Jérémie Jayet
email: jeremiejayet@gmail.com

MD Raphaël Coscas
email: rcoscas@gmail.com

PhD Frédéric Heim
email: frederic.heim@uha.fr

PhD Olivier Goeau Brissoniere
email: olivier.goeau-brissonniere2@orange.fr

Isabelle Javerliat
email: ijaverliat@yahoo.fr

MD Nabil Chakfe
email: nabil.chakfe@chru-strasbourg.fr

PhD Marc Coggia
email: mpcoggia@aol.com

LASER USES IN NON-CORONARY ARTERIAL DISEASE

Keywords: Excimer Laser, In stent restenosis, Atherosclerotic Plaques, In situ fenestration

Objectives: In the past decade, excimer laser angioplasty (ELA) has emerged in the field of peripheral atherosclerotic disease (PAD). Laser indications now extend to off-label uses, such as in situ fenestration of aortic endograft. The aim of this study was to review the different therapeutics applications of lasers in arterial disease treatment.

Review Methods:

We reviewed the English-language literature using the Preferred Reporting Items for Systematic Reviews and Meta-Analysis (PRISMA) guidelines. We selected 106 relevant papers. We excluded unrelated papers (n= 67), letters and commentaries (n = 6) and review articles (n=7), leaving 26 articles to form the basis of this review.

Results: A total of 18 articles were included in the analysis of ELA applications in PAD. Nine articles were related to atherosclerotic plaques. With a mean follow-up of 15±7 months, primary patency was 65%±20%.

Mean distal embolism rate during the procedure was 5%. Eight more articles focused on in-stent restenosis. The mean technical success was 98%, and the rate of distal embolism during the procedure was 9%. With a mean follow-up of 10±4 months, primary patency was 68%±18%. Eight articles described "off-label" excimer laser indications in endovascular therapy, including five papers regarding in situ fenestrations for complex aortic aneurysms.

Conclusion:

Laser atherectomy and laser assisted techniques are an important part of a vascular surgeon and interventionalist's armamentarium.

INTRODUCTION

Since 1960, light amplification by stimulated emission of radiation (laser) has appeared as an applicable energy source for medical use thanks to its unidirectional, pulsatile and monochromatic characteristics. The different physical mechanisms account for the many ways to exploit the capacity of laser technology in medical utilization [START_REF] Mlacker | Laser and light-based treatments of venous lakes: a literature review[END_REF][START_REF] Sjogren | Use of the carbon dioxide laser for tracheobronchial lesions in children[END_REF][START_REF] Davoudi | Application of Laser Irradiation for Restorative Treatments[END_REF][START_REF] Gupta | Is the holmium:YAG laser the best intracorporeal lithotripter for the ureter? A 3-year retrospective study[END_REF][START_REF] Park | Clinical efficacy of photodynamic therapy[END_REF][START_REF] Otsuji | Three-year results of a modified photodynamic therapy procedure (Ironing PDT) for age-related macular degeneration patients with large lesions[END_REF]. In this last decade, laser technology has emerged as a new tool in endovascular therapy [START_REF] Cochennec | Early Results of Physician Modified Fenestrated Stent Grafts for the Treatment of Thoraco-abdominal Aortic Aneurysms[END_REF][START_REF] Khoury | Evolution of atherectomy devices[END_REF]. Lasers in endovascular therapy were applied in the endovenous laser ablation for treating saphenous insufficiency [START_REF] Jibiki | Effect of the wide-spread use of endovenous laser ablation on the treatment of varicose veins in Japan: a large-scale, single institute study[END_REF]. Onlabel indications of excimer laser angioplasty (ELA) in peripheral artery disease (PAD), specifically in-stent restenosis [START_REF] Laird | Excimer laser with adjunctive balloon angioplasty and heparin-coated self-expanding stent grafts for the treatment of femoropopliteal artery instent restenosis: twelve-month results from the SALVAGE study[END_REF] and non-crossable chronic occlusions [START_REF] Bosiers | Excimer laser assisted angioplasty for critical limb ischemia: results of the LACI Belgium Study[END_REF], have appeared. More recently, other off-label indications have emerged for material ablation and fabric welding to perform in situ fenestration of aortic endografts [START_REF] Murphy | Endovascular repair of acute traumatic thoracic aortic transection with laser-assisted in-situ fenestration of a stent-graft covering the left subclavian artery[END_REF] .

The main laser used in arterial surgery is the excimer laser using the photoablative laser's characteristics. An excimer laser is produced by a high-energy voltage associated with a dimeric solution of xenon and hydrochloride. The high-voltage energy excites the dimer XeCl and creates a photon. The laser is conducted by optic fibers, at a wavelength of 308 nm located in the blue spectrum. Whereas many other lasers deliver their energy in the warm red spectrum, the excimer laser is a cold laser. This last characteristic allows vascular surgeons and interventionalists to use excimer laser with a theoretical low risk of thrombus formation or deterioration of the arterial wall. The light penetration depth is around 0.05 mm, and each photon carries enough energy to break a single carbon-carbon bond. Intracellular lipids and proteins absorb this high energy and are quickly destroyed. Finally, all the intracellular liquid is vaporized. Microscopic subcellular debris are created and washed distally with a theoretical benefit in terms of clinic emboli.

Whereas the first lasers were continuous-wave lasers, the excimer laser delivers its energy by pulse to avoid the heat diffusion from the catheter tip and the damage of surrounding tissues.

Each catheter conducts its energy from a generator to the catheter tip, composed of multiple optic fibers arranged around a guidewire lumen. Different diameters of the catheter exist according to the surgical applications, from 0.9 mm to 2.5 mm. Settings (Fluence (mJ/mm2) and rate (Hz)) can be modified per the power needed. In fact, for calcified lesions or occlusions, the average power should be increased to obtain a maximum debulking.

Two types of devices are commercially available. First, Turbo-Tandem (TT) (previous generation: Turbo-Booster (TB)/ CliRpath) (Spectranetics, Colorado Springs, CO, USA) is a laser-guided catheter combined with a laser atherectomy catheter, whereas Turbo-Elite (TE) (Spectranetics, Colorado Springs, CO, E-U) is just a laser atherectomy catheter. TT is preferred for diameters of target arteries over 5 mm or to obtain maximum debulking. Both devices progress on the wire after crossing the lesion or with a "step-by-step technique". A speed progression of the catheter of 1 mm/s is advised to be more effective.

The aim of this study is to review the different therapeutics applications of excimer lasers in endovascular therapy.

METHODS

A literature's review was performed using of the Preferred Reporting Items for Systematic Reviews and Meta-Analysis (PRISMA) guidelines [START_REF] Liberati | The PRISMA statement for reporting systematic reviews and meta-analyses of studies that evaluate healthcare interventions: explanation and elaboration[END_REF] Figure.

Search Strategy

We reviewed the English-language literature regarding the use of excimer laser on several medical databases:

Medline databases using a PubMed interface, the Cochrane Database, Web of Science, and Scopus. The search period was from June 2005 to May 2017. We used the key words "Excimer Laser", "in stent restenosis," "in situ fenestration."

Study Selection

Studies were included if they met the following criterion: laser uses in arterial disease including PAD and aortic or visceral procedures.

Clinical and experimental papers were studied. Only published data were included in this study. Two independent analysts (J.J. and R.C.) selected and further analyzed 106 relevant papers. We excluded unrelated papers (n= 67), letters and commentaries (n = 6) and review articles (n=7). Finally, 26 articles were included in the qualitative synthesis.

Data extraction

Data were extracted regarding the type of paper (clinical or experimental and case report or case series) and summarized using data extraction sheets. Relevant data were considered: on-label or off-label indications, number of subjects, device used (TE, TT or TB, or both), demographics, technical success, in situ fenestration type (retrograde or anterograde), in situ fenestration technique (catheter's diameter, graft type), technical success rate, and early and late results (primary patency, target lesion revascularization). Data were managed using three independent analyses: atherosclerotic plaques, in-stent restenosis, and off-label indications.

RESULTS

In selected articles, TE catheters were used in 1,107 cases (79%) [START_REF] Zhou | Laser atherectomy for lower extremity revascularization: An adjunctive endovascular treatment option[END_REF][START_REF] Dave | Excimer laser recanalization of femoropopliteal lesions and 1-year patency: results of the CELLO registry[END_REF][START_REF] Shammas | Distal embolic event protection using excimer laser ablation in peripheral vascular interventions: results of the DEEP EMBOLI registry[END_REF][START_REF] Serino | Excimer laser ablation in the treatment of total chronic obstructions in critical limb ischaemia in diabetic patients. Sustained efficacy of plaque recanalisation in mid-term results[END_REF][START_REF] Van Den Berg | Endovascular treatment of in-stent restenosis using excimer laser angioplasty and drug eluting balloons[END_REF][START_REF] Shammas | Safety and One-Year revascularization outcome of excimer laser ablation therapy in treating in-stent restenosis of femoropopliteal arteries: A retrospective review from a single center[END_REF][START_REF] Gandini | Treatment of chronic SFA in-stent occlusion with combined laser atherectomy and drug-eluting balloon angioplasty in patients with critical limb ischemia: a single-center, prospective, randomized study[END_REF][START_REF] Wu | Comparison of immediate and 2-year outcomes between excimer laser-assisted angioplasty with spot stent and primary stenting in intermediate to long femoropopliteal disease[END_REF][START_REF] Schmidt | Photoablation using the turbo-booster and excimer laser for in-stent restenosis treatment: twelve-month results from the PATENT study[END_REF][START_REF] Van Den Berg | In-stent restenosis: mid-term results of debulking using excimer laser and drug-eluting balloons: sustained benefit?[END_REF][START_REF] Dippel | Randomized controlled study of excimer laser atherectomy for treatment of femoropopliteal in-stent restenosis: initial results from the EXCITE ISR trial (EXCImer Laser Randomized Controlled Study for Treatment of FemoropopliTEal In-Stent Restenosis)[END_REF][START_REF] Sultan | Cool excimer laser-assisted angioplasty (CELA) and tibial balloon angioplasty (TBA) in management of infragenicular arterial occlusion in critical lower limb ischemia (CLI)[END_REF][START_REF] Armstrong | Laser Atherectomy for Treatment of Femoropopliteal In-Stent Restenosis[END_REF][START_REF] Wissgott | Excimer laser atherectomy after unsuccessful angioplasty of TASC C and D lesions in femoropopliteal arteries[END_REF][START_REF] Mallios | Laser atherectomy for the treatment of peripheral arterial disease[END_REF], whereas TT or TB [START_REF] Laird | Excimer laser with adjunctive balloon angioplasty and heparin-coated self-expanding stent grafts for the treatment of femoropopliteal artery instent restenosis: twelve-month results from the SALVAGE study[END_REF][START_REF] Dave | Excimer laser recanalization of femoropopliteal lesions and 1-year patency: results of the CELLO registry[END_REF][START_REF] Serino | Excimer laser ablation in the treatment of total chronic obstructions in critical limb ischaemia in diabetic patients. Sustained efficacy of plaque recanalisation in mid-term results[END_REF][START_REF] Shammas | Safety and One-Year revascularization outcome of excimer laser ablation therapy in treating in-stent restenosis of femoropopliteal arteries: A retrospective review from a single center[END_REF][START_REF] Wu | Comparison of immediate and 2-year outcomes between excimer laser-assisted angioplasty with spot stent and primary stenting in intermediate to long femoropopliteal disease[END_REF][START_REF] Schmidt | Photoablation using the turbo-booster and excimer laser for in-stent restenosis treatment: twelve-month results from the PATENT study[END_REF][START_REF] Dippel | Randomized controlled study of excimer laser atherectomy for treatment of femoropopliteal in-stent restenosis: initial results from the EXCITE ISR trial (EXCImer Laser Randomized Controlled Study for Treatment of FemoropopliTEal In-Stent Restenosis)[END_REF][START_REF] Armstrong | Laser Atherectomy for Treatment of Femoropopliteal In-Stent Restenosis[END_REF][START_REF] Rastan | Initial experience with directed laser atherectomy using the CLiRpath photoablation atherectomy system and bias sheath in superficial femoral artery lesions[END_REF] devices were used in 230 cases (16%), and CliRpath (first laser-guided catheter generation) was used in 51 cases (5%) [START_REF] Bosiers | Excimer laser assisted angioplasty for critical limb ischemia: results of the LACI Belgium Study[END_REF].

