Michel Vert
email: michel.vert@umontpellier.fr

Refrigerator as Model of How Earth's Water Manages Solar and Anthropogenic Heats and Controls Global Warming

The relation between global warming and the role of anthropogenic carbon dioxide (CO 2 ) is confusing. Ocean level and atmospheric temperature rises are predicted dramatic in distant future whereas global ices disappearance is already dramatic and increasing. In this article, we called on the heat control machinery exploited in a refrigerator to show that water behaves as a refrigerant to manage solar and anthropogenic heats and also any heat generated from sources localized on Earth. Year 2018 was taken as example for quantitative evaluation of heat energy transfers involved in water phases and interphase exchanges. It was concluded that ice melting and evaporation-condensation equilibria are efficient physical factors to fight global warming. It is also shown that the pool of water present on Earth is progressively augmented by the water liberated parallel to CO 2 during the combustion of fossil hydrocarbons in which it was stored millions years ago. Water as source of hydrogen may be an alternative to the sources of energy produced and consumed by humanity provided that heat-cycle assessment from cradle to grave complements the life cycle assessment favorably.

Introduction

So far, the predictions of climate changes are those reported in successive Intergovernmental Panel on Climate Change (IPCC) reports (IPCC, 2014;IPCC, 2022) issued from an international consensual exploitation of the available literature to predict climate changes in distant future. The trends are still small but nevertheless detectable today. The consensus is adopted almost universally although controversies exist, the dispatching of which is limited to articles in open access archives, blogs and magazine outlets [START_REF] Dunlap | Climate Change Denial Books and Conservative Think Tanks: Exploring the Connection[END_REF].

Until recently, global climate changes were assigned to imbalanced inputs and outputs of electromagnetic infrared radiations and to anthropogenic greenhouse gas, especially CO 2, considered as sources of radiative anthropogenic heat release at the top of the troposphere (rAHR) (IPCC, 2014;NASA, 2009;[START_REF] Mackenzie | Heat Balance of the Atmosphere and Carbon Dioxide[END_REF] without consideration to heat in the low atmosphere, notably anthropogenic heat release (eAHR), also known as waste heat energy, generated by the sources of energy produced and exploited by humanity for works. In the past, only rAHR related to greenhouse gas was taken into account and considered as absorbed predominantly by oceans [START_REF] Hansen | Earth's energy imbalance and implications[END_REF][START_REF] Trenberth | Earth's Energy Imbalance[END_REF]IPCC, 2014). rAHR is said resulting from electromagnetic radiative flux that amounted annually from 0.5 to 1 W/m 2 in the early 2000s [START_REF] Trenberth | Earth's Energy Imbalance[END_REF]IPCC, 2014), i.e. between about 8 and 16 x 10 21 Joules (8 and 16 Zeta Joules (ZJ)). The AR6 IPCC reports an observed annual average rate of heating of the climate system at 0.79 [0.52 to 1.06] W m -2 (12.7 ZJ) for the period [START_REF] Mackenzie | Heat Balance of the Atmosphere and Carbon Dioxide[END_REF][START_REF] Scirocco | CO 2 is not driving the global-warming, Tower of Reason[END_REF](IPCC, 2022)). Regardless of its origin, heat energy released or generated in the atmosphere has to be evacuated to space otherwise it is absorbed and causes warming as it is proposed in the case of residual radiative forcing assigned to greenhouse gas. According to (IPCC, 2022), "ocean warming accounted for 91% of the heating in the climate system, with land warming, ice loss and atmospheric warming accounting for about 5%, 3% and 1%, respectively (high confidence)".

In general, global ice was considered a negligible heat absorber relative to oceans [START_REF] Hansen | Earth's energy imbalance and implications[END_REF]IPCC 2022). Based on outstanding facilities including satellites, NASA is the reference body to quantify ice imbalance and its role on the polar environment [START_REF] Scott | Sea Ice by NASA[END_REF]. The occurrence of dramatic global ice loss is now certain, especially over the recent years, and concerns different ices, namely ice caps, sea ice, glaciers and permafrost (Rignot et all, 2019;Slater et all, 2021). Ices melting is generally considered as a source of ocean rise [START_REF] Allan | Anticipated changes in the global atmospheric water cycle[END_REF][START_REF] Bengtsson | The global atmospheric water cycle[END_REF] on top of temperature-dependent dilatation. Long considered negligible, eAHR is now more and more regarded as a contributing factor to climate changes. The context and the history are well introduced in a recent publication [START_REF] Yang | A new global anthropogenic heat estimation based on high-resolution nighttime light data[END_REF] in which the authors proposed an algorithm to evaluate global eAHR. This approach consisted in calculations based on heat energy estimates derived from urban zones. Although there were limitations, the algorithm provided multi-scale anthropogenic heat information said reliable and useable for further research on regional or global climate changes and on urban ecosystems despite difficulties to establish ratios for converting energy consumption to anthropogenic heat.

