Yann Cortial

Adrien Peytavie

Eric Galin

Eric Guérin

Real-Time Hyper-Amplification of Planets

Keywords: Planets, Terrain modeling, Amplification, Adaptive parallel subdivision, Procedural generation

We propose an original method for generating planets with a high level of detail in real-time. Our approach relies on a procedural hyper-amplification algorithm: a controlled subdivision process that faithfully reproduces landforms and hydrosphere features at different scales. Starting from low-resolution user-defined control maps that provide information about the elevation, presence of large-scale water bodies and landforms types, we apply subdivision rules to obtain a high resolution hydrologically consistent planet model. We first generate a large-scale river network connected to inner seas and oceans, then synthesize the detailed hydrographic landscapes, including river tributaries and lakes, mountain ranges, valleys, plateaus, deserts and hills systems. Our GPU implementation allows to interactively explore planets that are produced by tectonic simulations, generated procedurally or authored by artists.

Introduction

The surface of planets represents a vast domain, typically several hundreds of millions of square kilometers, featuring a vast variety of landforms, and possibly a hydrosphere and an atmosphere. Modeling and generating huge scale environments with a high level of detail remains a complex problem in computer graphics. This challenge stems not only from the range of scales and their corresponding landforms and patterns that need to be synthesized, but also from the global geomorphological consistency that has to be preserved.

But for a few notable exceptions [START_REF] Ebert | Texturing and Modeling: A Procedural Approach, 3rd edn[END_REF][START_REF] Derzapf | River networks for instant procedural planets[END_REF][START_REF] Cortial | Procedural tectonic planets[END_REF], this challenge has seldom been investigated in computer graphics research. In contrast, the entertainment industry is investigating in the direction of large-scale procedural generation methods, a trend exemplified by the still-indevelopment game Star Citizen © . Pipelines for inter- active or real-time procedural planets generation and exploration have been proposed by professional studios. Those methods focus on control and mostly rely on blending heightfields authored by artists. Therefore, the generated terrains lack geomorphological coherence and consistency, for the most part due to the absence of hydrographic features. At the time of this writing, publicly available material allows to infer that the generated planets have a reduced 1:15 scale, i.e. a corresponding radius of ≈ 400km . A viable option for planet modeling would be to amplify a low resolution model by introducing details. Several terrain amplification methods such as sparse-modeling [START_REF] Guérin | Sparse representation of terrains for procedural modeling[END_REF] or deep learning [START_REF] Zhao | Multi-theme generative adversarial terrain amplification[END_REF] have been proposed for terrains, unfortunately those Fig. 2 Given a low-resolution representation of a planet (at ≈ 50km precision), our method performs a hierarchical procedural hyper-amplification process based on subdivision rules to generate a detailed representation of the relief (at ≈ 50cm precision) featuring a vast variety of coherent landforms at different range of scales, such as large rivers and mountain ranges, smaller valleys and hills, lake shores and river banks.

approaches are limited both in terms of amplification magnitude and size of the terrain that may be processed.

In this paper, we address the problem of generating detailed planets while allowing interactive exploration. Our method proceeds in two major steps. Starting with a CPU pre-processing phase, we generate a low-resolution model of the planet that describes the landforms and the river network at a large scale of about 50 km. This low-resolution model is then refined in a real-time, multi-resolution, hyper-amplification method based on hierarchical rule-based subdivisions on the GPU. Amplification allows the generation of new river branches, augmenting the initial network and producing realistic basins with drainage patterns, lakes, valleys with cross sections and landforms, driven by low-resolution user control maps (Figure 1). We implemented our method on graphics hardware which enabled real-time exploration of the synthesized planets at any-scale.

Our contributions are as follows: 1) We propose a real-time hyper-amplification algorithm for generating detailed planet relief with coherent water bodies. Our approach based on hierarchical subdivision rules generates high resolution elevation at a ≈ 50cm precision (Figure 2) from control maps at a ≈ 50km precision yielding a ≈ 10 5 × 10 5 amplification factor. 2) Our method generates river networks and synthesizes geomorphologically and hydrologically coherent planets with consistent valleys and landforms. 3) Our framework provides a high level control over the distribution of landforms and patterns; moreover additional specific landforms can be prescribed by using overriding global control maps and locally changing the final model. The generation of the detailed relief of the planet relies on a constrained subdivision process that lends itself for a parallel graphics hardware implementation (for reproducibility reasons, the source code will be released upon acceptance).

Related Work

Our work relates to procedural planet modeling, terrain amplification, and subdivision techniques. Here we briefly review those categories and refer the reader to a recent terrain modeling survey [START_REF] Galin | A review of digital terrain modeling[END_REF] for general terrain generation techniques.

Virtual Planets are in general procedurally generated, for computational efficiency reasons, by combining coherent noise functions at different scales and frequencies to approximate fractional Brownian motion and generate fractal relief [START_REF] Ebert | Texturing and Modeling: A Procedural Approach, 3rd edn[END_REF]. Mid-point displacement techniques were proposed to generate river networks over an entire planet [START_REF] Derzapf | River networks for instant procedural planets[END_REF]. Unfortunately, the underlying homogeneous and isotropic fractal model fails at generating realistic reliefs at all scales, from continents to local landforms such as mountains. A procedural approximation of plate tectonics was recently proposed in [START_REF] Cortial | Procedural tectonic planets[END_REF] to generate large-scale features such as continents, island arcs and mountain ranges. Relief details are produced by a real-time amplification of the planet using heightfield blending and combining noise functions, which cannot guarantee geomorphological coherence. The method does not generate river networks, and the resolution of the synthesized terrains is limited to ≈ 100m. In contrast, our approach generates a consistent global river network and relies on hierarchical subdivision rules to produce detailed river patterns.

Amplification techniques incrementally add details onto an initial low-resolution terrain. A commonly used technique consists in adding high-frequency noise scaled according to the characteristics of the input terrain [START_REF] Ebert | Texturing and Modeling: A Procedural Approach, 3rd edn[END_REF]. Sparse modeling [START_REF] Guérin | Sparse representation of terrains for procedural modeling[END_REF] replaces low-resolution local features by detailed landforms selected in a dictionary of atoms and generates more geomorphologically consistent details. The major drawback of these techniques is that they cannot guarantee the coherence of the drainage network. Recently, Generative Adversarial Networks [START_REF] Zhao | Multi-theme generative adversarial terrain amplification[END_REF] were proposed for learning styles from exemplars and amplifying terrains according to the analyzed details. While this method better preserves the overall hydrological consistency, it is limited to small amplification factors, in general about an order of magnitude. In contrast, we achieve a ≈ 10 5 × 10 5 amplification factor.

Subdivision techniques were used not only to generate reliefs but also create river networks that play an important part in the realism of large scale terrains. Diamond-square and square-square algorithms [START_REF] Fournier | Computer rendering of stochastic models[END_REF] synthesize fractal terrains with self-similar elevations using a unique random displacement rule applied after mid-point subdivision. Several enhancements were proposed to constrain the subdivision process with a view to providing better control. Prusinkiewicz et al. [START_REF] Prusinkiewicz | A fractal model of mountains and rivers[END_REF] introduced subdivision rules that account for the river network generation, and [START_REF] Belhadj | Modeling landscapes with ridges and rivers[END_REF] constrained subdivision to prescribed crests and rivers altitudes. Our method takes its inspiration from those methods: instead of relying on a single stochastic subdivision rule, we use a set of production rules at different levels of detail to generate a vast variety of landforms. [START_REF] Génevaux | Terrain generation using procedural models based on hydrology[END_REF] specifically directly addressed the problem of river network generation using a grammar-based network expansion, and then generated the elevation of the terrain according to the elevation of the river network. A similar strategy was employed in [START_REF] Argudo | Orometry-based terrain analysis and synthesis[END_REF] for synthesizing landscapes from graphs representing the ridges lines connecting peaks and the river network. Our method relies on consistent large-scale river networks generated at a low-resolution, and subdivision rules that automatically generate details.