A total of 18 articles were included in the analysis of the applications of ELA in PAD. The main objectives and results of treatment of atherosclerotic plaques and in-stent restenosis are respectively shown in Tables 1 and2.

Eight other articles described off-label" excimer laser indications in endovascular therapy, including five papers regarding in situ fenestrations for complex aortic aneurysms.

Atherosclerotic plaques

Nine articles [START_REF] Bosiers | Excimer laser assisted angioplasty for critical limb ischemia: results of the LACI Belgium Study[END_REF][START_REF] Zhou | Laser atherectomy for lower extremity revascularization: An adjunctive endovascular treatment option[END_REF][START_REF] Dave | Excimer laser recanalization of femoropopliteal lesions and 1-year patency: results of the CELLO registry[END_REF][START_REF] Serino | Excimer laser ablation in the treatment of total chronic obstructions in critical limb ischaemia in diabetic patients. Sustained efficacy of plaque recanalisation in mid-term results[END_REF][START_REF] Wu | Comparison of immediate and 2-year outcomes between excimer laser-assisted angioplasty with spot stent and primary stenting in intermediate to long femoropopliteal disease[END_REF][START_REF] Sultan | Cool excimer laser-assisted angioplasty (CELA) and tibial balloon angioplasty (TBA) in management of infragenicular arterial occlusion in critical lower limb ischemia (CLI)[END_REF][START_REF] Wissgott | Excimer laser atherectomy after unsuccessful angioplasty of TASC C and D lesions in femoropopliteal arteries[END_REF][START_REF] Mallios | Laser atherectomy for the treatment of peripheral arterial disease[END_REF][START_REF] Rastan | Initial experience with directed laser atherectomy using the CLiRpath photoablation atherectomy system and bias sheath in superficial femoral artery lesions[END_REF] related to atherosclerotic plaques were found. A total of 847 atherosclerotic plaques were treated, and 783 TE (88%) and 104 TT or TB (12%) devices were used. Rastan et al. and Wu et al. both included in stent restenosis and atherosclerotic plaques. CliRpath device was used for 51 revascularizations. Among the nine articles, four included femoropopliteal lesions [START_REF] Dave | Excimer laser recanalization of femoropopliteal lesions and 1-year patency: results of the CELLO registry[END_REF][START_REF] Wu | Comparison of immediate and 2-year outcomes between excimer laser-assisted angioplasty with spot stent and primary stenting in intermediate to long femoropopliteal disease[END_REF][START_REF] Wissgott | Excimer laser atherectomy after unsuccessful angioplasty of TASC C and D lesions in femoropopliteal arteries[END_REF][START_REF] Rastan | Initial experience with directed laser atherectomy using the CLiRpath photoablation atherectomy system and bias sheath in superficial femoral artery lesions[END_REF]. Sultan et al.

included infra popliteal lesions, and the four last authors included femoropopliteal, infra popliteal, and combined lesions [START_REF] Bosiers | Excimer laser assisted angioplasty for critical limb ischemia: results of the LACI Belgium Study[END_REF][START_REF] Zhou | Laser atherectomy for lower extremity revascularization: An adjunctive endovascular treatment option[END_REF][START_REF] Serino | Excimer laser ablation in the treatment of total chronic obstructions in critical limb ischaemia in diabetic patients. Sustained efficacy of plaque recanalisation in mid-term results[END_REF][START_REF] Mallios | Laser atherectomy for the treatment of peripheral arterial disease[END_REF], respectively. Five articles specified the lesion length [START_REF] Zhou | Laser atherectomy for lower extremity revascularization: An adjunctive endovascular treatment option[END_REF][START_REF] Dave | Excimer laser recanalization of femoropopliteal lesions and 1-year patency: results of the CELLO registry[END_REF][START_REF] Wu | Comparison of immediate and 2-year outcomes between excimer laser-assisted angioplasty with spot stent and primary stenting in intermediate to long femoropopliteal disease[END_REF][START_REF] Sultan | Cool excimer laser-assisted angioplasty (CELA) and tibial balloon angioplasty (TBA) in management of infragenicular arterial occlusion in critical lower limb ischemia (CLI)[END_REF][START_REF] Wissgott | Excimer laser atherectomy after unsuccessful angioplasty of TASC C and D lesions in femoropopliteal arteries[END_REF]. Mean lesion length treated was 13.3±4.6 cm. ELA was associated with percutaneous transluminal angioplasty (PTA)in 58%±37% of cases. Stent implantation was performed in 29%±28% of cases. Wu et al. compared spot stenting versus systematic stenting after ELA, and stenting was performed in 91% of cases. They concluded that primary stenting resulted in a longer primary patency rates at one year. Sultan et al. described the ELA technique for lower-limb arteries, and only 35% of the patients were treated by combined treatment ELA and stenting. No drug-eluting balloons were used for de novo arteries lesions.

Primary patency rates were available in five articles [START_REF] Zhou | Laser atherectomy for lower extremity revascularization: An adjunctive endovascular treatment option[END_REF][START_REF] Dave | Excimer laser recanalization of femoropopliteal lesions and 1-year patency: results of the CELLO registry[END_REF][START_REF] Serino | Excimer laser ablation in the treatment of total chronic obstructions in critical limb ischaemia in diabetic patients. Sustained efficacy of plaque recanalisation in mid-term results[END_REF][START_REF] Wu | Comparison of immediate and 2-year outcomes between excimer laser-assisted angioplasty with spot stent and primary stenting in intermediate to long femoropopliteal disease[END_REF][START_REF] Wissgott | Excimer laser atherectomy after unsuccessful angioplasty of TASC C and D lesions in femoropopliteal arteries[END_REF]. At 15±7 months, mean primary patency rate was 65%±20%. Mean distal embolism rate of four articles during the procedure was 5% [START_REF] Dave | Excimer laser recanalization of femoropopliteal lesions and 1-year patency: results of the CELLO registry[END_REF][START_REF] Wu | Comparison of immediate and 2-year outcomes between excimer laser-assisted angioplasty with spot stent and primary stenting in intermediate to long femoropopliteal disease[END_REF][START_REF] Sultan | Cool excimer laser-assisted angioplasty (CELA) and tibial balloon angioplasty (TBA) in management of infragenicular arterial occlusion in critical lower limb ischemia (CLI)[END_REF][START_REF] Rastan | Initial experience with directed laser atherectomy using the CLiRpath photoablation atherectomy system and bias sheath in superficial femoral artery lesions[END_REF].

In-stent restenosis

Regarding in-stent restenosis, inclusions criteria were met in eight articles [START_REF] Laird | Excimer laser with adjunctive balloon angioplasty and heparin-coated self-expanding stent grafts for the treatment of femoropopliteal artery instent restenosis: twelve-month results from the SALVAGE study[END_REF][START_REF] Van Den Berg | Endovascular treatment of in-stent restenosis using excimer laser angioplasty and drug eluting balloons[END_REF][START_REF] Shammas | Safety and One-Year revascularization outcome of excimer laser ablation therapy in treating in-stent restenosis of femoropopliteal arteries: A retrospective review from a single center[END_REF][START_REF] Gandini | Treatment of chronic SFA in-stent occlusion with combined laser atherectomy and drug-eluting balloon angioplasty in patients with critical limb ischemia: a single-center, prospective, randomized study[END_REF][START_REF] Schmidt | Photoablation using the turbo-booster and excimer laser for in-stent restenosis treatment: twelve-month results from the PATENT study[END_REF][START_REF] Van Den Berg | In-stent restenosis: mid-term results of debulking using excimer laser and drug-eluting balloons: sustained benefit?[END_REF][START_REF] Dippel | Randomized controlled study of excimer laser atherectomy for treatment of femoropopliteal in-stent restenosis: initial results from the EXCITE ISR trial (EXCImer Laser Randomized Controlled Study for Treatment of FemoropopliTEal In-Stent Restenosis)[END_REF][START_REF] Armstrong | Laser Atherectomy for Treatment of Femoropopliteal In-Stent Restenosis[END_REF]. A total of 427 femoropopliteal lesions were treated, and 316 TE (42%) devices and 123 TB or TT (58%) were used. Mean lesion length treated was 17.5±4.1 cm. The mean technical success was 98%, and mean rate of distal embolism during the procedure was 9%. ELA was systematically evaluated in combination with another treatment. Three studies combined ELA technique with drug-eluting balloons [START_REF] Van Den Berg | Endovascular treatment of in-stent restenosis using excimer laser angioplasty and drug eluting balloons[END_REF][START_REF] Gandini | Treatment of chronic SFA in-stent occlusion with combined laser atherectomy and drug-eluting balloon angioplasty in patients with critical limb ischemia: a single-center, prospective, randomized study[END_REF][START_REF] Van Den Berg | In-stent restenosis: mid-term results of debulking using excimer laser and drug-eluting balloons: sustained benefit?[END_REF], four associated ELA with PTA [START_REF] Shammas | Safety and One-Year revascularization outcome of excimer laser ablation therapy in treating in-stent restenosis of femoropopliteal arteries: A retrospective review from a single center[END_REF][START_REF] Schmidt | Photoablation using the turbo-booster and excimer laser for in-stent restenosis treatment: twelve-month results from the PATENT study[END_REF][START_REF] Dippel | Randomized controlled study of excimer laser atherectomy for treatment of femoropopliteal in-stent restenosis: initial results from the EXCITE ISR trial (EXCImer Laser Randomized Controlled Study for Treatment of FemoropopliTEal In-Stent Restenosis)[END_REF][START_REF] Armstrong | Laser Atherectomy for Treatment of Femoropopliteal In-Stent Restenosis[END_REF] , and the SALVAGE study [START_REF] Shammas | Safety and One-Year revascularization outcome of excimer laser ablation therapy in treating in-stent restenosis of femoropopliteal arteries: A retrospective review from a single center[END_REF] describe results of ELA followed by covered stenting.