Earth, as living systems, is too complex to be represented experimentally so that exploitations using climate models is necessarily based on local measurements or on global averaged data like radiative forcing in term of flux in W/m 2 . We recently attempted a different approach [START_REF] Vert | Global Anthropogenic Heat as Source of Ices Disappearance; Consequences for the Future of Earth and Humanity[END_REF] based on ice loss, fundamentals of chemistry and physics and annual global energy consumptions derived from various sources (fossil ones, biomass, nuclear electricity, etc.) found converted in oil-equivalents [START_REF] Martin-Amouroux | Consommation modiale d'énergie 1800-2000: Les résultats[END_REF]BP, 2019). According to [START_REF] Manowska | The Importance of Heat Emission Caused by Global Energy Production in Terms of Climate Impact[END_REF], eAHR corresponds to c.a. 60 % of the global energy consumption, the rest being consumed to provide work. On the basis of this estimate, it was deduced that eAHR released from all the energy sources in the low atmosphere between 1994 and 2017 provided enough thermal energy (7.2 ZJ) to melt 77% [START_REF] Vert | Global Anthropogenic Heat as Source of Ices Disappearance; Consequences for the Future of Earth and Humanity[END_REF] of the 28 trillion tonnes of disappeared ice reported recently for the same long period (Slater et all, 2021). The corresponding 0.31 ZJ annual average eAHR estimate was effectively negligible when compared with the 12.7 ZJ estimate of annual average rAHR deduced from the 0.79 W/m 2 annual average rate of heating of the climate system applied to the surface of the planet (IPCC AR6, 2022). As ices imbalance is a partial signature of heat energy supply regardless of its origin, the large dominance of rAHr, a source of energy assigned to CO 2 -based radiative forcing, raises a question: why rAHR that is said warming the environment does not cause much greater ices imbalance than presently observed since, in physics, any source of heat tend to transfer part of it to its environment up to equilibrium?

In attempt to answer this question, , let us consider that solar radiations have been heating the global environment over billions of years without dramatic heat accumulation despite occurrence of short and long and more or less important local ups (high temperature) and downs (glaciation) periods. The relative stability included natural greenhouse effect assumed the origin of a 15°C excess of average temperature relative to an atmosphere-free Earth. eAHR, rAHR and any other sources of heat on Earth have to be managed similarly and simultaneously to solar heat to keep Earth's environment and climate under relative control and compatible with Life. Indeed, the Earth can be schematically considered as a huge globe with land, solid matters, surface water and atmosphere heated locally since no matter or molecule can escape in intersidereal space. Only the energy stored in molecules can escape to space through radiation phenomena.

A few thousand years ago, humans began to use biomass as sources of heat and light. The generated eAHR remained very small compared with solar inputs until about 150 years ago when humans began to exploit fossil sources and, more recently, nuclear energy and renewable resources for the production of electricity in order to satisfy work, heat and comfort needs. The side effect was the appearance of increasing eAHR in the low atmosphere in addition to rAHR in the high troposphere [START_REF] Yang | A new global anthropogenic heat estimation based on high-resolution nighttime light data[END_REF]2017). Therefore, Earth can be compared to a mammalian body which has its metabolism generating heat in a closed space, the body. This body which burns foods has to be cooled to keep its temperature constant. Cooling is provided by the evaporation of sweat. If water cycle has been recognized for years as an important factor in climate control [START_REF] Allan | Anticipated changes in the global atmospheric water cycle[END_REF][START_REF] Bengtsson | The global atmospheric water cycle[END_REF], water evaporation and condensation have not been considered as important to limit the storage of radiative forcing in oceans.

The present article aims to compare Earth's water with the refrigerant that controls the temperature inside a refrigerator, a simpler example than human body, where inner heat has to be eliminated. Results are discussed relative to global warming and climate changes.

The refrigerator

From a thermodynamic viewpoint, a refrigerator is based on a simple rule: "when two substances are in contact, the hot one supplies heat to the cold one up to equilibrium". In a refrigerator, the transfer of heat proceeds by evaporationcondensation of a volatile fluid: the refrigerant. Heat is absorbed locally by the evaporation of the fluid, transported by the gas phase, and released from this gas by condensation outside as human and mammalian bodies do. The expulsed sweat cools the surface and the interior of the body by evaporation in the atmosphere until perspiration is no longer necessary.