Overview

Our algorithm (Figure 3) may be decomposed in three main steps: low-resolution planet synthesis from control maps, hyper-amplification using subdivision rules at different scales to generate details, and finally surface displacement to prescribe specific landform patterns.

Starting from a set of user-defined control-maps M, we first generate a low-resolution planet L as a spheri-cal triangulation whose vertices {p i } store control information such as mean crust elevation, age, wetness and landform type. The distance between two vertices of a triangle is ≈ 50km. This input can be either generated procedurally using fractal noise [START_REF] Ebert | Texturing and Modeling: A Procedural Approach, 3rd edn[END_REF], authored by artists, or even results from tectonic planet simulation methods [START_REF] Cortial | Procedural tectonic planets[END_REF]. The data structure of L embeds all the control parameters required to perform the real-time amplification of the planet surface, including large-scale main river networks, coastlines and mountain ranges.

The low resolution model is then recursively subdivided to generate a high-resolution representation of the planet H, according to landforms production rules S. The subdivision rules are controlled by the type of the landforms stored at the vertices and edges, the values of the corresponding control parameters, and the level at which subdivision rules are applied.

More precisely, the production rules rely on the following set of control parameters. Crust elevation C ∈ [-10 4 , 10 4 ] provides a hint about the relief of the planet at low-resolution, defining continents and oceans and the large-scale mountain ranges, massifs, and plains. As subdivision takes place, true elevations are produced and eventually characterize the exact relief of the surface of the planet. Orogeny age A ∈ [0, 10 8 ] allows to distinguish between young and ancient mountain ranges, and plays an important part in the choice of subdivision rules for producing smooth rounded mountains or high spiky mountains. Humidity W ∈ [0, 1] can be viewed as a precipitation map, defines arid and wet areas, and controls the distribution of lakes as well as specific landforms like mesas and terraces in rocky deserts. Plateau and hill presence, denoted as P ∈ [0, 1] and B ∈ [0, 1] respectively, control the presence of the corresponding landforms.

Low resolution model generation

Whenever the low resolution planet is not directly provided as a mesh, which may be the case for function- based representations [START_REF] Ebert | Texturing and Modeling: A Procedural Approach, 3rd edn[END_REF], we generate it as illustrated in Figure 5. We first sample the surface of the planet provided by the user using a Poisson Disk distribution [START_REF] Bridson | Fast poisson disk sampling in arbitrary dimensions[END_REF] at a 50km precision. From the samples, we construct a spherical Delaunay triangulation, using incremental algorithms adapted to the spherical domain, i.e. by relying on geodesic distances instead of Euclidean distances. The goal is to produce an initial irregular triangulation, in order to avoid rectilinear and otherwise unrealistic large-scale rivers. Our experiments show that an acceptable candidate is the triangulation of Poisson samples. Starting with an initial octahedron or icosahedron and using dyadic subdivision does not produce realistic rivers, even with strong jittering, since geometric patterns are still clearly detected by the human eye. The Delaunay property also garantees well formed triangles, which is important since triangles will undergo massive subdivision in our process. This triangulation is then regularized in order to produce well-defined coastal triangles, capable of producing estuaries (Figure 5d). This enables the generation of the river networks, starting from the coasts towards the centers of the continents and islands in a similar way to [START_REF] Génevaux | Terrain generation using procedural models based on hydrology[END_REF]. We finally compute the length of the rivers, their Horton-Strahler index [START_REF] Horton | Erosional development of streams and their drainage basins; hydrophysical approach to quantitative morphology[END_REF] which allows to evaluate the water flow.

λ = 11, ≈ 24m λ = 8, ≈ 200m λ = 5, ≈ 1.5km λ = 2, ≈ 12.5km
The triangulation of low-resolution planets involves two computationally intensive steps: the Poisson disc sampling and the Delaunay triangulation. They are performed once and for all during a pre processing step (on the CPU, generating 230k vertices and 460k triangles with an average edge length of 52km takes 9.2 seconds).

The computation of the parameters at the vertices p i and the parameters of the river network is performed in ≈ 0.5 second.

Adaptive subdivision

Our planet amplification scheme is based on a hierarchical rule-based subdivision process, which uses sets of rules operating at different scales.

We use a two stage approach for generating the surface details. First, we refine the triangles of the model using a dyadic scheme, i.e. inserting a new vertex at the center of every edge. It is a rule-based process, controlled by the various local configurations found in the triangulation. Both vertices and edges have types associated to them, which serve to identify these configurations. This first step produces an adaptively refined triangulation according to the desired level of detail (Figure 4).

The second stage involves the post-processing of the resulting triangulation, by displacing vertices vertically in order to shape riverbeds and valleys, as described in Section 6.

Subdivision

The real-time subdivision of the triangulation relies on a set of rules, which are triggered depending on the configuration of the vertices and edges. Let R, T and U denote the edge types associated to river, terrain, and unknown respectively. Let r, t, l, s, g and u denote the vertices types associated to river, terrain, lake, sea, gully and unknown respectively. In our implementation, aside from the necessary topology information, edges are characterized by their type. Vertices store their type and the parameters detailed in Table 1 and Section 5.2.

According to the desired level of detail, the triangulation is subdivided using a rule-based algorithm in order to obtain the desired landforms. The subdivision algorithm is sequentially divided in two steps. First, we subdivide each triangle edge with semantic production rules (Figure 6), and compute the associated parameters of each new vertex using a compute graph. Then,

a) b) c) d) r b r a t c

Symbol Description

x Type ∈ {River, Terrain, Lake, Gully, Sea} we create the three internal edges inside a split triangle and assign edges types using a second specific set of rules (Figure 11). Edge subdivision This process splits an edge into two edges and adds a new vertex. An input configuration composed of a triplet (u a , U ab , u b ) triggers a specific rule depending on the configuration. Rules associated with River and Terrain vertex types are:

R1 (r a , R ab , r b ) → (r a , R ac , r c , R cb , r b ) R2 (r a , T ab , r b ) → (r a , T ac , t c , T cb , r b ) R3 (r a , T ab , t b ) → (r a , T ac , t c , T cb , t b ) R4a (r a , R ab , t b ) → (r a , R ac , r c , R cb , t b ) R4b (r a , R ab , t b ) → (r a , R ac , r c , T cb , t b ) R5 (t a , T ab , t b ) → (t a , T ac , t c , T cb , t b )
R1 transforms a river into two river sections (Figure 7), R2 is used to create crests between two river vertices (Figure 8), and R3 creates a terrain vertex along the slope (Figure 9). Rules R4a and R4b are used to increase the density of the river network and generate

3D view

Side view

r
Ia (t a , U ab , t b ) → (t a , T ab , t b ) Ib1 (r a , U ab , t b ) → (r a , R ab , t b ) if β is satisfied Ib2 (r a , U ab , t b ) → (r a , T ab , t b ) otherwise Ic (r a , U ab , r b ) → (r a , T ab ,

Vertices parameters

New created vertices are assigned a set of parameters. The global control parameters (A, W, P, B) are simply propagated as the average of the two input vertices parameters, at every level of detail. For the other parameters default averaging also applies but specific rules override if needed with specific compute graphs in order to produce specific landform features.