Primary patency rates were available in six articles [START_REF] Laird | Excimer laser with adjunctive balloon angioplasty and heparin-coated self-expanding stent grafts for the treatment of femoropopliteal artery instent restenosis: twelve-month results from the SALVAGE study[END_REF][START_REF] Van Den Berg | Endovascular treatment of in-stent restenosis using excimer laser angioplasty and drug eluting balloons[END_REF][START_REF] Gandini | Treatment of chronic SFA in-stent occlusion with combined laser atherectomy and drug-eluting balloon angioplasty in patients with critical limb ischemia: a single-center, prospective, randomized study[END_REF][START_REF] Schmidt | Photoablation using the turbo-booster and excimer laser for in-stent restenosis treatment: twelve-month results from the PATENT study[END_REF][START_REF] Van Den Berg | In-stent restenosis: mid-term results of debulking using excimer laser and drug-eluting balloons: sustained benefit?[END_REF][START_REF] Dippel | Randomized controlled study of excimer laser atherectomy for treatment of femoropopliteal in-stent restenosis: initial results from the EXCITE ISR trial (EXCImer Laser Randomized Controlled Study for Treatment of FemoropopliTEal In-Stent Restenosis)[END_REF]. At 10±4 months, mean primary patency rate was 68%±18 %.

Finally, a clinical investigation focused on distal embolic events using ELA in 28 peripheral vascular lesions. A distal protection filter was deployed before laser therapy to recover debris produced by laser atherectomy. They highlighted 20% rate of clinically significant macrodebris [START_REF] Shammas | Distal embolic event protection using excimer laser ablation in peripheral vascular interventions: results of the DEEP EMBOLI registry[END_REF].

Off-label indications

Among the eight selected articles regarding off-label indications, five were related to in situ fenestration of aortic endografts [START_REF] Murphy | Endovascular repair of acute traumatic thoracic aortic transection with laser-assisted in-situ fenestration of a stent-graft covering the left subclavian artery[END_REF][START_REF] Ahanchi | In situ laser fenestration for revascularization of the left subclavian artery during emergent thoracic endovascular aortic repair[END_REF][START_REF] Redlinger | In situ laser fenestration during emergent thoracic endovascular aortic repair is an effective method for left subclavian artery revascularization[END_REF][START_REF] Sonesson | Laser Generated In situ Fenestrations in Dacron Stent Grafts[END_REF][START_REF] Qin | In Situ Laser Fenestration Is a Feasible Method for Revascularization of Aortic Arch During Thoracic Endovascular Aortic Repair[END_REF].

Seventy in situ laser fenestrations were performed, and results are described in Table 3. The main objective was to perform a retrograde fenestration from the left subclavian artery to a thoracic aortic endograft during emergency endovascular treatment of a thoracic aortic aneurysm. A total of 35 Talent endograft, 8 Gore TAG, 3 Cook TX2 and 2 LifeTech Scientific Corp. were fenestrated using the TE catheter or Lasemar catheter. Laser catheter diameter varied between 2.0 and 2.5 mm. Three authors specified that the contact between the endograft and the catheter tip was around 3 to 5s [START_REF] Ahanchi | In situ laser fenestration for revascularization of the left subclavian artery during emergent thoracic endovascular aortic repair[END_REF][START_REF] Redlinger | In situ laser fenestration during emergent thoracic endovascular aortic repair is an effective method for left subclavian artery revascularization[END_REF][START_REF] Qin | In Situ Laser Fenestration Is a Feasible Method for Revascularization of Aortic Arch During Thoracic Endovascular Aortic Repair[END_REF]. Two type II endoleak from the left subclavian artery, which was successfully treated by coil embolization were reported. Concerning the four clinical evaluations, the primary patency rate was 100% after 9±1-month follow-up. In the largest clinical study, technical success was achieved in 95.8% of cases [START_REF] Qin | In Situ Laser Fenestration Is a Feasible Method for Revascularization of Aortic Arch During Thoracic Endovascular Aortic Repair[END_REF] . An experimental study on pigs regarding embolism after anterograde fenestration of textile polyester stent grafts using a 2 mm TE catheter was performed. They concluded that the technique does not produce macroscopically visible emboli or clot.

Three articles described other off-label excimer laser indications in endovascular therapy. First, Chander et al. [START_REF] Chander | Recanalization of failed autogenous conduit utilizing laser revascularization[END_REF] reported a case series of 4 recanalizations of failed autogenous saphenous vein graft using laser revascularization. A 0.9 to 1.7 TE laser catheter was used with 100% technical success. Second, Topaz et al. [START_REF] Topaz | Utilization of excimer laser debulking for critical lesions unsuitable for standard renal angioplasty[END_REF] described a retrospective review of excimer laser debulking of 12 lesions unsuitable for standard renal angioplasty. The laser debulking using a 0.9 to 2 mm TE catheter was followed by renal artery stenting. No laser-induced complications and no controlled angiographic renal artery stenosis occurred. Finally, a case of excimer laser use to treat a severe central venous lesion downstream to an arterio-venous access was reported [START_REF] Yevzlin | Excimer laser assisted angioplasty in hemodialysis access intervention[END_REF]. A 2 mm TE catheter was introduced in the right subclavian vein followed by an 8 mm high pressure balloon angioplasty.

DISCUSSION

This work aimed to review the use of excimer laser in PAD and in other off-label indications such as in situ fenestration of aortic endografts.

The excimer Laser was first used for coronary revascularization specifically for treating in stent restenosis and atherectomy [START_REF] Hirose | Treatment of in-stent restenosis with excimer laser coronary angioplasty: benefits over scoring balloon angioplasty alone[END_REF][START_REF] Ollivier | Contribution of excimer laser to coronary angioplasty[END_REF]. Other cardiologic applications such as transvenous extraction of implanted pacemakers and implantable cardioverter-defibrillator leads have emerged [START_REF] Okamura | Initial experience using Excimer laser for the extraction of chronically implanted pacemaker and implantable cardioverter defibrillator leads in Japanese patients[END_REF]. Neurosurgeons and neuroradiologists have also used this technology and developed a new technique called excimer laser-assisted non-occlusive anastomosis to perform anastomosis on intracerebral arteries and have reported encouraging results [START_REF] Bremmer | Vessel wall perforation mechanism of the excimer laser-assisted non-occlusive anastomosis technique[END_REF]. The large size of the devices and difficulty implementing them limited laser use for medical indications; miniaturization has allowed laser technology to develop and for the number of applications in medical and surgical use to increase.

The ELA procedure represents an alternative for treating in-stent restenosis and atherosclerotic plaques [START_REF] Shammas | Distal embolic event protection using excimer laser ablation in peripheral vascular interventions: results of the DEEP EMBOLI registry[END_REF].

Neither significant arterial perforation nor saphenous nerve injury were reported. However, short and mid-term primary patency rates were available for only 11 articles among the 18 articles included in the analysis of ELA in PAD. Besides, bail out stenting was frequently needed in the treatment of atherosclerotic plaques because of local dissections following catheter crossing. Embolization rates were substantial following an ELA procedure. Our analysis highlights a 5% and 9% embolization rate following ELA in atherosclerotic plaques and in stent restenosis treatment, respectively. Specifically, the DEEPEMBOLI registry assessed the presence of embolic debris following ELA using systematic distal filter [START_REF] Shammas | Distal embolic event protection using excimer laser ablation in peripheral vascular interventions: results of the DEEP EMBOLI registry[END_REF]. A concerning rate of 20% of macrodebris was found. The authors suspected ELA treatment of complex atherosclerotic lesions and suboptimal debulking as risk factors for distal embolization [START_REF] Shammas | Distal embolic event protection using excimer laser ablation in peripheral vascular interventions: results of the DEEP EMBOLI registry[END_REF]. This raises the question of systematic distal filter protection during ELA procedure.

In-stent restenosis rates due to myointimal hyperplasia reach up to 50% [START_REF] Del Giudice | Atherectomy for superficial femoral artery in-stent restenosis: can lasers light the way to a better outcome?[END_REF][START_REF] Kornowski | In-stent restenosis: contributions of inflammatory responses and arterial injury to neointimal hyperplasia[END_REF]. Several treatments, such as cutting balloons, directional atherectomy, and drug-eluting balloons, have been evaluated to cure myointimal hyperplasia. Some authors have prospectively studied, the treatment of in-stent restenosis using paclitaxeleluting balloon angioplasty. After 1 year, the primary patency rate was 83.7% with a reintervention rate of 9.8% [START_REF] Bague | Femoropopliteal In-stent Restenosis Repair: Midterm Outcomes After Paclitaxel Eluting Balloon Use (PLAISIR Trial)[END_REF]. The excimer laser allows recalibrating the vessel lumen in the stent by destroying fibrous material. ELA was associated with adjunctive therapy, such as drug-eluting balloons, provides satisfactory results [START_REF] Gandini | Treatment of chronic SFA in-stent occlusion with combined laser atherectomy and drug-eluting balloon angioplasty in patients with critical limb ischemia: a single-center, prospective, randomized study[END_REF], but this treatment should be evaluated by large and randomized series [START_REF] Ducasse | Economic Evaluation Comparing Standard Balloon Angioplasty Versus Drug-eluted Balloon or Laser-Excimer in Association With Drug-eluted Balloon in the Treatment of Femoropopliteal Artery In-stent Restenosis[END_REF]. In the last decade, several off-label indications of ELA have emerged, mainly laser in situ fenestration of aortic endografts. Laser technology is an alternative to mechanical technique using transseptal needles or stiff guidewires [START_REF] Coscas | In Situ Fenestration Through the Contralateral Iliac Artery to Convert an Aortouni-iliac Into a Bifurcated Endograft[END_REF]. Recently, it was stressed that needles compared to laser catheters were not flexible enough to enter a directional sheath, thereby limiting their use for anterograde in situ fenestrations [START_REF] Glorion | A Comprehensive Review of In Situ Fenestration of Aortic Endografts[END_REF]. Laser in situ fenestration consists of puncturing the endograft with the laser catheter angled by steerable sheath, enlarging the hole created if necessary and stabilizing the fenestration by covered or uncovered stent. The successful treatment of a proximal type 1 Endoleak using an Endurant aortic cuff with triple antegrade in situ fenestration was recently reported [48]. However, the choice of the best graft and the impact of laser fenestration on textile remain unknown. More experimental studies must be conducted to assess biomechanical textile modification and long-term effects following laser fenestration, for the latter to become an "on-label technique." ELA's cost-effectiveness is yet to be demonstrated and remains a global concern. In our country, TE's price reaches 1 900€ (approx. 2,200US$) for the catheter and 175 000€ (approx. 204,000US$) for the CVX 300 generator (taxes not included). Combined with adjunctive therapy such, as drug-eluting balloons, stenting, and perclose systems, the cost of ELA procedures can become extremely high. This may limit ELA diffusion [START_REF] Shishehbor | Percutaneous Therapies for Peripheral Artery Disease[END_REF].