The transfer of heat from a hot medium to a cold one is spontaneous and rather slow. In contrast, heat exchanges from a cold medium to a hot one cannot be spontaneous. Some energy must be supplied. It is the role of the compressor present in air-conditioning machines and refrigerators. For humans, there is no compressor and the pressure in tissues is the sole driving force to push water outside. A schematic representation of a refrigerator is shown in Figure 1. There are four main stages to control the inner temperature:

Evaporation

From 1 to 2 in Figure 1, the volatile refrigerant enters the inner evaporator as a liquid. Going through this multi-tube device, the liquid absorbs part of the heat present in the closed space, including that of foods in it. As a result, the liquid is turned to gas at the outlet of the evaporator while the temperature inside the closed space decreases slightly.

Compression

From point 2 to point 3, the gas is pressurized in the compressor where it is superheated by compression and then transferred to the multi-tube condenser located outside, generally in the back.

Condensation

From point 3 to point 4, the hot pressurized gas enters the condenser. The initial part of the cooling process in the condenser is contact with the outer cold surface that decreases the temperature of the gas and finally turns it back to liquid. This step is where the inside thermal energy absorbed by the refrigerant at the evaporation stage is vented out to atmosphere. The condenser in the back of the refrigerator is hot as it can be easily observed.

Expansion of the subcooled and highly pressurized refrigerant

From point 4 to point 1, the high-pressure subcooled liquid passes through the expansion device which reduces its pressure and controls the flow of liquid into the evaporator (stage 1). The cycle is repeated until the temperature in the refrigerator reaches the temperature set at the thermostat otherwise the inner temperature would continue to decrease with ice formation on the walls of the internal compartment, something everybody can observe in a freezer.

Application to Solar energy management on Earth

The components of the environment (atmosphere, land, oceans, etc.) have been heated by the Sun for billions of years and kept without dramatic heat accumulation. These environmental elements can be compared to the foods placed inside a refrigerator where the temperature is controlled. However, there are differences. The compressor present in Figure 1 that allows and speeds up thermal exchanges from cold inside to hot outside is replaced by the mechanical and mixing actions of chaotic turbulences in atmosphere (winds, streams, tornadoes, hurricanes, storms, etc.) and oceans (hot and cold streams) that dispatch heat within the whole environment. The condenser is replaced by the cold zone of the atmosphere where vapor condenses at dew temperature to form clouds from which the heat stored at the evaporation stage is released to space. The refrigerant present in the cooling circuit of the refrigerator is replaced by water, and the heat energy released during cloud formation is eliminated from the high atmosphere partly by radiation to space, partly by return to the surface via rain and snow. The whole process is schematized in Figure 2. It is important to note that the concentration of water molecules above clouds is much lower than below. This low concentration is favorable to radiation transmission to space according to the Beer-Lambert law, in contrast to the case of CO 2, the concentration of which is not affected by condensation (Sirroco, 2018). In this scheme, the Sun (1) heats the whole environment as everybody feels it under sunshine (2 and 3). Natural greenhouse effect is included in (2'). Humid air ascension and atmosphere turbulences dispatch and tend to average local imbalanced heat and raise it to the multilayered atmosphere in contact with the very cold intersidereal medium on one side, and with ground, ice and surface water on the other side. It is worth noting that in contrast to humid air, the dense CO 2 tends to go down. The supply of geothermal heat is generally considered negligible as many other heat sources on Earth are, including the combustion of fossil fuels ( [START_REF] Zhang | Timescales and ratios of climate forcing due to thermal versus carbon dioxide emissions from fossil fuels[END_REF] and electricity-related ones. The temperatures of land surface and of oceans tend to increase but rising is unavoidably limited by heat absorption by the melting of ices (4' and 6') over the whole globe and also by the process of evaporation (evaporator) that cools ocean and surface liquid water (the refrigerant) and transfers the corresponding heat to the atmosphere as warm vapor (4). The air enriched in warm vapor being less dense than dry air, it rises up to a zone cold enough to condense the vapor as dispersed droplets and ice particles forming clouds from which the released heat is eliminated by radiation (7) (such a mechanism of radiative heat energy elimination to space from water located above clouds was recently proposed [START_REF] Gueskens | L'effet de serre et le bilan énergétique de la Terre[END_REF] and rains and snow (6) that close the cycle. In reality, the Sun does not heat continuously. Earth inclination and rotation lead to cyclic heating like day and night, summer and winter, North and South hemispheres, and the Sun long cycles. The process of ices melting and reformation is thus cyclic with ups and downs as in a refrigerator. If all the ice disappears inside the refrigerator, the inner temperature starts rising up to the outside one unless the thermostat restarts the cycle to reform ice. On Earth, the thermostat consists in water interphase equilibria. In hot summers, ices melt. In cold winter, ices are restored but the process is more and more imbalanced. If ice imbalance continues to grow, all ices will disappear sooner or later and warming will then be controlled by the sole right shift of evaporation ↔ vapor ↔ condensation interphases equilibria. This will occur progressively over the years with more and more clouds to form a thick cover that will tend to limit the solar input like durst particles and aerosols do. Less solar heat will lead to ices regeneration like in past glacial eras [START_REF] Miller | Abrupt onset of the Little Ice Age triggered by volcanism and sustained by sea-ice/ocean feedbacks[END_REF]. The temperature control by evaporation-condensation depends on the latent heat of evaporation but it depends also on many dynamic factors that are major obstacle to quantification. Anyhow, temperature rise or not, the more heat to be dispatched over the globe, the stronger and the more frequent chaotic environmental have to be, at least qualitatively (Fig. 2), a trend already observed today (Reed et al., 2021) although temperature rise is no more than a few hundredths of a Celsius degree annually. Water cycle has been already proposed as climate factor but generally without involving ices and not in terms of quantitative water interphase equilibria.

