTopology.cpp b/Sofa/framework/Core/src/sofa/core/topology/BaseMeshTopology.cpp
index f1fbc45235f..7eb1494c17d 100644
--- a/Sofa/framework/Core/src/sofa/core/topology/BaseMeshTopology.cpp
+++ b/Sofa/framework/Core/src/sofa/core/topology/BaseMeshTopology.cpp
@@ -23,7 +23,6 @@
 #include <sofa/helper/io/MeshTopologyLoader.h>
 #include <sofa/helper/system/FileRepository.h>
 #include <sofa/core/objectmodel/BaseNode.h>
-
 namespace sofa::core::topology
 {
 
diff --git a/Sofa/framework/Core/src/sofa/core/topology/BaseMeshTopology.h b/Sofa/framework/Core/src/sofa/core/topology/BaseMeshTopology.h
index 2a5348f3eb3..b8b36581ab4 100644
--- a/Sofa/framework/Core/src/sofa/core/topology/BaseMeshTopology.h
+++ b/Sofa/framework/Core/src/sofa/core/topology/BaseMeshTopology.h
@@ -85,6 +85,9 @@ class SOFA_CORE_API BaseMeshTopology : public core::topology::Topology
 public:
     void init() override;
 
+    /// Method to be overriden by child class to create all the topology buffers
+    virtual void computeCrossElementBuffers() {}
+
     /// Load the topology from a file.
     ///
     /// The default implementation supports the following formats: obj, gmsh, mesh (custom simple text file), xs3 (deprecated description of mass-springs networks).
diff --git a/applications/plugins/MultiThreading/src/MultiThreading/component/collision/detection/algorithm/ParallelBVHNarrowPhase.cpp b/applications/plugins/MultiThreading/src/MultiThreading/component/collision/detection/algorithm/ParallelBVHNarrowPhase.cpp
index db0659a8504..3c1a0a06af7 100644
--- a/applications/plugins/MultiThreading/src/MultiThreading/component/collision/detection/algorithm/ParallelBVHNarrowPhase.cpp
+++ b/applications/plugins/MultiThreading/src/MultiThreading/component/collision/detection/algorithm/ParallelBVHNarrowPhase.cpp
@@ -132,22 +132,10 @@ void ParallelBVHNarrowPhase::initializeTopology(sofa::core::topology::BaseMeshTo
     auto insertionIt = m_initializedTopology.insert(topology);
     if (insertionIt.second)
     {
-        // The following calls force the creation of some topology arrays before the concurrent computing.
-        // Those arrays cannot be created on the fly, in a concurrent environment,
+        // We need to make sure all topology buffers are well created.
+        // Those arrays cannot be created on the fly later, in a concurrent environment,
         // due to possible race conditions.
-        // Depending on the scene graph, it is possible that those calls are not enough.
-        if (topology->getNbPoints())
-        {
-            topology->getTrianglesAroundVertex(0);
-        }
-        if (topology->getNbTriangles())
-        {
-            topology->getEdgesInTriangle(0);
-        }
-        if (topology->getNbEdges())
-        {
-            topology->getTrianglesAroundEdge(0);
-        }
+        topology->computeCrossElementBuffers();
     }
 }