Finally, reported results of the excimer laser open prospects for new applications such as arteriovenous accesses management. Venous stenosis caused by myointimal hyperplasia lead to high rates of reinterventions that could be simplified by laser use. Similarly, in situ fenestration was frequently performed using textile polyester endograft, but polytetrafluoroethylene (PTFE) endograft testing could be relevant to get away the fenestration from filament textile deterioration and extend the indication to the endovascular treatment of femoral bifurcation and popliteal occlusive disease.

CONCLUSION

The number of excimer laser applications is increasing. Laser technology represents a physical alternative to current mechanical means to treat various arterial diseases. Limitations include a concerning intra-operative embolism rate when treating PAD and a high cost. Long-term results and prospective comparative studies are lacking to validate the excimer laser as standard use in endovascular therapy.

LEGENDS :

Table 1

:Table 2 :

 2 Tabular review of paper regarding de novo lesions treatment using ELA PP: Primary patency, TLR: Target lesion revascularization, CLI: critical limb ischemia, FP: Femoropopliteal, ABI: Ankle brachial index, DEB: Drug eluted balloon, TBA: Tibial balloon angioplasty, NA: Not available, applicable Tabular review of paper regarding in stent restenosis treatment using ELA PP: Primary patency, TLR: Target lesion revascularization, TVR: Target vessel revascularization, FPISR: Femoropopliteal in stent restenosis, ABI: Ankle brachial index, DEB: Drug eluted balloon, PTA: Percutaneous transluminal angioplasty, NA: Not available, applicable

Table 3 :

 3 Tabular review of paper regarding laser in situ fenestration LSCA: Left Subclavian artery, TEVAR: Thoracic endovascular aneurysm repair, ISF: in situ fenestration, PP: Primary Patency, NA: Not available, applicable Figure : Flow chart depicting articles selection for the current review according to the PRISMA (Reporting Items for Systematic Reviews and Meta-Analysis) guidelines.

							Results
	Reference	Main objective	Study Design	N (Lesions)	Technical (%) success	Follow-(months) up	PP (%)	TLR (%)	Others relevant results
	Bosiers 2005	Efficacy of Laser angioplasty in CLI	Prospective multicentric	51	NA	6	NA	NA	74% limb salvage
	Zhou 2006	Evaluate effectiveness ELA+PTA for CLI	Retrospective monocentric	15	84	6	57	NA	NA
	Rastan 2007	Safety and efficacy of ELA bias sheath catheter for SFA	Prospective monocentric	6	79	1	NA	NA	ABI 0.8 increase and Rutherford increase 3 points
	Dave 2009	Evaluate EL recanalization for FP lesions	Prospective multicentric	65	100	6 and 12	59 and 54	23.1 (12 months)	NA
	Serino 2010	ELA for treatment of CLI in diabetic patients	Prospective monocentric	51	88	12 and 24	97.6 and 82.7	13.4 and 17.3	Limb salvage 100% and 94%
	Wisgott 2013	Application of ELA for refractory FP lesions	Retrospective monocentric	40	90	12	58.9	NA	Primary assissted Patency and Secondary assissted Patency 67.8% and 83.2%
	Wu 2013	ELA+Spot stent vs ELA+systematic stenting FP disease	Retrospective monocentric	106	100	24	25 (ELA+spot stent) vs 45 (ELA+systematic stenting) (P=.03)	65 (ELA+spot stent) vs 45 (ELA+systematic stenting)	Earlier restenosis 67% (ELA+spot stent) vs 32% (ELA+systematic stenting) (P=.001)
									Sustained clinical improvement
	Sultan 2013	Compare outcome of CoolELA vs TA	Retrospective monocentric	42	81	36	NA	14.8% (ELA) vs 36.2 (TBA) (P=.873)	ELA 81% vs 63.8% TBA (P=.013), Amputation free-survival 95.2% ELA vs
									78.7%TBA (P=.016)
		Clinical results of
	Mallios 2017	laser atherectomy in the treatment of	Retrospective monocentric	471	99	28	NA	20	Freedom from major amputation 90% at 5years
		PAD

Acknowledgments :

We thank the "Société Française de chirurgie vasculaire et endovasculaire" (SCVE), the "Association chirurgicale pour le développement et l'Amélioration des techniques de Dépistage et de Traitement des maladies Cardiovasculaires" (ADETEC), and the « Association pour la Recherche et la Formation Chirurgicale en Ile de France » (ARFCIDF) for providing funding for this study.


Marie-Ange Lebre

Antoine Vacavant

Manuel Grand-Brochier

Hugo Rositi

Armand Abergel

Pascal Chabrot

Benoit Magnin

Benoît Magnin

Automatic segmentation methods for liver and hepatic vessels from CT and MRI volumes, applied to the Couinaud scheme

Keywords: Medical Imaging, Liver Segmentation, Vessel Segmentation, Couinaud, CT and MRI volumes

de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Introduction

Medical imaging systems such as Magnetic Resonance Imaging (MRI) and Computed Tomography (CT) provide useful information on the liver. Extraction of the organ and its vessels from images is essential for analysing disease and planning surgical operations. A scheme developed by Couinaud allows the division of the liver into eight functionally independent segments by identification of the main blood vessels (Figure 1). [START_REF]Liver segment classification by Couinaud, by Was a bee, is licensed by CC-BY-SA-2.1-JP[END_REF] This analysis is most frequently performed by a radiologist This research has been supported by Région Auvergne with the grant "Nouveau chercheur" 1440NCAA and French National Agency for Research (ANR) with the reference ANR-18-CE45-0018 (R-Vessel-X project). via visual inspection and manual segmentation. It is a timeconsuming task, performed slice-by-slice, and the result depends on the skill and experience of the medical expert performing it. Moreover, segmentation is arduous because of noise, overlapping fuzzy contours, highly variable shapes and appearances, low contrast and complex backgrounds (the presence of other organs and tissues with similar intensities and shapes) [START_REF] Peng | A region-appearance-based adaptive variational model for 3-D liver segmentation[END_REF]. To obtain the Couinaud segmentation, the liver must first be segmented, and then its vascular structure defined. Three main types of method are used for liver segmentation: classification, active contour detection, and model-based methods. Classification methods consist of grouping individual components of the image such as pixels or sub-images and exploiting their similarities as region-growing methods [START_REF] Ruskó | Automatic segmentation of the liver from multi-and single-phase contrast-enhanced CT images[END_REF][START_REF] Yuan | A method for automatic liver segmentation from multi-phase contrast-enhanced CT images[END_REF], histograms with thresholds [START_REF] Foruzan | Liver segmentation by intensity analysis and anatomical information in multi-slice CT images[END_REF], voxel classification algorithms [START_REF] Lim | Automatic liver segmentation for volume measurement in CT Images[END_REF], and graph cuts [START_REF] Campadelli | Automatic abdominal organ segmentation from CT images[END_REF]. They often lead to over-segmentation. Conversely, contour approaches seek dissimilarities [START_REF] Shi | A hierarchical local region-based sparse shape composition for liver segmentation in CT scans[END_REF][START_REF] Liu | Liver segmentation for CT images using GVF snake[END_REF][START_REF] Soler | Fully automatic anatomical, pathological, and functional segmentation from CT scans for hepatic surgery[END_REF][START_REF] Yang | A hybrid semi-automatic method for liver segmentation based on level-set methods using multiple seed points[END_REF]. Model-based methods can be statistical or supported by an atlas [START_REF] Brunton | Statistical shape spaces for 3-D data: a review[END_REF][START_REF] Massoptier | A new fully automatic and robust algorithm for fast segmentation of liver tissue and tumors from CT scans[END_REF][START_REF] Farzaneh | Liver segmentation using location and intensity probabilistic atlases[END_REF]. Among these statistical models, the active appearance model (AAM) [START_REF] Linguraru | Automated segmentation and quantification of liver and spleen from CT images using normalized probabilistic atlases and enhancement estimation[END_REF] and active shape model (ASM) [START_REF] Shi | Low-rank and sparse decomposition based shape model and probabilistic atlas for automatic pathological organ segmentation[END_REF][START_REF] He | Fast automatic 3-D liver segmentation based on a three-level AdaBoost-guided active shape model[END_REF][START_REF] Okada | Automated segmentation of the liver from 3-D CT images using probabilistic atlas and multi-level statistical shape model[END_REF][START_REF] Wang | Shape-intensity prior level set combining probabilistic atlas and probability map constrains for automatic liver segmentation from abdominal CT images[END_REF] have been widely used as high-level techniques in computer vision and image processing [START_REF] Cootes | Statistical models of appearance for medical image analysis and computer vision[END_REF][START_REF] Cootes | Others, Comparing active shape models with active appearance models[END_REF]. Statistical models based on appearance or shape are parametric; thus, they require good initialization conditions and optimization of the parameters to obtain proper convergence.