Compute graph

In order to control the terrain types and ensure continuity in our model, we combine a set of procedural nodes in a graph operating on continuous parameters, that we call a compute graph. Each procedural generation node is parameterized by the two input vertices parameters of the edge being split and defines specific features like mountains, hills, or plateaus. Depending on the configuration, and therefore the triggered rule, specific graphs are chosen. Figure 10 depicts the graph used for the (t, T , t) configuration, Figure 13 for the (r, T , r) configuration, and Figure 12 the (r, T , t) configuration. These are the most frequent configurations. Other configurations are similar or simpler.

Procedural nodes The purpose of these nodes is to compute vertices parameters. Among these parameters, the output elevation h i is derived from two input elevations h a and h b of the two parent vertices t a and t b as illustrated in Figure 7, 8 and 9. Thanks to the tagging of vertices with types (mainly river and terrain), these procedural nodes can guarantee natural landforms such as crests or valleys. Appendix A gives the detailed expressions we use for terrain nodes. Horizontal displacement In order to break the regularity and linearity of landforms, we apply a deterministic random horizontal displacement to the vertices. This translation is made with barycentric coordinates inside a randomly chosen triangle incident to the edge. To prevent self-intersections the new position is chosen inside a safe zone determined by the barycenters of the neighboring triangles (see Figure above). This step is especially important for rivers, lakes and dry rocky landscapes.

Specific landforms

Gullies are defined by vertices g, similar to river ones and have the same production rules R1 to R5. They have different generation parameters: they may have steeper slopes, and do not drain water, i.e. they act as dry drainage patterns.

Without lake With lake

Flat water surface Fig. 14 A lake is created as an extension of the river. Specific water height computation is introduced to guarantee its flatness.

Lakes are not endorheic, i.e. they are connected to the local river network (Figure 15). Our model handles lakes as an extension of rivers by taking advantage of the river transverse cross section prescription (Section 6). Generation rule R3 is modified to generate a lake and replace the terrain vertex into a lake. This is randomly triggered at a specific level of detail, based on a probability depending on the local wetness W(p). Lake vertices serve as an extension of the riverbed. Specific water height computations are triggered for lakes in order to guarantee that locally, the river and its neighboring lake will become planar and not flow as usual (Figure 14). Once the subdivision is complete, we perform an important subsequent and final amplification step to produce realistic landforms conforming to the archetypes described in geomorphology (Figure 16).

Reference elevation Lakes

We modify the elevation of the subdivided terrain, on a per-vertex basis, according to the distance to the nearest river d r and its elevation h r to carve the riverbed and shape the valleys (Figure 17). The cross-section of the valley, both in steepness and width, is determined by the river flow estimate ||φ||, which is also a pervertex parameter carried through the subdivision. We use a power law [START_REF] Argudo | Orometry-based terrain analysis and synthesis[END_REF] for the relationship between the flow value and the valley shape, higher drainage induce less slope and broader valleys. A cubic Hermite interpolation is used to blend the resulting profile with the existing raw subdivided terrain, in order to avoid unnatural slope discontinuities at boundaries. The cross-section of the valley is defined by a reference e r to an archetype one-dimensional curve representing the normalized valley elevation. Transverse cross sections archetypes have been proposed for different types of valley in geomorphology and have been used successfully for carving valleys as in [START_REF] Argudo | Orometry-based terrain analysis and synthesis[END_REF]. Our framework relies on parametrized template models that lend themselves for on the fly evaluation and graphics hardware implementation. Real cross-sections from earth data-sets could be used instead, resulting in more re- alistic valley shapes, at the expense of a more memory intensive data-driven terrain representation.

Implementation details

A key feature of our method is that it lends itself for parallel implementation on graphics hardware, which allows for real-time exploration of the planet (Figure 18).

Architecture The hyper-amplification subdivision and its post-process are performed using GPGPU compute shaders through a number of sequenced stages. The triangulation stays in video memory during this process, thus avoiding expensive transfers. The whole process is run once every n ≈ 10 frames, and the output is directly streamed to the graphics pipeline for rendering.

During each modeling run, the target level of detail is first reached by iteratively calling four sequenced jobs: edge splitting, ghost-vertex marking, ghost-edge splitting and face splitting. Ghost operations guarantee a crack-free terrain geometry: ghost vertices are located at the middle of unsplit edges that belong to faces that need to be split. These four jobs represent one level of subdivision: they are repeated until no more edges remain to be split according to the desired level of detail.

We then displace the vertices of the triangulation according to the cross sections of the rivers and valleys. This process is followed by the bulk parallel creation of the water vertices, wherever visible, i.e. when the current vertex parameters obey h w > h. The water vertices are connected using the same topology as the underlying terrain mesh. The modeling run ends with the repositioning of the terrain ghost vertices affected by the cross sections, and the computation of terrain normals. Finally, the rendering stages build the indexed graphics primitives (i.e. terrain and water triangles) from the obtained modeling data for the current frustum-culled view, and performs the final deferred shading.

Determinism The output of the pipeline is deterministic and guarantees the coherent production of the terrain at different scales. All compute operations of stochastic nature need to be reproducible. Compute nodes produce elevations that need to be deterministic, i.e. invariant across subdivision runs. This is ensured by using a unique seed tied to each vertex, which is created as the sum of the seeds of the two vertices of each edge, as in [START_REF] Derzapf | River networks for instant procedural planets[END_REF]. Parallelism is also an issue, the computation of the new internal edges in a triangle needs to be handled with care, as different neighboring triangles could access the same vertex concurrently. To ensure that a branching river is always created in the same incident triangle to the main river edge, we rely on choosing among the two incident faces by drawing a random number from the seed tied to the junction river vertex.

Precision Issues arising from the large scale range are handled by making use of log-z depth buffering [START_REF] Cozzi | 3D engine design for virtual globes[END_REF] and of double-precision floating point representation wherever possible.

While double precision poses no problem in compute shaders, at least when using core OpenGL features, it remains challenging for the graphics stages. Note that the use of double precision is mandatory for virtual true-to-scale planets, as we need more than 7 significant digits to fully represent a given position at centimeter precision -for planet Earth (radius 6370km) indeed 9 digits are required. We use double floats projection matrices and vertex positions, however hardware interpolation for fragments is performed using single-precision only. To overcome this limitation, we interpolate and store in a 32 bits float the distance of the fragment to the camera; later in the fragment shader, we cast it to double precision and reconstruct the world position using the inverted double precision projection-view matrix. This allows for tri-planar texturing using shadercoded bi-linear interpolation performed on the double precision world coordinates. In our experiments, this approach provides stable, flicker-free texturing of the terrain even for textured details down to the order of the centimeter.