The evolution after the appearance of Anthropogenic Heat

The controlling process described in the previous section worked for billions of years to manage Sun, volcanoes and biomass-burning heats by cyclic ice melt and reformation and by radiation to space. The exploitation of fossil energy started bringing in extra heat in the middle of the 19th century and alerted people recently. In parallel, both natural gas and, more recently, electricity provided progressively more waste heat in the low atmosphere. The new situation is schematically represented in Figure 3.

The comparison between Figures 2 and3 does not reveal important differences relative to the heat managing thermal machinery. Solar energy still heats the Earth dominantly (2) but now with anthropogenic heat releases eAHR (2"). Both rAHR and eAHR anthropogenic heat issued from the consumed energy are dispatched in the atmosphere (4' and 4") for averaging over the whole planet. The corresponding surplus of heat is absorbed by oceans, ices melt (8) and water evaporation (4) to close the ring like in section 2. Having to dispatch more thermal energy, local chaotic climate perturbations (hurricanes, tornados, storms, rains, streams, etc...) become more important and more frequent. In contrast to Sun, rAHR and volcanoes that caused discrete heating, eAHR warming related to human activities around the globe occurs over days and nights.

Attempts to quantify the action of water as refrigerant

In this section, we look at where the mechanisms schematized in Figures 2 and3 can lead on the basis of thermodynamics characteristics typical of the water cycle, namely, the 333.55 KJ/Kg latent heat of ice melting, the 2,447 KJ/Kg latent heat of evaporation at 14°C, the 2.11 KJ/Kg/°C specific heat capacity of solid ice and the 4.184 KJ/Kg/°C specific heat of water, various factors with minor effects like salinity, CO2 dissolution in ocean and cloud liquid water, dusts, etc. being neglected (Engineering Tool Box, 2003).

To estimate and compare rAHR and eAHR in terms of Joules, the following data available for year 2018 were used:

-14°C, the average temperature of Earth's surface determined from multiple land and ocean local measurements (NOAA; 2021), a value considered common to low atmosphere and ocean surface water; -0.79 W/m2 the average radiative forcing (IPCC, 2022); -0.03°C and 3.7 mm, the temperature and ocean level respective changes (IPCC, 2022); -1.5 trillion tonnes ice imbalance assumed similar to the estimate of 2017 deduced from Figure 4 in [START_REF] Slater | [END_REF]; -20°C, the average temperature of global ices, a temperature proposed in [START_REF] Slater | [END_REF]; and -13.864 GT of oil equivalent, the global energy consumption (BP, 2019), 60 % of which generated 0.35 ZJ eAHR according to 44 MJ/Kg, the average heat of combustion.

According to the specific heat capacity of ice, 1.5 trillion tonnes of ice at -20°C required about 0,063 ZJ to reach 0°C, the melting temperature of ice. Then, the temperatures of ice and formed liquid water remained constant at 0°C during the melting of the whole mass of disappeared ices that required c.a. 0.50 ZJ of thermal energy according to ice latent heat of fusion. The heat energy necessary to melt 1.5 trillion tonnes of ice at -20°C and form 1.5 10 15 Kg of liquid water at 0°C required about 0.56 ZJ. In addition, bringing 1.5 trillion tonnes of water from 0 °C up to 14°C, required about 0.09 ZJ according to the specific water heat capacity. In total, the heat energy necessary to turn the disappeared ices at -20°C to water at 14°C was thus about 0.65 ZJ (0.56 + 0.09). In other words, the disappeared 1.5 million tonnes of ices absorbed 0.65 ZJ of heat energy introduced in the low atmosphere, regardless of its origin.