For segmentation of the vascular structure of the liver, the most popular vessel enhancement filters used by the community are based on analysis of the Hessian matrix [START_REF] Frangi | Multiscale vessel enhancement filtering[END_REF][START_REF] Sato | 3-D Multi-scale line filter for segmentation and visualization of curvilinear structures in medical images[END_REF][START_REF] Erdt | Automatic hepatic vessel segmentation using graphics hardware[END_REF]. And their combined use brings improved results [START_REF] Conversano | Hepatic vessel segmentation for 3-D planning of liver surgery: experimental evaluation of a new fully automatic algorithm[END_REF][START_REF] Marcan | Segmentation of hepatic vessels from MRI images for planning of electroporation-based treatments in the liver[END_REF][START_REF] Zeng | Liver vessel segmentation based on extreme learning machine[END_REF]. Morphological filters are also developed by ranking the orientation responses of path operators (RORPO) [START_REF] Merveille | Curvilinear structure analysis by ranking the orientation responses of path operators[END_REF], an efficient tubular structure detection filter based on morphological path operators [START_REF] Passat | From Real MRA to Virtual MRA: Towards an Open-Source Framework[END_REF]. Some studies are based on region-growing or level-set methods [START_REF] Oliveira | Segmentation of liver, its vessels and lesions from CT images for surgical planning[END_REF][START_REF] Lu | Hepatic vessel segmentation using variational level set combined with non-local robust statistics[END_REF], and centerline extraction is also used [START_REF] Wink | Multiscale vessel tracking[END_REF][START_REF] Schneider | Joint 3-D vessel segmentation and centerline extraction using oblique Hough forests with steerable filters[END_REF]. A few methods combine tubular objects into connected networks via skeletonization [START_REF] Bauer | Segmentation of interwoven 3-D tubular tree structures utilizing shape priors and graph cuts[END_REF][START_REF] Pock | Multiscale medialness for robust segmentation of 3-D tubular structures[END_REF]. Regardless of the approach used, most studies that present the Couinaud scheme propose a complete method, with the segmentation of the liver, its vessels and the anatomical segments. Oliveira et al. [START_REF] Oliveira | Segmentation of liver, its vessels and lesions from CT images for surgical planning[END_REF] use a deformable model with level sets for the liver, a region-growing method for vessels and builtin anatomical knowledge used to construct four planes, splitting the liver into the Couinaud regions. Chen et al. [START_REF] Chen | Functional region annotation of liver ct image based on vascular tree[END_REF] propose a vessel-tree-based liver annotation method. A thinning algorithm allows users to obtain a spatial skeleton of liver vessels and a hierarchical vascular tree is constructed to divide the liver. Selle et al. [START_REF] Selle | Analysis of vasculature for liver surgical planning[END_REF] present a method for semi-automatic contour selection for liver segmentation, using a region-growing approach for the vessels and graph analysis for identification of the eight segments. Huang et al. [START_REF] Huang | A fast method to segment the liver according to Couinaud's classification[END_REF] propose a method based on 3-D thinning, vascular tree pruning, classification and projection. Soler et al. [START_REF] Soler | Real-time 3-D image reconstruction guidance in liver resection surgery[END_REF] have developed a computer-assisted surgical procedure based on patient-specific geometrical and anatomical modeling. They show that Couinaud's segmentation is not perfect, and describe some of its limitations; however, they agree it is the most widely used classification for surgery planning.

It is important to note that most researchers who work on the liver and its components present their results on CT images; few studies on MRI exist, though the latter modality is a subject of substantial interest for routine clinical oncology and diagnosis due to its superior soft tissue contrast and the lack of radiation exposure. In this study, we propose a complete automatic framework to obtain the Couinaud scheme from medical images acquired with different modalities-MRI and CT-and from patients with various degrees of progression of liver disease. First, we propose a robust, generic and efficient automatic segmentation algorithm using a model based on liver shape variability to construct a 3-D representation of any patient's liver. Then, we introduce a 3-D automatic method based on cooperation the processes of between segmentation and skeletonization, with detection of the main centerlines of the vascular structure. At this step, the quality of the vessel segmentation is highly dependent on the pathological state of the liver. Indeed, the vessels of a healthy liver are more visible those of a patient with cirrhosis due to decreased liver function [START_REF] Zhao | The relationship between liver function and liver parenchymal contrast enhancement on gd-boptaenhanced mr imaging in the hepatocyte phase[END_REF] and advanced cirrhosis results in a variation of the volumes of some segments and irregular borders, rendering it a challenging task. Finally, the skeleton obtained from the vascular structure allows us to produce the Couinaud segmentation. The paper is organized as follows: Section 2 describes the complete framework, from liver segmentation to the Couinaud scheme by way of the vascular network extraction. Section 3 presents the experimental setup, evaluation framework and results, first for the liver segmentation, then the vascular network extraction, and finally, we introduce a new measure for the Couinaud scheme. We present our conclusions in Section 4.

Methods

In the following three sections we describe the 3-D segmentation methods. We begin with liver segmentation, followed by extraction of the vascular network, and finally, we present the method to obtain the Couinaud scheme. Our methods are automatic and work on CT and MRI volumes.

To help understand the complete method, we present a table summarizing the annotations used throughout the article. The parameterization is explained in the results Section (Section 3).

Notations

Liver

Our segmentation of the liver is based on a model of its shape variability; its construction is described in this section.

Construction of the shape model

The shape model is constructed with data from 68 manually segmented livers these are noted M j∈{1,m} , with m the number of slice for each volume M. They come from three different sources: Shape 2015, IRCAD and SLIVER [START_REF] Kistler | The virtual skeleton database: An open access repository for biomedical research and collaboration[END_REF]42,[START_REF] Heimann | Comparison and evaluation of methods for liver segmentation from CT datasets[END_REF]. On all of the binary images, we proceed using 3-D cubic interpolation with a 1-mm voxel size to obtain uniform volumes. We construct a bounding box, BB, with the mean bounding box of the volumes, and the mean 3-D gravity center, GV. We align the gravity center of each volume with GV. We then define the variability of segmented images, σ M , as the percentage of voxels measured outside the BB that belong to the liver:

σ M = Card(L M \ BB) Card(L M ) × 100 ( 1
)
L M is the set of voxels that belong to the liver in M j∈{1,m} , and Card(L M ) its cardinality. Thus, L M \ BB represents voxels that belong to the liver but are measured outside BB. Then, we construct four liver sets, S k = {M j∈{1,m} } k , with k ∈ {1, 4}:

S 1 = {M j∈{1,m} , 0% ≤ σ M < 2%} S 2 = {M j∈{1,m} , 2% ≤ σ M < 6%} S 3 = {M j∈{1,m} , 6% ≤ σ M < 8%} S 4 = {M j∈{1,m} , σ M ≥ 8%} (2)
S 1 gathers the smallest livers, S 2 and S 3 represent standard livers, and S 4 those livers bigger than BB. In each set S k , we construct for each 2-D slice a probability map for the liver's presence. We obtain one volume for each S k , denoted by

M k = M j∈{1,m k } . A pixel value M(s, t) ∈ [0, 1] in a j-slice is defined by: M(s, t) = 1 m k m k n=1 M(s, t), (3)
with m k =max{m, M j∈{1,m} ∈ S k }.

Shape models are built using 68 manual segmentations. We obtain a probability map that reflects a standard position of the liver, and employ a rigid alignment to preserve invariants of pose that allows us to account for different patient positions.

Segmentation

Let P j∈{1,p} , with p the number of slice of the volume, represent the CT or MRI images of a patient. The box BB provides an approximate position of the liver within the volume, so after a cubic interpolation (1 mm voxel size), we crop the volume on P j∈{1,p} . In this new volume, many pixels belong to the liver and have similar intensities. So, using the intensity histogram with the highest peak, we find the slice with the largest liver surface, P I , I ∈ {1, p}. Then, we find the slice MJ 1 with J 1 ∈ {1, m 1 } with the maximum binary area of the first shape model M 1 . We note R( MJ 1 ), the resolution of this image, and R(P I ), the resolution of the image P I . If the condition

R(P I ) ≤ R( MJ k ∈ M k ) (4)
is false, the shape model M k = M 1 is too small, so we test a larger value of k: k + 1. Once an appropriate value of k is chosen, we apply MJ k as a mask on P I by considering pixels with a probability higher than a fixed percentage γ 1 on the shape model. The image obtained is then denoted by PĪ. We consider D the pixel intensity distribution of PĪ, with µ its mean and δ its standard deviation. We threshold the pixel distribution on the histogram with the following normality test:

µ -κ(δ)δ ≤ D ≤ µ + κ(δ)δ, (5)
with κ(δ) = 34.64 × δ -0.384 . κ(δ) has a descending exponential form, that allows us to include more pixels in cases with a small value of δ (see steps 1 and 2 in Figure 2). To limit detection of the surrounding organs, we focus our segmentation on the maximum binary area of the shape model (step 3 in Figure 2).

3-D representation

Finally, we apply an anisotropic diffusion filter [START_REF] Draoua | A new iterative method for liver segmentation from perfusion CT scans[END_REF]. It requires three parameters: the number of iterations to be performed (n it1 ), the time step (ts) and the conductance parameter (ξ). We compute the gradient magnitude to detect the contours; the accentuated images contours are denoted by P j∈{1,p} . We align the shape model M j∈{1,m k } with the patient data by the correspondence between PĪ and MJ k (see Section 2.1.2). Then, we choose pixels with a probability higher than γ 2 (step 4 in Figure 2). We denote the results by BP j∈{1,p} (step 5 in Figure 2). We apply BP j∈{1,p} as a mask on P j∈{1,p} . Finally, a fast marching method [START_REF] Sethian | Level set methods and fast marching methods: evolving interfaces in computational geometry[END_REF] is initialized with the center (x, y) of the connected component in the shape model with pixels with a probability higher than γ 2 . We now have a 3-D binary mask, MP j∈{1,p} , with some segmentation errors. We use the Z-convexity property [START_REF] Kim | Digital straight lines and convexity of digital regions[END_REF] of the liver shape to perform an adjustment. Let MP l , l ∈ {1, p}, the mask with the maximum binary area. Before l, each surface S ur f ace(MP j ) must be included in the next one, S ur f ace(MP j+1 ), so pixels that do not belong to the liver are set to 0 in MP j . After l, each surface S ur f ace(MP j ) must be included in the previous one, S ur f ace(MP j-1 ) (see Figure 3). To construct a 3-D representation, we use the marching cubes algorithm [START_REF] Cline | Marching cubes: A high resolution 3-D surface construction algorithm[END_REF] commonly used in medical imaging processing (see Figure 4).

Vessels

In this section, we describe a segmentation of the main vessels of the liver delimited in the previous section on medical exams, denoted by I (see (a) in Figure 5). We extract the centerlines and reconnect the detected vessels with an iterative algorithm.

Principal components extraction

We first apply Sato's filter [START_REF] Sato | 3-D Multi-scale line filter for segmentation and visualization of curvilinear structures in medical images[END_REF] on I with three parameters: σ to choose the scale of the detected structures, α 1 to approach the tubular similarity and α 2 to recover non-homogenous contrast; from this, we obtain I 1 s (see (b) in Figure 5). This filter retains many noise patterns; nonetheless, the brightest vessels are detected. The segmentation presented in Section 2.1 does not allow extraction of the confluence of the hepatic veins, which is outside the liver. To extract it, we select the largest 2-D area of the liver from among the first ten slices of I and search for the largest component (see (c) in Figure 5). Figure 5 (d) shows the first result. From this 3-D image, we extract q components C k∈{1,q} , working from the largest to the smallest volume (see (e) in Figure 5).

Centerline extraction and extension

We extract the 3-D centerline, l k , of each component C k with a decision tree-based approach without user-defined parameters [START_REF] Homann | Implementation of a 3-D thinning algorithm[END_REF] (see (f) in Figure 5). If |l k | > 1, we compute the direction vectors at both extremities of C k . We call the direction at the beginning b k and at the end e k (Algorithm 1). To be in accordance with the direction, we use λ > 0 voxels for long components and all the voxels for the shorter ones (smaller than λ voxels). l k [ j] is the voxel of l k at position j ∈ {1, n} and n = |l k | the number of voxels of l k .