Results

We tested our prototype on an Intel i7-6700K clocked at 4.0 GHz with an NVIDIA GTX 1080Ti graphics card. Planets had approximately the size of the earth, (i.e., radius of 6370 km) and the maximum ground resolution was 50 cm at the highest level of detail (see accompanying video). We achieved a rendering frame rate of approximately 25 Hz for worst case low-altitude Fig. 19 Our method allows for the generation and control of a wide range of landforms features, like rivers and lakes (using W), hills (using B), young vs. old mountains (using A) and plateaus (using P).

views with computationally intensive shading for water animation, atmospheric effects and double-precision terrain texturing. Relief generation, performed every 10 frames, including subdivision, cross section specification and post-processing, took on average 80 ms, but this result is highly varying, depending on how close to the ground the camera gets, with worst-case peaks above 100 ms for close-to-ground views at centimeter precision where the total number of terrainonly triangles reaches 4 millions. The break-down of an average modeling run is as follows, the subdivision takes ≈ 50 ms (of which 44% is devoted to splitting edges, 15% on ghost operations and 41% to splitting faces) while riverbeds and valleys carving represents a few 3 ms, lastly the post-processing of the mesh takes roughly 30 ms. The cost of the adaptive surface generation is amortized over the 10 frames, and the GPU is free to schedule the compute jobs alongside graphics passes -this in turn allows for real-time exploration as demonstrated in the accompanying video.

Control Our method offers control capabilities to the user with both high-level and localized expression. Highlevel control is achieved through global planet-scale specification in the form of input maps. Figure 20 showcases a reproduction of the earth obtained by providing the relief of continents and wetness maps at 50 km resolution into the system. Local control is possible, by overriding amplification during the per-vertex elevation displacement post-process, through the prescription of specific height fields at user-specified locations.

Figure 19 shows a variety of features produced by our model. Lakes were produced in regions where the wetness W was high. Plateaus and hills appeared where the types P and B had high values respectively. The continuity of the generated terrains is guaranteed by the interpolation of the parameters in the spatial domain and the smooth combination of the elevations in the compute graph. The shape of mountains was influenced by the orogeny age A, which produced more gentle, eroded, slopes for old mountains. The wetness parameter also influenced the shape and shading of the terrain as illustrated in Figure 21. Gullies and drainage patterns (Figure 23) also play an important part in the overall visual aspect of the detailed planetary surface.

We did not endeavor to test the authoring and editing potential of our system. However, it can be seen from the good performances we demonstrate, that such an approach would make sense. One can imagine altering the control maps by directly painting over the planet, both on a local or a global scale. In our current implementation half a second is needed to regenerate the whole low-resolution mesh including the base river network, whereas the subdivision and rendering are instantaneous. This is sufficient for interactive feedback and would therefore enable fluid authoring sessions. Discussion Our method compares favorably to standard subdivision techniques [START_REF] Fournier | Computer rendering of stochastic models[END_REF] as can be seen in Figure 1 and 22. This is the result of an adaptive subdivision process that accounts for the level of detail and adjusts to local features. Compared to other planet synthesis methods [START_REF] Ebert | Texturing and Modeling: A Procedural Approach, 3rd edn[END_REF][START_REF] Derzapf | River networks for instant procedural planets[END_REF][START_REF] Cortial | Procedural tectonic planets[END_REF], our approach provides a unified framework to synthesize and combine a variety of landforms such as river networks, mountain ranges, valleys and plains. Particularly, [START_REF] Derzapf | River networks for instant procedural planets[END_REF] is able to generate the surface of a planet along with a river network, but suffers from a very simple subdivision scheme for the terrain that does not exhibit special features such as our method. On the other hand, [START_REF] Cortial | Procedural tectonic planets[END_REF] shows large-scale features that are the consequence of tectonic phenomena, but cannot produce a river network. This method also relies heavily on a data driven amplification method, which is expensive in terms of storage. Contrary to most of the previous methods, our method provides a direct high-level control by allowing the user to define the low-resolution elevation L that influences the hyperamplification.

Limitations Our method is memory demanding and requires more than 2GB on the graphics card. The subdivision algorithm requires many parameters plus all the necessary topology information and flags stored in the triangulation. 32 bytes are used to store an edge,

Basic subdivision Our hyper-amplification

Fig. 22 Our method integrates landform features such as rivers, valleys, lakes, plateaus that look more natural than standard subdivision techniques.

32 bytes for a triangle, 48 bytes to represent the topology of vertex and 112 bytes to store the parameters. The use of double-precision for positions has a important impact. Water vertices buffers and other specific graphics buffers significantly increase the amount of required memory. Our prototype implementation could be optimized by packing some generation parameters such as W and P.

Although our method is efficient and capable of synthesizing realistic models, it yields undesirable artifacts when it comes to the shading of the geometry. This can be seen in the accompanying video most noticeably on snow-covered peaks, where the snow effect depends on vertex slope which varies from one subdivision run to another every ≈ 10 frames. This could be mitigated by applying a temporal anti-aliasing technique, or more thoroughly by introducing progressive morphing between the modeling runs. Note that the last option would be memory demanding, and not a trivial extension to our method. With this in mind, we leave such an extension as future work.

In terms of realism, the final river network is not dense enough compared to real data, which comes from the geometric constraints in the subdivision scheme. More realistic peaks and crests could be obtained by re-using orometry concepts recently introduced in [1], we left this implementation as a future work and focused on the hierarchical subdivision algorithm.

Without gullies

With gullies Fig. 23 Comparison of a terrain generated from a river edge with the corresponding influence region highlighted in green without (left) and with (right) drainage patterns.

Conclusion

We have introduced a hyper-amplification algorithm that generates the detailed relief of planet according to a low-resolution representation. The method relies on a multi-scale and landforms-aware subdivision scheme that generates a coherent river network. Our parallel implementation on graphics hardware shows real-time performance as for procedural noise-based terrains, but with a better variety and control over the generated landscapes.

In the quest for realism, an interesting direction consists in bridging the gap between our subdivision algorithm and data-driven approaches. In particular, the concept of exemplars of cross sections of real terrains could be generalized to shape more realistic valleys, enhance the distribution and the silhouette of peaks.

A Appendix -Procedural nodes

Here we detail the formulas used by the procedural nodes for the (t a , T ab , t b ) configuration represented in Figure 10. These nodes act as generators in the compute graph. We refer to the source code for the detailed calculation of the blending applied between nodes. Let ξ ∈ [0, 1] denote a pseudo-randomly generated number that depends on a seed attached to the new vertex, without loss of generality we consider the parent vertices t a and t b with minimum and maximum elevations h a < h b respectively. Let ∆ be the dependency on the current scale, λ being the Level of Detail, an integer starting with λ = 0 for the low-resolution model L: Hills offset This procedural node produces an elevation offset applied to the terrain surface:

∆ = 1 -
H i = min(H max , (

Fig. 3

 3 Fig.3Given several control maps M defining the crust elevation C, the orogeny age A, the wetness W and the landform type P or B, we synthesize an initial low-resolution model L which is recursively amplified in real time by using subdivision rules to generate details.

Fig. 4

 4 Fig. 4 Four different levels of detail λ from the same viewpoint.

Fig. 5

 5 Fig. 5 The pre-processing stage: (a) control maps M, (b) Poisson disk sampling yielding vertices p i , (c) spherical Delaunay triangulation, (d) coast processing, (e) river network growth and computation of the hydrographic characteristics such as Horton-Strahler index, flow φ i and water elevation.

Fig. 6

 6 Fig. 6 Illustration of two subdivision steps: a) starting triangle, b) dyadic subdivision and insertion of 3 new vertices, c) internal edges creation and instantiation of a river tributary, d) the process recursively repeats at increasing λ.