The estimate of eAHR did not take into account the injection of Joules in the atmosphere by mammalians (humans, cattle and animals with hot blood), hydrogen-using rockets, criminal wildfires and volcanoes. Based on 80 W per capita, 7.5 billion humans generate about 0.02 ZJ annually to which a minimum of 0.01 ZJ can be added due to cattle. In 2018, 80 volcanoes were active, the Hawaii eruption being the largest with c.a. 0.76 10 9 cubic meters of lava. Assuming density, specific heat capacity and difference of temperature of lava being 2.6, 840 J/Kg/°C and 1000°C, respectively, the heat released by the Hawaiian volcano after cooling was c.a. 0.002 ZJ. Assuming an average of 0.001 ZJ/volcano, heat released by volcanoes was in the range of 0.08 ZJ. Wildfires could hardly be estimated but like volcanoes, they are very likely negligible relative to the 0.35 ZJ of eARH that finally represent less than 3% of the 12.7 ZJ of radiative forcing deduced from the 0.79 W/m 2 annual average rate of heating of the climate system for the period 2006-2018 applied to the surface of the planet (IPCC, 2022). This large difference of magnitude between annual e and rAHRs has already been pointed out in the literature [START_REF] Chaisson | Long-term global heating from energy usage[END_REF][START_REF] Zhang | Timescales and ratios of climate forcing due to thermal versus carbon dioxide emissions from fossil fuels[END_REF] but for different systems and under different conditions.

In terms of thermodynamics, the estimate of total anthropogenic heat energy released in the atmosphere in 2018 stored in the climate system was about 13 ZJ (0.35 + 12.7). 0.65 ZJ were absorbed by the lost ices, leaving 11.7 ZJ absorbed by oceans (90% of 12.35 ZJ) and land and atmosphere for the rest based on IPCC's mechanisms. Basically, the storage of heat energy in liquid raises the temperature of this medium unavoidably. However, when ice is present, melting fights temperature rise like when an ice cube is in a glass of water under summer sun. Therefore, one may ask why the 2018 ice imbalance was not much greater than the 1.5 trillion tonnes estimate [START_REF] Slater | [END_REF]. There are several possible reasons. Firstly, radiative forcing was largely overestimated, a hypothesis going against the current universal CO 2 -based claim but defended by some specialists of electromagnetic radiations who goes up to denying CO2-related anthropogenic warming (Sirroco, 2016;[START_REF] Humlum | The state of the climate in 2021[END_REF][START_REF] Gueskens | L'effet de serre et le bilan énergétique de la Terre[END_REF]. In this case, the share of eAHR would become predominant or the only source of anthropogenic heat to be eliminated. Secondly, atmospheric and oceanic streams were far from equilibrium and thus were not efficient enough to dispatch and homogenize the radiative forcing up to the surface. Last but not least, the heat absorbing capacity of evaporation was able to absorb the huge excess of eAHR and justify the absence of more important ice imbalance. Evaporation was mentioned about 200 times in IPCC's AR5 WG1 report (IPCC, 2014), but only relative to its effect on salinity, pan evaporation, balance of evaporation-precipitation, localization and not in terms of heat absorption and temperature regulation. Secondly, the AR6 2022 report mentions only "it is virtually certain that evaporation will increase over the oceans" with no consideration to associated heat exchanges.

In 2018, the average ocean level rise was about 3.7 mm in rather good agreement with the 4 mm generated by a surplus of 1.5 trillion tonnes of icederived liquid water in oceans. In parallel, the annual average global ocean and land temperature rises was estimated about 0.02-0.03 °C (NOAA, 2021). Temperature rising observed when a compound is heated depends on the thermal characteristics and the mass of this compound. Based on the 4.184 KJ/Kg/°C heat capacity of salt-free water, a 1 dm thick layer of ocean surface water (361 10 14 dm3 or 361 10 14 Kg) is able to absorb about 0.15 ZJ of heat energy for 1° C rise. This means that a minimal layer of more than 200 m would be necessary to absorb 11.7 ZJ with 0.03°C homogeneous temperature rise. In contrast, evaporation, that plays an essential role in a refrigerator, is able to absorb 2,247 KJ/Kg according to the latent heat of water evaporation at 14°C, the temperature of the warmly heated source being maintained constant, basically. The surface of Earth covered by water being about 390 10 6 km 2 or 390 10 14 dm 2 , the evaporation of 1dm layer of ocean water can absorb 95.5 ZJ without temperature change. Therefore, evaporation is about 600 times more efficient than ocean surface water to absorb global anthropogenic heat energy and fight global temperature change due to warming conditions.