Algorithm 1 Centerline vectors

Require: l k , k ∈ {1, q} Ensure: e k , b k , k ∈ {1, q} n = |l k | with n > 1, m = min(n, λ) for k = 1 : p do b k = l k [m] -l k [1] e k = l k [n -m + 1] -l k [n] end for
We extend the centerlines from both extremities until they reach another component and determine if a reconnection is biologically possible (see (g) in Figure 5). If |l k | = 1 (l k has one voxel), the connection process is different because of the lack of information about its direction. We search for the four nearest (Euclidean distance) components of C k (Figure 6).

Connection and validation

We note E k,l , the extended centerline between C k and the encountered component C l . We evaluate the intensity

I 1 s [i] with i ∈ {1, |E k,l |} of each voxel of E k,l in I 1 s and I 2 s [i] with i ∈ {1, |E k,l |} in I 2 s . I 2
s is the result of applying Sato's filter to I, which detects larger tubular structures than parameters chosen for I 1 s (Table 3). We then compute two rates r j with j ∈ {1, 2}:

r j = |E k,l | i=1 I j s [i] max(I j s ) × |E k,l | (6)
To evaluate if a connection is physically realistic, we compute the sinus of the angle β formed by E k,l and the direction of C l (see Figure 6 parts 2-3). If |l k | > 1 and the following condition is true, we connect the components:

(r 1 > t or r 2 > t) and (|sin(β)| < ω 1 ) (7)
with t ∈ [0, 1] and ω 1 ∈ [0, 1]. If C l is the confluence of the hepatic veins, we directly validate the connection. In cases where |l k | = 1, we proceed along the four lines in the same way for computation of r j . In this last case, the candidates for the connection are ranked according to their Euclidean distance from unique voxel l k . Then, we check the condition or (r 1 > 2tγ and

r 2 > 2tγ) (r 1 > tγ or r 2 > tγ) and (|cos(β)| > ω 2 ) ( 8
)
where γ varies in function of the distance of each component and ω 2 ∈ [0, 1]. Finally, if the centerline extension is too long, values r 1 and r 2 can be higher than the fixed threshold due to the high number of voxels considered, so we correct using an iterative process bounded by a given maximal value n it2 > 0.

After processing all components, we obtain an image with new principal components. At this stage, the process is re-iterated to add more connections (see (h) in Figure 5).

3-D reconstruction

We obtain a partial skeleton S partial . We apply RORPO [START_REF] Merveille | Curvilinear structure analysis by ranking the orientation responses of path operators[END_REF] to I to obtain I R . RORPO uses the notion of path operators from mathematical morphology with thin voxels oriented along their length:

L n R = L min × f n R -1 , ( 9
)
L min is the minimal path length to detect, f ∈ R is for the geometric sequence of scales and n R is the number of scales (Table 3). Our method uses different vesselness filters to gather different types of information about structure. Sato's filter is sensitive to different diameter ranges [START_REF] Sato | 3-D Multi-scale line filter for segmentation and visualization of curvilinear structures in medical images[END_REF] and RORPO is based on length [START_REF] Merveille | Curvilinear structure analysis by ranking the orientation responses of path operators[END_REF]. We decided to apply RORPO at this last step instead of using I directly because RORPO preserves the intensity of curvilinear structures, reduces the intensity of other structures, and is robust to noise. An anisotropic diffusion filter is then applied on I R [START_REF] Whitaker | Variable-conductance, level-set curvature for image denoising[END_REF]. We also compute the magnitude of the gradient and use a sigmoid function to focus on a particular set of values. Finally, we initialize a fast marching phase at each voxel of S partial [START_REF] Sethian | Level set methods and fast marching methods: evolving interfaces in computational geometry[END_REF] (Figure 7).

Couinaud representation

At this stage, we have a 3-D segmentation of the liver. From this volume, derived from either MRI or CT, we extract its 3-D vascular structure. In the last step of our approach, we separate the liver into the eight functionally independent segments described by Couinaud [START_REF] Couinaud | Le foie: études anatomiques et chirurgicales[END_REF].

Segmentation of the largest vessels

To achieve this, we first erode the vessel segmentation to retrieve the largest vessels. This process allows us to erase the smallest vessels detected in the previous section. The liver receives its blood supply from two large vessels, the portal vein and the hepatic artery. The latter carries blood from the liver to the inferior cava vein, while the first carries blood from the stomach, spleen, intestines and gallbladder to the liver. Detoxified blood leaves the liver through another large vessel, the hepatic vein. The hepatic and portal veins are not connected. After erosion, and thanks to this disconnection, we extract the two principal components, as shown on two MR images from our database in Figure 8. Our method works on the livers patients with advanced cirrhosis, as shown in Figure 8. Livers are severely deformed by cirrhosis and some other diseases; thus, segmenting vessels becomes a challenging task, because they are smaller and thinner than in a healthy liver. However, we are able to reconstruct the largest vessels, which is sufficient to construct Couinaud's scheme. Indeed, we based our method on the four main directions of the hepatic and portal veins, we explain it in the next section.

Main directions

There are three hepatic veins in the liver, converging into an extra hepatic vein (inferior cava vein). These three directions make it possible to divide the organ vertically into a left, middle and right part. Next, the portal vein is characterized by a split into two horizontal veins that divide the liver horizontally. We want to extract these three main directions of the hepatic veins and this horizontal axis of the portal vein. After extraction of the hepatic and portal vein components in the previous section, intermediate vessels still exist; however, we seek to extract only the main direction of the largest vessels, as shown in Figure 9. To extract them, we proceed with two methods, one for the hepatic veins and one for the portal vein. For the hepatic veins, we keep only the first three appearances of the vessels, along the Z-axis, in a radius near the central trunk corresponding to the beginning of the three hepatic veins. Then, we make an intersection of the 2-D binary images along the Z axis with this image (Figure 10 (a)). At the end, we obtain three oval components. We stop this process at the ith image, which corresponds to the next division of the hepatic vessels. To compute the vectors of the three directions, we use the center of the common trunk and the center of the three components detected at the i-th image. We construct three planes with these three directions. For the portal vein, we detect the longest horizontal component along the Z-axis (Figure 10 (b)). We compute the direction using its position along the Z-axis and the longest central axis of the component to obtain a horizontal plane.

3-D Representation

With the four planes, we are able to divide the liver into the eight segments of the Couinaud representation. Figure 11 represents a liver segmentation performed with our automatic algorithm presented in Section 2.1, and the four planes constructed from the vascular segmentation presented in Section 2.2.

Results

In the first part of this section, we evaluate our complete automatic framework by applying it to both CT and MRI. We first evaluate the segmentation of the liver presented in Section 2.1 by comparison with other semi-automatic and automatic methods. Then, we present results of the vessel segmentation presented in Section 2.2. Finally, we present a new method to measure the accuracy of the Couinaud segmentation. The steps of our method can be viewed in a video 1 . We implemented all algorithms with ITK-VTK [START_REF] Yoo | Engineering and algorithm design for an image processing API: a technical report on ITK-the Insight Toolkit[END_REF][START_REF] Schroeder | The visualization toolkit[END_REF]. 1 https://youtu.be/FNN6Yo5qxbQ

Data and parameters

To evaluate our automatic method, we use CT images from two freely available databases: 20 from the SLIVER database [START_REF] Heimann | Comparison and evaluation of methods for liver segmentation from CT datasets[END_REF] and 20 from the IRCAD database [42]. Both databases are widely used in research because some manual segmentations (of liver or/and vessels) are available and they are, therefore, directly comparable. We do not use Shape 2015 database, here, because medical examinations are not available in this dataset. Then, during the shape model construction (see Section 2.1), some of those testing data are used. To avoid bias, each of the set used in the shape model chosen are removed. The image sizes are 512 × 512 × 64-394, with a voxel size of 0.56-0.87 × 0.56-0.87 × 0.7-5 mm 3 .

We also use 40 MRI volumes from different local hospitals (CHU Clermont Ferrand, France and CH Emile Roux, France). Image sizes are 250 -512 × 320 -512 × 56-112, with a voxel size of 0.82-1.40 × 0.82-1.40 × 1.8-3 mm 3 . The 40 liver images in our MRI database come from patients with diseases such as advanced cirrhosis and cancers (including hepatocellular carcinoma). In these cases, segmentations are a challenging task, because the image quality decreases considerably with more heterogeneous liver tissue density; moreover, as mentioned above, livers are severely deformed by the progression of these diseases and there is a decrease in the liver-vessel contrast. Parameters used in the method described in Section 2 are presented in Table 3. Some parameters are chosen based on the literature, including those for RORPO [START_REF] Merveille | Curvilinear structure analysis by ranking the orientation responses of path operators[END_REF], and Sato's filter [START_REF] Sato | 3-D Multi-scale line filter for segmentation and visualization of curvilinear structures in medical images[END_REF]. Others were derived from the anisotropic diffusion filter in the liver segmentation (n it1 , ts, ξ). We have modified the conductance ξ to adapt the process to our dataset. Then, some parameters are determined empirically. These parameters are sufficiently generic to work with all images, like t, that allows us to consider intensity values on the results of the Sato's filters; ω 1 and ω 2 , which reflect a connection between two vessels close to a right angle; and n it2 , which limits the size of the centerline extension. We spent time manually optimizing other parameters, like the percentages γ 1 and γ 2 in the liver segmentation; the number of components q to be detected, and the direction of the component λ in the vessel segmentation. In the future we may consider developing automatic calculation processes to pick the best parameters (optimization) using training datasets.

Liver results

Manual segmentations of the liver are available for the CT images from SLIVER and IRCAD, and our experts segmented livers on three MRI volumes. Quantitative results are presented in Table 4. Our automatic method and experts' manual segmentations of the liver are compared by widely used metrics designed to quantify accuracy. We use True Positive (TP) and False Negative (FN) rates in the range 0-1 to evaluate the REcall value (RE), the PREcision value (PRE), the Jaccard index (J) and the Dice coefficient (D). We now compare our method with automatic algorithms based on statistical models. Massoptier et al. [START_REF] Massoptier | A new fully automatic and robust algorithm for fast segmentation of liver tissue and tumors from CT scans[END_REF] report a superior Dice coefficient of 0.94. The similarity of our model is not as high as theirs, but it is close, and offers a time advantage: their method requires 11.4 seconds for processing a 512 × 512pixel slice, while ours requires only 5-6 s. For purposes of comparison, a manual expert segmentation generally requires 180-240 s for one slice [START_REF] Hermoye | Liver segmentation in living liver transplant donors: comparison of semi-automatic and manual methods[END_REF]. Okada et al. [START_REF] Okada | Automated segmentation of the liver from 3-D CT images using probabilistic atlas and multi-level statistical shape model[END_REF] obtain a Jaccard coefficient of 0.86 for 8 CT scans; we obtain 0.87 for the 20 SLIVER images. Farzaneh et al. [START_REF] Farzaneh | Liver segmentation using location and intensity probabilistic atlases[END_REF] obtain a Dice coefficient higher than 0.89 on 11 similar images in pixel spacing. The mean Dice value in our study is 0.905 for 40 different datasets.