Fig. 7

 7 Fig. 7 Illustration of R1 where a river edge is subdivided and creates a new river vertex. The computation of this new vertex elevation has to respect the flowing of the river.

Fig. 9

 9 Fig.9Illustration of R3 where a terrain vertex is created along the slope.

Fig. 11

 11 Fig.11Internal edge type computation. We subdivide the triangle face by adding 3 edges linking the 3 new vertices of the previous step. The edge type is obtained by using specific rules for the internal edges. Blue indicates river vertices and edges, whereas gray indicates terrain.

Fig. 12

 12 Fig.12Elevation compute graph for the case (r, T , t).

Fig. 13

 13 Fig. 13 Elevation compute graph for the case where river vertices are connected by a Terrain edge (r, T , r).

Fig. 15

 15 Fig. 15 Our method allows for the generation and control of lakes: left image shows a reference elevation map produced by our hyper-amplification algorithm, whereas right image show the same region with lakes.

Fig. 16

 16 Fig. 16 Comparison between hyper-amplification using subdivision only (left) and with additional landform carving with riverbed and valley transverse cross section prescription (right). Both steps are performed in real-time on the GPU.

Fig. 17

 17 Fig. 17 Illustration of the transverse valley and riverbed generation, given the per-vertex parameters d r , h r and φ.

Fig. 18

 18 Fig. 18 Overview of the GPU pipeline: (orange) compute shaders, (blue) graphics pass.

Fig. 20

 20 Fig. 20 Example of hyper-amplification performed on a lowresolution representation of the earth, showcasing a progressive zoom on the South American continent.

Fig. 21

 21 Fig. 21 Influence of the wetness parameter W resulting in slightly different landscapes: (left) presence of water, smooth low-altitude terrain slopes, (right) stronger horizontal displacement hinting towards eolian erosion, dry riverbeds and terrace effects on rocky slopes.

2 (ξ γ - 1 )= ξ 2 C

 212 Classic mountainThe elevation h is obtained by a fractal interpolation of the 2 heights h a and h b .h = (1 -α)h a + αh bThe blending coefficient α depends on the mountain type (young, old, wet or dry):Peaks Peak elevations are defined according to the Crustelevation C : Old Dry h = ξC Old Wet h = (1 -ξ 2 )C Young hTerraced Mountain This node modifies an input elevation h i to obtain terrace features on dry bedrock areas:h = T +β 2 (3-2β)τ with T = h i τ τ, β = h i -T ττ represents the elevation step used for the terraces, which can be itself modulated by procedural nodes, although in our implementation we used a simple constant of 700 meters. Note that the Hermite interpolation factor β is clamped to [0, 1].

1 --||t a -t b || 3 ,

 13 if χ < 0.5 ||t a -t b ||, otherwise where ||t a -t b || is the current edge length, H max is a constant in our implementation indicating the maximum hills elevation (we used 800 m), and χ is a uniform random number in [0, 1].

Table 1

 1 Parametrization of the terrain vertices

	h	Elevation
	h w	Water elevation
	h r , d r	Nearest riverbed elevation and distance
	φ	River flow
	e r	River cross-section reference
	s h , s d	Nearest gully elevation and distance

  Illustration of R2 where a crest is created between two valleys. The new elevation shall be higher than the two river altitudes.new river branches by adding a new tributary, it is only possible after the second subdivision, i.e. when internal edges have been created. R4b is applied when the level of detail has reached a threshold, this prevents rivers to be too close to mountains peaks.

				h max
	r a	t ab	r b	h ab h min h a	t ab
				a		r b
	r a Fig. 8 3D view t ab	t b	r a h ab h a h max h min	Side view t ab	t b

  r b ) Rules Ib1 and Ib2 are variants, the production of Ib1 allows the triggering of rule I4a in return, which makes the river network denser (Figure11 right). This rule is applied only if β is satisfied. The condition β combines several tests. A first test is checked on the angle between the existing river edge and the new one, Elevation compute graph for the case where terrain vertices are connected by a Terrain edge (t, T , t).which should be less than 90°to avoid a counter intuitive visual aspect of the confluence point. Another test consists in being on the right level of detail, in practice a tributary appears on internal edges of length ranging in ≈[START_REF] Bridson | Fast poisson disk sampling in arbitrary dimensions[END_REF] 25] km. Additionally, this internal river edge should always appear in the same triangle incident to the main river edge, this is guaranteed by enforcing determinism as described in Section 7. If the condition β passes then the new river edge appears, otherwise we add a new gully instead.

		Old Dry Mountain	Old Wet Mountain	Young Mountain	Terraced Mountain	Old Dry Peak	Old Wet Peak	Young Peak	Hills	multiply
		blend		blend		blend		blend	blend	blend	Hills	Wetness W, LOD λ Distance to river d r
	Wetness W Base Terrain		Age A	Wetness W, age A, LOD λ, elevation h	Peaks	Wetness W	Age A	LOD λ	+	Plateau P blend	Elevation Final
	Fig. 10 r a r a r a
	r ab		t ac	r ab		t ac	r ab	t ac
	r b	t bc	t c	r b	t bc	t c	r b	t bc	t c

Adaptive Subdivision

(each N frames)


Guy H Fontaine

Guoliang Li

Ardan M Saguner

Robert Frank
email: robertfrank@sfr.fr

Frank Robert

Mechanisms of torsade de pointes tachycardia in patients with spontaneous high-degree AV block: A modern look at old data

Keywords: ECG Leads, Waveform Morphology, Adult torsade de pointes, electrocardiogram, endocardial mapping, atrioventricular block

Introduction: The mechanisms of torsade de pointes tachycardia (TdP) are incompletely understood. In this study, we aimed to illustrate to mechanisms of torsade de pointes tachycardia in patients with spontaneous high-degree AV block. Methods: This retrospective study reviewed old TdP recordings after ventricular temporary pacing interruption in 16 patients with spontaneous high-degree AV block (AVB). Five of them had also bipolar endocardial right ventricular (RV) apex recordings. Results: The QT interval during AVB at a mean heart rate of 38.9 ± 7.5 bpm was 653 ± 67.2ms. The critical coupling interval (CCI) between the last escape QRS during AVB and the first premature ventricular complex (PVC) was significantly shorter before the onset of TdP than before single PVCs and couplets. A morphologic crescendo of the escape T wave was observed before the onset of TdP, followed by a rhythmic and morphologic crescendo of PVCs. The escape RV apex electrograms showed the constant pattern of a rapid deflection similar to a Purkinje potential 40 to 80ms after the onset of the QRS, superimposed on a smooth low amplitude signal in 4 of them. Conclusions: This suggests a local fast conducting fiber among electrically depressed apical myocardium. The major endocardial T wave prolongation before the earlier initiating PVC suggests a phase 2 reentry mechanism due to early after depolarization. The induced TdP can be due to the changing outputs from one or two simultaneous RV moving reentry circuits between depressed fibers and fast conducting ones, possibly located in the thin crista supraventricularis structure which has several connections with the septum and the RV free wall.

COVER LETTER

Dear Prof. Adrian Baranchuk, Editor-in-Chief, Journal of Electrocardiology It is our great privilege to submit this original manuscript entitled "The mechanism of torsade de pointes tachycardia in patients with spontaneous high-degree AV block: A modern look at old data" to Journal of Electrocardiology.