Water released from fossil hydrocarbons

In the previous section, the discussion was based on a constant mass of water on Earth dispatched as solid, liquid, vapor and clouds since matter cannot escape to space. However, the combustion of all hydrocarbons (oil, natural gas, and biomass) that generates hot CO 2 from the carbon content generates also water as hot vapor from the atoms of hydrogen included in molecules. Once the heat stored in these hot gases is transferred to the environment; the cooled and condensed hot water constitutes a surplus that joins the existing pool of liquid water. It is important to note that heat produced by biomass burning is not compensated at the stage of biomass formation because this renewal requires solar light at ambient and not heat.

Quantifying the amount of extra water from hydrocarbons is as difficult as quantifying heats of e and rAHR-types. Nevertheless, estimates of the overall consumptions (close but slightly less than productions when heat release is concerned) of fossil oil and natural gas are available in oil equivalents and provide means to estimate the surplus of water. Between 1870 and 2018, about 180 Gt of oil and 30 GToe of natural gas have been extracted [START_REF] Martin-Amouroux | Consommation modiale d'énergie 1800-2000: Les résultats[END_REF]BP, 2019) i.e. about 210 Gt of hydrocarbons. To compensate the complex composition of oil and natural gas, one can assume these fossil hydrocarbons, including methane (CH 4 ), composed of alkanes only, the general chemical formula of which is C n H 2n+2 reasonably simplified to nCH 2 . Accordingly, 210 Gt of oil equivalent contain c.a. 180 Gt of carbon and 30 Gt of hydrogen. From the general equation CH 2 + 3 O 2 → CO 2 + H 2 O + heat, 14 g of hydrocarbon (12 + 2) generates 44 g of CO 2 (12 + 32) and 18 g of water (16 + 2), both compounds being hot. One can deduced that 210 Gt of hydrocarbons produced about 270 Gt of hot water in about 150 years. In 2018, 8 GT of oil equivalent of the hydrocarbon-type generated about 11.3 GT of hot water, an amount negligible compared with the heat absorption capacity of 1,500 GT of disappeared ices and of surface water evaporation.

According to section 5 and 6, the waste heat derived from the production and the consumption of energy on Earth seems negligible today relative to the radiative forcing estimate. However, this may change in the future if the production of energy continues to grow while the production of anthropogenic CO 2 and the corresponding radiative forcing are decreased as recommended to politicians by IPCC.

Can hydrogen from water be a solution?

Apart from limiting CO 2 production, climate scientists propose the development of new sources of energy among which hydrogen is more and more regarded as an attractive alternative [START_REF] Johnston | Hydrogen: the energy source for the 21st century[END_REF] provided it can be produced from water with regeneration of water after exploitation as source of electric energy according to the following catalyzed reactions: energy + H 2 O → H 2 + ½ O 2 → H 2 O + electricity. So far, hydrogen is primarily produced from fossil resources. Catalytic electrolysis is of interest only if the energy needed to dissociate water in hydrogen and oxygen is produced using environmentallyfriendly sources of electricity [START_REF] Gardner | Hydrogen production from renewables[END_REF]. What is presently missing to decide whether a source of energy is better than another is a heat-cycle assessment from cradle to grave, as it is currently done with life-cycle assessment to compare processes and materials that impact the environment [START_REF] Muralikrishna | Life Cycle Assessment[END_REF]. So far, we did not find any quantitative information relative to heat-cycles of wind turbines and of other CO 2 -free sources of electricity in comparison with fossil and radioactive sources of energy in terms of thermal impact on the climate. Hydro-electricity may be of particular interest in this regard. However, one can wonder whether large enough amounts of hydrogen will be producible from CO 2free sources of energy. It will be the task of specialists in thermodynamics, and physics together with climatologists and chemists to collect information's necessary to decide.

Conclusion

The mechanism by which the temperature in a refrigerator is controlled appeared a rather consistent model of how the average temperature of the global environment may be controlled if water is given the role of refrigerant with: -ice melting and water evaporation as heat absorbing phenomena, -chaotic climatic events like hurricanes, tornadoes, ocean streams and humid air ascension to move the warm vapor to condensation zones as the compressor does in a refrigerator; and -clouds as source of radiative elimination to space of the transferred heat they release because of water condensation. Accordingly, surface temperature and thus sea level rises should be smaller than IPCC's calculated values for the next decades. In contrast, climatic events (flooding, drought, local temperatures, etc.) should increase in strength or magnitude and frequency if human population and its standard of living continue to grow and generate more and more anthropogenic heat release, regardless of its origin. In terms of thermodynamics, the refrigerant role of Earth's water appears a credible means to avoid heat accumulation on Earth and promote radiative elimination to space. The predominance of radiative forcing relative to anthropogenic heat releases suggested that 2018 ice imbalance should have been much larger than observed except if evaporation is taken into account or if scientists who deny radiative forcing turn to be right. In parallel, the amount of liquid water stored for millions of years in fossil hydrocarbons and released by combustion was shown negligible relative to the amount generated by disappeared ices. In the future, the contribution of anthropogenic heat residue of energy sources could become no longer negligible if the deny of CO2 as source of radiative forcing defended by some specialists of electromagnetic radiations is recognized. Presently, relying on the reduction of carbon-containing sources of energy may appear insufficient to limit climate evolution and ice imbalance growth if the replacing sources of energy, including water as source of hydrogen, generate similar amounts of waste heat. Heat amounts and heat transfers estimated in the present essay will have to be assessed more precisely by suitable interdisciplinary consortia attempting to understand and to take into account the complexity of Earth like biologists are doing for the human body.