Then, we compare our method with the results of efficient liver segmentations applied to the IRCAD and SLIVER datasets. Linguraru et al. [START_REF] Linguraru | Automated segmentation and quantification of liver and spleen from CT images using normalized probabilistic atlases and enhancement estimation[END_REF] present an automatic method with a 0.96 Dice value for the SLIVER database, but their atlas-based method requires 3000-3600 s per slice. Our results do not perform as well as methods described in [START_REF] Yang | A hybrid semi-automatic method for liver segmentation based on level-set methods using multiple seed points[END_REF][START_REF] Shi | Low-rank and sparse decomposition based shape model and probabilistic atlas for automatic pathological organ segmentation[END_REF][START_REF] Wang | Shape-intensity prior level set combining probabilistic atlas and probability map constrains for automatic liver segmentation from abdominal CT images[END_REF][START_REF] Wimmer | Implicit active shape model employing boundary classifier[END_REF][START_REF] Moghbel | Automatic liver tumor segmentation on computed tomography for patient treatment planning and monitoring[END_REF]; however, all of these studies concentrate their task only on CT scans. Moreover, the process presented by Yang et al. [START_REF] Yang | A hybrid semi-automatic method for liver segmentation based on level-set methods using multiple seed points[END_REF] is user-dependent. The advantage of our methodology is that it is automatic, generic, and works on both CT and MRI volumes with promising results.

Few studies have reported results for both modalities; we compare our results with those of the most recent studies to do so [START_REF] Gotra | Comparison of MRI-and CT-based semi-automated liver segmentation: a validation study[END_REF][START_REF] Chartrand | Liver segmentation on CT and MR using laplacian mesh optimization[END_REF][START_REF] Suzuki | Computerized segmentation of liver in hepatic CT and MRI by means of level-set geodesic active contouring[END_REF][START_REF] Heinrich | Multi-modal multi-atlas segmentation using discrete optimisation and self-similarities[END_REF]. The performance of our method is similar to the other reported methods, but ours offers some advantages; for example, methods presented by Gotra et al. [START_REF] Gotra | Comparison of MRI-and CT-based semi-automated liver segmentation: a validation study[END_REF], Chartrand et al. [START_REF] Chartrand | Liver segmentation on CT and MR using laplacian mesh optimization[END_REF] and Suzuki et al. [START_REF] Suzuki | Computerized segmentation of liver in hepatic CT and MRI by means of level-set geodesic active contouring[END_REF] are user-dependent, while ours is automatic. Moreover, in one study [START_REF] Gotra | Comparison of MRI-and CT-based semi-automated liver segmentation: a validation study[END_REF], the same patients were used for CT and MRI, which limits the variability of the data and the range of liver shapes. Finally, our results are better than those obtained by Heinrich et al. [START_REF] Heinrich | Multi-modal multi-atlas segmentation using discrete optimisation and self-similarities[END_REF], see

Vessel segmentation results

We first evaluate our method presented in Section 2.2 on 10 synthetic vascular images from the March 2013 VascuSynth database used by Cheng et al. [START_REF] Cheng | Accurate vessel segmentation with constrained B-snake[END_REF]. Averages with standard deviations of True Positives (TP), False Positives (FP), False Negatives (FN) and Overlap Measure (OM) [START_REF] Cheng | Accurate vessel segmentation with constrained B-snake[END_REF] are reported in Table 6. We do not have false positives in our results, because our method of extraction of the main components and our partial skeletonization process efficiently handles synthetic data without noise. Moreover, RORPO is an efficient algorithm for the enhancement of vascular structures. Our algorithm has better results than those of article [START_REF] Cheng | Accurate vessel segmentation with constrained B-snake[END_REF] for these specified criteria.

Then, we apply our vessel segmentation on CT images from the public IRCAD database [42]. In this database, different contrast agents are used and therefore different levels of contrast enhancement are present. IRCAD offers manual segmentation sets {artery, portal vein, venous system, vena cava}, which allow for further comparison with other methods. Unfortunately, most of the methods described in the literature were tested using private databases, and did not publish their code, making retrospective comparative studies impossible [START_REF] Conversano | Hepatic vessel segmentation for 3-D planning of liver surgery: experimental evaluation of a new fully automatic algorithm[END_REF][START_REF] Zeng | Liver vessel segmentation based on extreme learning machine[END_REF][START_REF] Bauer | Segmentation of interwoven 3-D tubular tree structures utilizing shape priors and graph cuts[END_REF].

As far as we know, there are no open MRI datasets available for liver vessels. A medical expert working with us has segmented portal and hepatic veins for an MRI volume at the portal and arterial phases (times after contrast agent injection), when vessels are most visible. Using these data we quantitatively compare our method with RORPO and Sato's filter (which were thresholded beforehand) based on several classic metrics: accuracy (ACC), specificity (SPE), sensitivity (SENS) and precision (PRE). To measure misclassification, we also compute the false positive and negative rates (FPR, FNR). The FPR represents the degree of over-segmentation and the FNR the under-segmentation. We only evaluate these metrics on the area delimited by the liver segmentation presented in Section 2.1. The accuracy, sensitivity and precision values for CT and sensitivity and precision values for MRI suggest that our method is more accurate than other tested methods, see Table 7. The principal components are well-distributed in the liver; however, the detection step fails in places where large vessels are not present, explaining the high FNR results. Moreover, noise is present in the manual MRI segmentation because of the software used by the expert. In addition, the image quality decreases because we are quantitating diseased liver tissue.

Couinaud segmentation results

We present here a new process to evaluate the Couinaud representation. We use MR images, MRI i with i ∈ {1, 4}, from our database for which an expert validated our visual results, and CT scans, CT i with i ∈ {1, 8} from the IRCAD database. Among these four MRI volumes, some of the imaged livers have cirrhosis too advanced (with the presence of tumors in many segments) to allow for surgical planning. The Couinaud scheme is useful for localized, resectable tumors; as explained in Section 2.3, it uses the horizontal portal vein orientation and the three vertical hepatic veins axes to divide the liver into eight functionally independent segments (see Figure 1). Vessel segmentation explained in Section 2.2 allows us to construct this representation. This segmentation is used in daily clinical practice to indicate the exact positions of tumors, which is of high interest in surgical planning. In the state-of-the-art, evaluation of Couinaud segmentation is done by volumetric validation [START_REF] Chen | Functional region annotation of liver ct image based on vascular tree[END_REF][START_REF] Huang | A fast method to segment the liver according to Couinaud's classification[END_REF]; by graft volumetry accuracy and visual comparison [START_REF] Yang | Segmentation of liver and vessels from CT images and classification of liver segments for preoperative liver surgical planning in living donor liver transplantation[END_REF]; or solely by visual comparison [START_REF] Oliveira | Segmentation of liver, its vessels and lesions from CT images for surgical planning[END_REF]. In our study, we evaluate the Couinaud scheme relative to tumors' positions as presented in medical reports by hospital staff.

Patient

Segments: Number of Tumors' positions tumors found (medical reports) with correct position MRI is a very effective medical imaging tools for many purposes, including the early detection of primary liver cancer, metastases and characterization of hepatic nodules, and it is the main modality used for this purpose by the experts we consulted. For each patient, we have access to two or three reports that correspond to different examination dates, which allows us to confirm the evolution of tumors' positions. We also evaluate our Couinaud segmentation by comparison with CT scans of livers with advanced cirrhosis. Some large tumors can be observed in different segments, as seen for MRI 2 and CT 1 for segments {V, V I, V II} and {IV, V} respectively in Table 8. We observe that tumors appear in the positions indicated in the patients' medical reports, confirmed by our Couinaud segmentation with a large variety of localization within liver (see examples in Figure 12 (a) and (b)). However, our method fails for CT 1 to detect the tumor in the segment {III}, instead the lesion is found in segment {IV}; one of the Couinaud axes (in red in the Figure 12 (c)) is false because of a wrong detection of the hepatic vein. For two volumes, CT 6 and CT 7 , the tumors occupy the whole liver, despite this condition the algorithm is efficient. It also works on the healthy liver in CT 8 that has no tumors. Couinaud segmentation is sensitive to the state of health of the liver, because livers are deformed by the progression of cirrhosis.

MRI 1 1 in {V II} 1 MRI 2 1 in {V III} and 1 at {V, V I, V II} 2 MRI 3 1 in {IV} and 1 in {V III} 2 MRI 4 2 in {III} 2 CT 1 1 in {III}, 1 in {IV, V} 3 1 in {V II} and 1 in {V III} (missed 1 in {III}) CT 2 1 in {V, V III} 1 CT 3 1 in {I}, 1 in {II} and 1 in {IV} 3 CT 4 1 in {IV, II} 1 CT 5 1 in {V} 1

Discussion

In this article, we present a complete method to segment the liver and its vessels to obtain the Couinaud representation. Our algorithms are automatic and work on CT and MRI images obtained from different machines and acquisition parameters. First, we are able to automatically segment the liver using a model-based method that takes into account the variability in liver shape. This method can be used to process any medical image by overcoming the parametric constraints imposed by the machines and leads to a 3-D reconstruction for CT and MRI volumes. Few studies have reported results for both modalities [START_REF] Gotra | Comparison of MRI-and CT-based semi-automated liver segmentation: a validation study[END_REF][START_REF] Chartrand | Liver segmentation on CT and MR using laplacian mesh optimization[END_REF][START_REF] Suzuki | Computerized segmentation of liver in hepatic CT and MRI by means of level-set geodesic active contouring[END_REF][START_REF] Heinrich | Multi-modal multi-atlas segmentation using discrete optimisation and self-similarities[END_REF]]. Among them, we outperform the automatic method [START_REF] Heinrich | Multi-modal multi-atlas segmentation using discrete optimisation and self-similarities[END_REF]; the others require user interaction. We obtain a mean Dice coefficient of 0.915 for all volumes across both modalities. Our method is efficient even in the case of advanced cirrhosis with a dysmorphic liver, these studies do not all describe results for diseased livers. From our liver segmentation, we propose an automatic 3-D vessel segmentation based on an iterative partial skeletonization process. There are few methods that combine tubular objects in connected networks via skeletonization [START_REF] Bauer | Segmentation of interwoven 3-D tubular tree structures utilizing shape priors and graph cuts[END_REF][START_REF] Pock | Multiscale medialness for robust segmentation of 3-D tubular structures[END_REF], it's an originality of our work. We present this concept combined with the use of a partial skeletonization process. Even though the analysis can be complex due to the severity of the pathology, we are able to segment enough vessels to correctly extract the vessels.