Prof. Fontaine passed away last March, and left an unfinished text about his vision of torsade de pointes (TdP) that we completed. He was among the pioneers of modern electrophysiology, contributing to the understanding of bradycardia and tachycardia during the last 50 years We thought it could be a way to honor his contributions to our domain, his often original ideas, for instance in this paper, which is also a revue on long coupling torsade de pointes.

He retrieved 50 years old tracings, including 5 endocardial ones, in 16 patients without apparent cardiomyopathy besides a high-degree AV block, and reexamined them at the light of actual knowledge. It already showed TdP initiation via an increased dispersion of repolarization in adjacent ventricular myocardial fibers of patients with high degree AVB. Data are in keeping with phase 2 reentry as the triggering factors for TdP, and dual ventricular activation during TdP. He proposed the hypothesis that the RV crista terminalis, with its thin structure and wide surface and multiple connections could be the site for moving reentries with changing exits.

We confirm the manuscript is not under simultaneous consideration elsewhere. This study is an extension of previous data (ref [START_REF] Allessie | Circus movement in rabbit atrial muscle as a mechanism of tachycardia. III. The "leading circle" concept: a new model of circus movement in cardiac tissue without the involvement of an anatomical obstacle[END_REF][START_REF] Vandersickel | Short-Lasting Episodes of Torsade de Pointes in the Chronic Atrioventricular Block Dog Model Have a Focal Mechanism, While Longer-Lasting Episodes Are Maintained by Re-Entry[END_REF][START_REF] Birati | The site of origin of torsade de pointes[END_REF], and substantially adds to our previous findings. All authors are responsible for the contents and have read and approved the final version of the manuscript for submission toEuropace.

Thanks in advance for your consideration, Dr Robert FRANK robertfrank@sfr.fr, Institut de Cardiologie, Unité de Rythmologie, Hôpital de la Salpêtrière, 47-83 boulevard de l'Hôpital, 75651, Paris, France. Phone: + 33 6 09 07 82 94; Fax: 33-Torsade de pointes tachycardia (TdP) a rare but important cause of sudden death in young people with the genetically determined long QT syndrome. In these patients, the length of the QT interval is directly related to the arrhythmic risk modulated by genetic factors. TdP is also a major concern of the pharmaceutical industry for the development of cardiac and non-cardiac drugs. It is also important to understand the basic mechanisms of this form of polymorphic ventricular tachycardia (VT) when it occurs in patients with high-degree atrioventricular (AV) block. In 1966, this arrhythmia received the descriptive term of "Torsade de pointes". This name was chosen to describe the QRS that twists around the isoelectric line by Desertenne. [START_REF] Dessertenne | Ventricular tachycardia with 2 variable opposing foci[END_REF] Scientists from Germany reproduced this ECG pattern experimentally by pacing both ventricles in isolated pig hearts and confirmed the original hypothesis of two alternating activation sites [START_REF] D'alnoncourt | Torsade de pointes" tachycardia. Re-entry or focal activity?[END_REF]. Moreover, cellular electrophysiologists. [START_REF] Brachmann | Bradycardia-dependent triggered activity: relevance to drug-induced multiform ventricular tachycardia[END_REF][START_REF] Damiano | Effects of pacing on triggered activity induced by early afterdepolarizations[END_REF] determined that early after depolarization (EAD) should be the initial fundamental mechanism, as EAD are bradycardia-dependent and favored by QT prolongation, as are TdP. However, their perpetuation mechanism remains still discussed between automaticity and reentry. The role of M cells remains also discussed with diverging data from myocardium wedge preparations and from whole intact hearts. [START_REF] Kohl | Resolving the M-cell debate: mechanics matters[END_REF] The ECG recordings presented in this manuscript were performed between 1964 and 1970, at a time when most of these data was unknown. Some patients with coronary artery disease had "transient ventricular fibrillation (VF)", a term associated with poor prognosis, and others with complete AV block had what was called "tachyrhythmia" in English publications. [START_REF] Jensen | Adams-Stokes seizures due to ventricular tachydysrhythmias in patients with heart block: prevalence and problems of management[END_REF] There was also a waiting period with temporary pacing leads in those early times of pacemaker (PM) implantation. These original studies were undertaken to demonstrate that the arrhythmia could be prevented by pacing in some of these patients and that it reoccurred when pacing was interrupted. When this was confirmed, permanent pacemaker implantation became a routine procedure, but the exact mechanism of TdP and their relation to VT and VF was not fully elucidated.

In this study, we aimed to synthesize the actual knowledge with the data from these old observations. We also propose a potential site for the localization of this type of TdP.

Methods

Definitions

TdP has a complex definition, and what is specific is not really the torsade of QRS by itself, as there are other types of polymorphic VT, but its initiating complex, with a long short sequence on a long QT. In this series of AVB induced long QT, aborted sequences could be limited to the initial PVC or followed by one or several cycles of non-sustained VT with the same or different morphologies, with abrupt or progressive morphological changes, and sometimes degenerating into VF.

Study population

The study population consisted of 16 patients exhibiting 107 typical episodes of TdP during spontaneous high-degree AV block, and studied by surface ECG recordings 50 years ago. As explained above, these patients were waiting for definite PM implantation, PM replacement, and therefore had a temporary pacing bipolar electrode connected to an external pacemaker.

They were >65 years old (range 66-80 years), thirteen women and three men, and none was taking drugs known to prolong the QT interval. All had normal serum laboratory tests including serum potassium levels. There were no data on any familial disease. They all presented with type 2 second degree (Mobitz II) or third degree AVB. Most of them had well tolerated short episodes of TdP (less than 5 sec) preceded by premature ventricular complexes (PVCs), couplets, triplets etc. After the recording of several episodes on a standard ECG recorder, it was noticed that some of them had the same QRS morphologies at the initiation of the TdP. Therefore, to gain further insight, long-term bipolar ECGs were tape recorded in all, between a negative skin electrode placed in position V1 and a positive one placed in position V4, similar as lead II orientation, but in front of the right ventricle and the septum. Five of them had a simultaneous endocardial recording with the 1.2 cm bipolar pacing endocardial electrode. The precordial as the endocardial electrodes were connected to Tektronix 3A9 differential amplifiers with a band pass of DC to 60 Hz, in those times when specific electrophysiological equipment was not available. The amplifier output was connected to a tape recorder (Ampex SP 300, Redwood City, CA, USA). The tapes were subsequently reviewed with an oscilloscope (Tektronix 561A-3A72) to select episodes of TdP, which were printed on a channel ECG machine (Sanborn EH101371 Cambridge, MA, USA), later on a dual channel industrial ink pressure recorder (Clevite Brush 220 Chart Recorder Cleveland, OH, USA). All data were collected and reviewed by one of us (GHF) before they were entered into a spreadsheet for statistical analysis (Dell Statisticav12, Tulsa, OK, USA).

The critical coupling interval (CCI) between the last beat during AVB and before the first abnormal ventricular events such as PVCs, couplets, triplets and TdPs (defined by >3 consecutive complexes) were identified, numbered and measured with a caliper with a precision < 20ms. Finally, the occurrence of TdP after pacing interruption was repeatedly assessed. The CCIs and the amplitude of the last TdP beats were also analyzed. Histograms of each numeric variable were drawn to identify outliers. The comparison of populations with continuous variables was performed by the Student's test. A p value<0.05 was considered significant.