Acknowledgement

The author is indebted to CNRS and University of Montpellier for providing access to local facilities in the framework of an Emeritus CNRS Research Director position.

I am also indebted to the Editor-in-Chief of Earth's Future because he first accepted the submitted version after reviewing but faced complains later on and had to deny the acceptance on the basis of the reports of 5 extra reviewers. As I was not given the chance to reply to reviewer's reports although many comments and criticisms were disputable, the rejected submission was revised and the pointby-point reply at the origin is available on e-mail request from readers who would like to appreciate the consistency of the reviewing and of the work.

Figure 1 :

 1 Figure 1: Schematic representation of a Vapor Compression-Refrigeration cycle.

Figure 2 :

 2 Figure 2: Schematic representation of the machinery that manages residual solar heat energy through water phase exchanges.

Figure 3 :

 3 Figure 3: Schematic representation of the management of increasing amount of anthropogenic heat through evaporation-condensation-evaporation and ices melting.

Conflict of Interest

The author does not have any conflict of interest to report


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Keywords: intercondylar notch width (NWI), lateral femoral condylar index (LFCI), posterior tibial slope, ACL rupture, morphological risk factors

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

Reported risk factors for anterior cruciate ligament (ACL) injury include anatomic, hormonal, and neuromuscular parameters and bony morphological features including femoral condylar depth, lateral femoral notch, tibial plateau slope, and intercondylar notch shape. [START_REF] Burnham | Bony morphologic factors affecting injury risk, rotatory stability, outcomes, and re-tear rate after anterior cruciate ligament reconstruction[END_REF][START_REF] Eck | Femoral intercondylar notch shape and dimensions in ACL-injured patients[END_REF][START_REF] Hewett | Anterior cruciate ligament injuries in female athletes, part 1: mechanisms and risk factors[END_REF][START_REF] Musahl | The influence of bony morphology on the magnitude of the pivot shift[END_REF][START_REF] Pfeiffer | An increased lateral femoral condyle ratio is a risk factor for anterior cruciate ligament injury[END_REF][START_REF] Souryal | Bilaterality in anterior cruciate ligament injuries: associated intercondylar notch stenosis[END_REF] Pedoia et al [START_REF] Pedoia | Three-dimensional MRIbased statistical shape model and application to a cohort of knees with acute ACL injury[END_REF] suggested that variations of the femoral intercondylar width, including narrow femoral notch volume, which is associated with a higher incidence of ACL injuries, may predispose individuals to ACL injuries. [START_REF] Hoteya | Association between intercondylar notch narrowing and bilateral anterior cruciate ligament injuries in athletes[END_REF][START_REF] Wratten | Three-dimensional femoral notch volume in anterior cruciate ligament-deficient versus anterior cruciate ligament-intact patients: a matched case-control study with inter-gender comparison[END_REF][START_REF] Zhang | The correlation between common 2D femoral notch parameters and 3D notch volume: a retrospective MRI study[END_REF] More recently, a spherical appearance of the lateral femoral condyle or an excessive posterior femoral condylar offset has been implicated in an increased risk of ACL injury. [START_REF] Hodel | Introducing the lateral femoral condyle index as a risk factor for anterior cruciate ligament injury[END_REF][START_REF] Pfeiffer | An increased lateral femoral condyle ratio is a risk factor for anterior cruciate ligament injury[END_REF] An increased posterior tibial slope appears to predispose to primary ACL rupture [START_REF] Brandon | The association between posterior-inferior tibial slope and anterior cruciate ligament insufficiency[END_REF][START_REF] Feucht | The role of the tibial slope in sustaining and treating anterior cruciate ligament injuries[END_REF][START_REF] Hohmann | Is there a correlation between posterior tibial slope and non-contact anterior cruciate ligament injuries? Knee[END_REF] or failure after ACL reconstruction, [START_REF] Grassi | Patients with failed anterior cruciate ligament reconstruction have an increased posterior lateral tibial plateau slope: a case-controlled study[END_REF][START_REF] Lee | Does posterior tibial slope affect graft rupture following anterior cruciate ligament reconstruction?[END_REF][START_REF] Webb | Posterior tibial slope and further anterior cruciate ligament injuries in the anterior cruciate ligament-reconstructed patient[END_REF] with the lateral plateau having a more pivotal role compared with the medial plateau. [START_REF] Christensen | Lateral tibial posterior slope is increased in patients with early graft failure after anterior cruciate ligament reconstruction[END_REF][START_REF] Hodel | Introducing the lateral femoral condyle index as a risk factor for anterior cruciate ligament injury[END_REF] Identification of these bony factors may represent an important step in the development of prevention strategies for ACL injuries. [START_REF]International Olympic Committee Pediatric ACL Injury[END_REF] Most studies have focused on ACL bony morphological risk factors in patients with ACL ruptures or reruptures, but none have assessed the rates of participants estimated to be at risk for ACL injury in a healthy population.