Our method is also efficient on CT and MR images, even images of livers with thinner vessels due to advanced disease, with a mean accuracy equal to 0.97; for more on this result, see [START_REF] Lebre | Automatic 3-D skeleton-based segmentation of liver vessels from MRI and CT for Couinaud representation[END_REF]. Finally, we extract the main directions of the largest vessels, the hepatic and portal veins, in order to construct the Couinaud representation. Evaluation of the scheme is usually done by volumetric validation or visual comparison [START_REF] Huang | A fast method to segment the liver according to Couinaud's classification[END_REF][START_REF] Chen | Functional region annotation of liver ct image based on vascular tree[END_REF][START_REF] Yang | Segmentation of liver and vessels from CT images and classification of liver segments for preoperative liver surgical planning in living donor liver transplantation[END_REF][START_REF] Oliveira | Segmentation of liver, its vessels and lesions from CT images for surgical planning[END_REF]; in this study, we present an evaluation based on medical reports. As this representation is used for the location and resection of tumors, it is useful to evaluate it through these tumors' positions. In future work, this representation of Couinaud can be improved by considering curved surfaces instead of straight planes to cut the segments.

For the execution time, we specified that it took 5-6 seconds for a 512 * 512 image for the liver segmentation. To segment the vascular structure, it takes 8 minutes for a 3-D volume ; the 3-D ITK algorithm to find the centerlines implies a long time. As a future work, we could use another algorithm to speed up the complete pipeline. The execution time for tumors detection is presented by Pavan et al. [START_REF] Pavan | A parallel framework for HCC detection in DCE-MRI sequences with wavelet-based description and SVM classification[END_REF], it depends on image patch size and number of processors used in our parallel approach. The best time is 5 sec. for a single patient (with 16 processors).

The method outlined in this paper has some limitations. First, we need to improve the different planes of the Couinaud segmentation in order to improve accuracy in the process of detecting tumors. Second, vessel segmentation and the detection of the hepatic and portal veins are based on location of the largest vessels. However, when the patient has advanced cirrhosis, the vessels are atrophied and our method may fail. Finally, we need more data to test the vessel segmentation, the Couinaud classification and to quantify the level of deformities acceptable by our algorithms. To become part of the clinical routine, the algorithm must be faster. Therefore, improvement of the (currently slow) centerline extraction algorithm will be necessary.

Conclusion

Our contributions are multiple. First, the algorithm is multimodal, it can handle both computed tomography and MRI. Then, it is automatic from the segmentation of the liver to the Couinaud division. We propose a complete framework whatever the modalities used. Finally, we propose an evaluation of our Couinaud scheme that goes beyond the simple visual inspection, as in similar studies. Our approach is easy-toimplement and can be easily deployable for a clinical way.

In the future, we will add comparisons with skeletonisation process, evaluate more results from MRI data, and create standard annotations for benchmarking. We are currently working with different MRI acquisition times (portal, arterial, diffusion, etc.). We employ 3-D reconstructions of these dynamic MRI volumes to develop a method for automatic tumor detection, as radiologists do with visual criteria based on the different acquisition times; the Couinaud representation serves as the validation step. Thanks to these complete 3-D segmentations, we are already able to detect hepatic tumors such as hepatocellular carcinoma [START_REF] Pavan | A parallel framework for HCC detection in DCE-MRI sequences with wavelet-based description and SVM classification[END_REF], and to study blood flow in order to locate the onset of possible dysfunctions [START_REF] Lebre | Medical image processing and numerical simulation for digital hepatic Parenchymal Blood Flow, Simulation and Synthesis in Medical Imaging[END_REF].

Figure 1 :

 1 Figure 1: Illustration of the Couinaud segments. Image from [1]

Figure 2 :

 2 Figure 2: The complete framework for segmenting the volume of a liver

Figure 3 :

 3 Figure 3: Adjustment to address segmentation errors. Red regions correspond to the difference between two adjacent masks due to over-segmentation

Figure 4 :

 4 Figure 4: 3-D liver reconstructions on (a) MRI and (b) CT volumes

Figure 5 :

 5 Figure 5: The complete framework for segmenting the vessels of a liver: (a) Liver segmented, I, (b) Sato's filter result, I 1 s , (c) Extraction of the confluence of the hepatic veins, (d) Result of (b) and (c), (e) Extraction of q components, (f) Centerlines extraction, (g) Centerlines extension, (h) Connection and validation

Figure 6 : ( 1 )

 61 Figure 6: (1) Computation of directional vectors and centerline extension of C k with |l k | > 1; (2) Evaluation of β, the angle between C k and C l ; (3) Validation of the connection; (4) Computation of the four closest components of C k with |l k | = 1 and the directional vectors; (5) Evaluation of β, the angle between the directional vectors and each of four components; (6) Validation of the connections, here, a case of two validations among four possible

Figure 7 :

 7 Figure 7: Our 3-D liver vessel segmentation approach applied to (1) MRI and (2) CT volumes.

Figure 8 :

 8 Figure 8: Results of hepatic veins (blue) and portal vein (green) extraction on MR images of patients with advanced cirrhosis.

Figure 9 :

 9 Figure 9: Main directions of the liver vascular structure on a CT scan from our database

Figure 10 :

 10 Figure 10: Extraction of the main directions of the hepatic veins (blue) and the portal vein (green) from an MRI vessel segmentation

Figure 11 :

 11 Figure 11: Couinaud representation of MRI volumes (a) Left, middle and right part of the liver delimited by the three hepatic veins, (b) Upper and lower part of the liver delimited by the portal vein. Illustration was created from an MRI from our database of a liver from a patient with advanced cirrhosis.

  3.63 ± 1.05 5.95 ± 1.37 96.37 ± 1.05 95.78 ±1.23 Ours 2.41 ± 1.99 0 97.58 ± 1.1 98.77 ± 1.03

Figure 12 :

 12 Figure 12: Tumors found in red with correct position: (a) segment {V II} for MRI 1 (b) segment IV for CT 3 ; (c) Our method fails for CT 1 : the tumor is found in segment {IV} instead of in the segment {III}. The red axis has been incorrectly calculated.

Table 1 :

 1 Annotations used for the liver segmentation method (Section 2.1)

		Definitions
	M j∈{1,m}	Manual liver segmentation from available
		dataset (IRCAD, SLIVER, Shape 2015)
	BB	Mean bounding box of all M j∈{1,m}
	GV	Mean 3-D gravity center of all M j∈{1,m}
	σ M	Variability of segmented images
	L M	Set of voxels that belong to the liver in M
	Card(L M )	Cardinality of L M
	S k , k ∈ {1, 4}	Liver sets according to the variability
	M k = M j∈{1,m k }	Mean volume constructed with each set S k
	P j∈{1,p}	Medical images of a patient (CT or MRI)
	P I , I ∈ {1, p}	Slice I with the largest surface of the liver
	MJ 1 , J 1 ∈ {1, m k }	Slice with the maximum binary area in the
		shape model M k
	R(.)	Resolution of an image
	γ 1	Fixed percentage chosen on the shape
		model to select pixels on P I
	PĪ	Image obtained thanks to γ 1 applied on P I
	µ	Mean value of the pixel intensity distribu-
		tion of PĪ
	δ	Standard deviation of the pixel intensity
		distribution of PĪ
	κ(δ)	Function for the normality test for the first
		thresholding
	n it1	Number of iterations of the anisotropic dif-
		fusion filter
	ts	Time step of the anisotropic diffusion filter
	ξ	Conductance of the anisotropic diffusion
		filter
	P j∈{1,p}	Volume of the patient after thresholding,
		anisotropic diffusion filter and gradient
		magnitude computation
	γ 2	Fixed percentage chosen on the shape
		model to select pixels on P j∈{1,p}
	BP j∈{1,p}	Binarization result after the used of γ 2
	MP j∈{1,p}	Final binary mask: result of our liver seg-
		mentation
	2

Table 2 :

 2 Annotations used for the vessels segmentation method (Section 2.2)

Table 3 :

 3

	Liver parameters	n it1	ts	ξ	γ 1 (%)	γ 2 (%)
		5	0.1	1	30	30
	Vessel Parameters	q	λ	t	n it2	ω 1 , ω 2
		40	8	0.2	5	0.9, 0.3
	Sato I 1 s	σ	α 1	α 2
		2	0.1	0.9
	Sato I 2 s	σ	α 1	α 2
		2	3	0.9
	RORPO I R	L min	f	n R
		40	1.32	4

Fixed parameters used to segment the liver in Section 2.1 and vessels in Section 2.2, listed with their corresponding values.

Table 4 :

 4 Liver segmentation accuracy on CT and MRI volumes

	Dataset	RE	J	D
	IRCAD	0.87± 0.05	0.78± 0.06	0.88± 0.03
	SLIVER	0.92± 0.03	0.87± 0.04	0.93± 0.02
	MRI	0.91±0.08	0.82±0.04	0.90±0.02
		FN	TP	PRE
	IRCAD	0.13±0.05	0.85±0.07	0.89±0.04
	SLIVER	0.8±0.03	0.92±0.03	0.94±0.03
	MRI	0.9±0.07	0.90±0.10	0.88±0.06

Table 5 ,

 5 who present an atlas for registration of CT and MRI data.

			CT			MRI
	Method, Ref	Data	D	J	Data	D	J
	Auto, ours	SLIVER	0.93	0.87	private	0.90	0.87
		IRCAD	0.88	0.78
	Semi-Auto, [58] 2015	private	0.93		private	0.93
	Semi-Auto, [56] 2017	private		0.90	private		0.88
	Semi-Auto, [57] 2017	SLIVER		0.94	private		0.92
	Auto, [59] 2015	private	0.92		private	0.80

Table 5 :

 5 Comparison with other methods on CT and MRI volumes

Table 6 :

 6 Segmentation results of our method on synthetic vascular images (March 2013 VascuSynth database)

Table 7 :

 7 Results of our automatic algorithm to segment vessels on CT and MRI.

	CT	ACC	SPE	SENS	PRE		FPR	FNR
	Ours	0.97±0.01 0.98±0.01 0.69±0.10 0.61±0.07 0.01±0.01 0.32±0.09
	RORPO	0.90±0.02 0.97±0.01 0.20±0.06 0.41±0.09 0.02±0.01 0.80±0.06
	Sato	0.89±0.03 0.97±0.02 0.24±0.10 0.46±0.17 0.03±0.01 0.75±0.10
	MRI		ACC SPE SENS PRE FPR	FNR
	Ours (hepatic)	0.98	0.98	0.54	0.30	0.010	0.45
	Ours (portal)	0.97	0.98	0.70	0.51	0.002	0.32
	RORPO (hepatic)	0.96	0.98	0.23	0.30	0.016	0.78
	RORPO (portal)	0.98	0.99	0.56	0.46	0.007	0.43
	Sato (hepatic)	0.97	0.97	0.39	0.27	0.012	0.60
	Sato (portal)	0.97	0.90	0.10	0.39	0.030	0.90

Table 8 :

 8 Validation of tumor position in the Couinaud segmentation based on medical reports