Preliminary results of this study have been previously published. [START_REF] Fontaine | A New Look at Torsades de Pointesa[END_REF][START_REF] Li | Intramyocardial block in patients with atrioventricular block[END_REF][START_REF] Li | Fragmented endocardial signals and early afterdepolarizations during torsades de pointes tachycardia[END_REF] This study is a more detailed and extended analysis of these previous reports.

Results

The QT interval during AV block at a mean heart rate of 38.9 ± 7.5 bpm was 653 ± 67.2ms

Ventricular event timings

All ventricular arrhythmic events were preceded by long diastoles from 1000 to more than 1500ms terminated by a junctional or ventricular escape (Figure 1A). After this escape beat, PVC occurred late, after the end of the prolonged T wave. Single PVCs were observed in 160 episodes with a CCI of 672 ± 44 ms (550-760), 121 couplets with a CCI of 676 ± 37 ms (560-760), 21 triplets with a CCI of 644 ± 39 ms (560-720), and TdP in 107 episodes with a CCI of 639 ± 52 ms (500-760) (p<0.05 for TdP vs. single PVCs and couplets), suggesting a trend to shorter coupling intervals for the onset of sustained TdP. The case presented in Figure 1A was the only one in which TdP did degenerate into fast regular VT and then VF. In the five patients with endocardial recordings (Figure 1B), the onset of endocardial activation on the RV apex diagnostic catheter was observed prior to or at the same time as the initiating PVC. TdP occurred separated by long periods without PVC in 11 patients.

Repolarization crescendo

The severe bradycardia induced progressive modifications of the T wave durations and shapes of the escape rhythms reflect an increasing dispersion of repolarization (Figure 1A, 2A and 2C) during several seconds before the first PVC. This "morphologic crescendo" announcing the onset of TdP was observed in 12 patients (75%), sometimes associated with monstrous "bumps" better seen on the endocardial recordings, bumps which could also progressively regress (Figure 2B), with PVC's disappearance.

Rhythmic crescendo

TdP episodes were generally preceded by a "rhythmic crescendo" of isolated PVCs, then couplets, triplets, quadruplets etc. (Figure 1A and 2A) inducing the classical long-short initiating cycle sequence. This was observed in all 16 cases. A decrescendo of these arrhythmias was observed in 11 patients after the end of a TdP period.

Ventricular complex morphologies

Periods of non-sustained TdP (up to around 30 seconds) showed several repetitive, almost identical morphologies, which could be classified into four major categories: 4 patients had a single one, 5 patients had 2, 6 patients had 3, and one had 4 morphologies (Figure 2C) with fusion beats. Of these, the initiating PVC morphology could be negative or positive in the bipolar precordial ECG recordings in the same patient (Figure 2C and2D). An abrupt change of QRS orientation from upward to downward is illustrated in Figure 3A, at the end of the TdP and was observed in four cases, the others without major change from the preceding cycles.

The single bipolar precordial derivation from the tape recordings did not allow a clearer identification of the site of PVC origin than a leftward and descending activation for a positive wave, which could be originating from the RV outflow tract (RVOT), and a negative one from the inferior part of the ventricles (Figure 2C), and fusions complexes.

Endocardial data were available from 5 patients, all from the RV apex bipolar electrode, and detailed elsewhere. [START_REF] Li | Intramyocardial block in patients with atrioventricular block[END_REF][START_REF] Li | Fragmented endocardial signals and early afterdepolarizations during torsades de pointes tachycardia[END_REF] All had an escape electrogram (EGM) with a sharp Purkinje-like potential synchronous with the middle of the QRS, superimposed to a low voltage surrounding signal in 4 of them (Figure 1B). A similar potential could be observed at the onset of the initiating PVC in case 1 from Figure 1B), preceded by a smooth potential before the QRS onset in continuity with the T wave of the escape beat, interpreted as EAD's from the same region. This kind of thin potential was observed at other moments of the recording with a later timing, during PVC's of other morphologies (Figure 2D) in the same patient.

Fragmentations were recorded in the next beats suggesting local inhomogeneity of the activation process (Figure 1B and2D). On the nowadays retrieved tracings, complete endocardial recordings during TdP were only available for one patient (Figure 3B).

Discussion

Since the original description of TdP in complete AV block, [START_REF] Dessertenne | Ventricular tachycardia with 2 variable opposing foci[END_REF] the electrocardiographic predictors of this situation are still discussed. Many previous work made possible to explain some of the observations made in our old ECG recordings. They gave further insight into the mechanisms of initiation and perpetuation of TdP in high-degree AV block. We are potentially dealing with a functional arrhythmogenic substrate, reflected by EGM fragmentations [START_REF] Li | Fragmented endocardial signals and early afterdepolarizations during torsades de pointes tachycardia[END_REF] which are not due to a fixed anatomic obstacle such as fibrosis resulting from the sequel of myocardial infarction, but likely to anisotropic propagation creating functional blocks. A relation with the familial forms of LQTS has also been proposed, as not all patients with chronic AV block develop long QT and TdP. There is genetic predisposition. [START_REF] Probst | Haploinsufficiency in combination with aging causes SCN5A-linked hereditary Lenegre disease[END_REF] The initiating complex TdP were reproducibly observed in all patients. After interruption of ventricular pacing there is a junctional escape rhythm with severe bradycardia and progressive T wave prolongation and shape modifications (Figure 1B and2). They reflect an increase in the physiologic heterogeneity of action potential durations. [START_REF] Moe | Functional block in the intraventricular conduction system[END_REF] After an abrupt change of the cycle length these modifications are progressive, but also differ between myocardial and Purkinje fibers. [START_REF] Denker | Effects of abrupt changes in cycle length on refractoriness of the His-Purkinje system in man[END_REF] This progression explains the rhythmic as well as the morphologic crescendo with irregular huge T wave bumps (Figure 1A and2A), announcing the occurrence of TdP. This increased repolarization duration can induce a prolonged repolarization dependent re-excitation, early afterdepolarisations, a phase 2 reentry marked as above by bumps on the prolonged action potentials descending part. These potentials can activate excitable neighboring myocardium, giving rise to the initiating PVC. It has been also demonstrated in patients, in familial TdP as in chronic AVB by RV endocardial map recordings. [START_REF] Bonatti | Recording of monophasic action potentials of the right ventricle in long QT syndromes complicated by severe ventricular arrhythmias[END_REF][START_REF] Zhou | Role of early afterdepolarization in familial long QTU syndrome and torsade de pointes[END_REF][START_REF] Miwa | Monophasic action potentials in patients with torsades de pointes[END_REF] It was also recognized on our bipolar recordings at the RV apex with wide open filters, which allowed to display early slow potentials superposed on the end of the T wave (Figure 2A) before the initiating PVC. The initiating role of subendocardial Purkinje fibers has been recognized as a possible source for EAD. It has also been shown at the onset of idiopathic VF. This was probable in one of our cases (Figure 2D).

The following QRS's

There is still a controversial debate about the nature of those following PVC's, new phase 2 reentry from the previous PVC's, namely EAD, or a sizable reentry circuit. However, as action potentials progressively shorten with further shorter cardiac cycles, phase 2 reentry should stop after some of them. Perpetuation should be due to another mechanism. Conversely the prematurity of the triggering PVC also enhances the repolarizations disparities, thus enhancing the anisotropic substrate allowing a functional reentry circuit to appear, as demonstrated in Allessie's leading circle model in a thin myocardial preparation without fibrosis. [START_REF] Allessie | Circus movement in rabbit atrial muscle as a mechanism of tachycardia. III. The "leading circle" concept: a new model of circus movement in cardiac tissue without the involvement of an anatomical obstacle[END_REF] Its moving location can explain the QRS changes, many times reproduced in experimental myocardial preparations as in full heart models, and interpreted as a rotor moving within the ventricles. This is consistent from El Sherif´s experimental acute dog model with AV block in 1997, and Vandersickel et al [START_REF] Vandersickel | Short-Lasting Episodes of Torsade de Pointes in the Chronic Atrioventricular Block Dog Model Have a Focal Mechanism, While Longer-Lasting Episodes Are Maintained by Re-Entry[END_REF] in a chronic one, with TdP induced after one or several EAD's. They show reentry around zones of functional blocks, with changes in circuit locations explaining the morphological changes. This is the most probable mechanism in the majority of experimental setups in AV block with drug induced TDP. It seems difficult to demonstrate it in humans, as it had been for rotors in ventricular fibrillation. However, the coexistence of fast conducting fibers with depressed ones suggested by our endocardial recordings are consistent with a substrate for localized reentry.

In our series some patients had sometimes only one morphology after the initiating complex, but the others had at least two main upward and downward orientations (Figure 2C, 2D and 3A) with fusion beats in between. For instance, in Figure 3B, once the TdP initiated, our RV apex endocardial bipolar signal changed cycle after cycle, with small modifications on the ECG bipolar precordial lead. When compared with the surface QRS the electrograms appear sometimes early, sometimes late, due to fusion from at least two distinct activation zones, with early positive or negative components, according to the direction of the passing front through the bipolar apex electrode. We are therefore led to think that at least two different simultaneous ventricular activation sites are available. This was the explanation in the initial hypothesis by Dessertenne. In our series the heart rate during TdP ranges up to 250-300 bpm. This speed is limited by the ventricular refractory periods, but as these progressively shorten with the cycle length the rate will accelerate. Moreover, at these rates, the myocardium may become ischemic and TdP can degenerate into VF as shown in Figure 1A after 30 seconds of tachycardia. These tracings during TdP are similar to another clinical situation where two different ventricular activation fronts also compete, in the WPW syndrome with two accessory pathways in atrial fibrillation (Figure 3C).

TDP interruption

TdP may stop spontaneously after any form of intramyocardial block, as presented in Figure 3A and 3B, or when there is less dispersion of repolarization visible on the surface tracing as shown on Figure 2B, or when reestablishment of pacing prematurely invades the myocardium in the opposite direction precluding reentry (Figure 3C).

Site of origin

The site of origin of the initiating beat has been studied by Birati et al [START_REF] Birati | The site of origin of torsade de pointes[END_REF] from surface ECG recordings in a population of 50 patients with various TdP etiologies, familial, drug induced or AV block. They found no correlation between etiology and QRS morphologies. From 874 impending episodes, 70% had initial PVC morphologies suggesting an RVOT site, 13% from the RV inferior wall, and 17% from the LV inferior wall. Limited to the 216 episodes with 12 lead ECG recordings, 48% were RVOT, 41% LV inferior wall, 11% RV inferior wall. 151 of those episodes were followed by TdP, of which 56% had an initial PVC compatible with an RVOT site, and the others from LV (32%) or RV (13%) inferior walls. Despite the limitations of QRS analysis, it shows that most of the initiating complexes came from the RV. It fits with the early occurrence of the RV apical endocardial potentials in our 5 patients as shown in Figure 1B. It was also the site of EAD recordings in patients with familial LQTS. [START_REF] Zhou | Role of early afterdepolarization in familial long QTU syndrome and torsade de pointes[END_REF][START_REF] Miwa | Monophasic action potentials in patients with torsades de pointes[END_REF] To our knowledge, there has been no other endocardial recording of an RV initiating PVC in AVB related TdP than in our 5 patients. However, as the patients without EGM recording had the same morphologies on their bipolar precordial ECG, we can assume that they could also have a RV origin.

Anatomical site for the reentry

It is interesting to speculate that if a thin structure exists in the ventricles, apt to propagate a circular activation front, as in Allessie's model, it should be in the right one, which has a thickness of 2-3mm as opposed to 5 to 9mm for the left one. GHF speculated that the region of interest for TdP to propagate could be the crista supraventricularis. In the anatomic study of two hearts from two patients (Figure 4 A, B andC), the crista has a thickness of one to three millimeters, as Thomas James published in 1985, [START_REF] James | Anatomy of the crista supraventricularis: its importance for understanding right ventricular function, right ventricular infarction and related conditions[END_REF] and can get thinner on its course. [START_REF] Kosinski | Morphogenetic aspects of the septomarginal trabecula in the human heart[END_REF] Therefore, to the best of our knowledge, we are the first to propose that in the human heart, the crista supraventricularis, the thinnest part of the RV, could be the anatomical substrate for most of those TdP. The crista supraventricularis is described by T.

James as a U-shaped folded structure connected to the high septal area, and with fibers diverging as a fan to the anterior RV. He stated that the crista "is crucially located to join the interventricular septum and left ventricle to much of the RV free wall". [START_REF] James | Anatomy of the crista supraventricularis: its importance for understanding right ventricular function, right ventricular infarction and related conditions[END_REF] This structure can be linked to the interventricular septal Purkinje net and could transmit activation to the antero-superior and postero-inferior sulci. In that structure the genesis of the QRS changing from upward to downward activation morphologies with fusion could be (Figure 4D) two simultaneous circuits with slightly different cycle lenghts and entrance block from one another, as suggested in our Figure 3A. Another mechanism could be one moving circuit with slight cycle length changes and dual changing exits, with Wenckebach type conduction block to the rest of the ventricle (Figure 4D). This second hypothesis could explain the abrupt changes in two opposite directions observed at the beginning and at the end of a TdP (Figure 3A), the two exit sites being then able to activate one after the other.

Nowadays elaborate 3D mapping systems should be able to verify these propositions, at least with the opportunity of the rare cases with ablation of PVC´s initiating TdP. This was a retrospective study. All data in this study were obtained from patients treated in our hospital before 1970. The tape recordings are no more available. Only a single precordial bipolar ECG lead, in front of the RV and the septal area, was recorded in most of the tracings. Therefore, some interesting information may have been missed. Endocardial recordings only explored the RV apex, and there is no data on other locations, as recordings from the crista supraventricularis and from the left ventricle.

Conflict of interest

Authors have no conflict of interest to disclose. or "Depressed" (1): One moving circuit and two exit points (2), or two different simultaneous circuits isolated one from the other (3). Since reentry can happen within a small area of myocardium two different circus movement tachycardia circuits can be simultaneously present, yielding different morphologies and cycle lengths as illustrated in 3B.

Figure legends:

Figure 1 A

 1 Figure 1

Figure 2 A

 2 Figure 2

Figure 3 A 4 A

 34 Figure 3

Acknowledgements

We extend our gratitude to Frank I. Marcus, MD for his collaboration in the editing of the manuscript and Yvette Wingfield for her secretarial assistance, The University of Arizona College of Medicine, Tucson, AZ, USA.

Funding

This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors

Ethics

This is a retrospective study. When Guy H. Fontaine carried out these studies between 1965 and 1970, there were no ethical standards of a responsible committee on human experimentation (institutional or regional) as established 10 years later. This investigation was approved by the chief of cardiology as there was a clinical need for these patients to define in whom PM implant would be useful. An oral approved consent by the patient was obtained before the procedure.