The primary aim of the present study was to establish normal values of femoral and tibial bony parameters that are generally associated with ACL tears. Second, the rates of participants considered to be at risk according to the published thresholds reported in the literature were assessed. Third, interindividual variations of these bony values according to demographic characteristics were analyzed. It was hypothesized that a large proportion of healthy participants would exceed critical reported thresholds considered to pose a risk of ACL injury. Abbreviations used in this article are defined in Table 1.

METHODS

A computed tomography (CT) scan-based modeling and analysis system on .15,000 bone segments was used for this study (Stryker Orthopaedic Modeling and Analytics [SOMA]; Stryker). [START_REF] Schmidt | Stryker Orthopaedic Modeling and Analytics (SOMA): a review[END_REF] The SOMA database consists of .25,000 bone models obtained from .3600 participants worldwide. All scans were obtained as per local legal and regulatory requirements, which included ethical board approval and informed patient consent, where appropriate. CT scans were acquired exclusively for medical indications such as polytrauma (20%), CT angiography (70%), and other reasons (ie, total joint arthroplasty) (10%). A total of 382 participants (184 men and 198 women; mean age, 59.6 6 15.9 years; mean body mass index [BMI], 24.7 6 4.7) had reliable and complete data imaging sets that were selected and included (Table 2).

The study sample consisted of participants from different ethnic backgrounds (196 White and 186 Asian participants). The anatomic patterns of the pelvis, bilateral femur, bilateral tibia, and patella were examined. The healthy population consisted of participants without bone or joint abnormalities including no substantial osteoarthritis (Ahlba ¨ck grade I, without osteophytes) or evidence of previous surgery, including ACL reconstruction. CT scans were performed in different institutions worldwide and were included in the study only if the thickness of the slices was \1.5 mm and no motion artifacts were present. These measurements were then profiled to each bone on the database by the automated software. The measurements resulted in reproducible and consistent parameters for each participant with an associated margin of error of \2 mm and \1°. [START_REF] Banerjee | Innovations in hip arthroplasty three-dimensional modeling and analytical technology (SOMA)[END_REF][START_REF] Schro ¨der | Automated morphometric analysis of the femur on large anatomical databases with highly accurate correspondence detection[END_REF] The medial condylar width, lateral condylar width, intercondylar notch width, notch width index (NWI), lateral condylar flexion circle radius (LCFCR), lateral condylar extension circle radius (LCECR), lateral femoral condylar index (LFCI), medial posterior plateau tibial angle (MPPTA), lateral posterior plateau tibial angle (LPPTA), and difference between LPPTA and MPPTA (DPPTA) were assessed for each knee. The values were then profiled relative to the database within a margin of error \2 mm and 1°. [START_REF] Banerjee | Innovations in hip arthroplasty three-dimensional modeling and analytical technology (SOMA)[END_REF][START_REF] Schro ¨der | Automated morphometric analysis of the femur on large anatomical databases with highly accurate correspondence detection[END_REF] Medial and lateral condylar widths were measured on the widest part of the distal femur. The width of the intercondylar notch was measured at the level of the axial slice where both condyles showed their largest width. NWI was defined as the ratio between the width of the intercondylar notch and the width of the distal femur. The LCFCR and LCECR were determined by the flexion and extension curvature of the lateral femoral condyle approximated by 2 circles. Radii of these circles were then measured. To estimate the sphericity of the lateral femoral condyle, the LFCI was then determined. The LFCI was calculated according to the method described by Hodel et al, [START_REF] Hodel | Introducing the lateral femoral condyle index as a risk factor for anterior cruciate ligament injury[END_REF] dividing the radius of the flexion circumference by the radius of the extension circumference (Figure 1).

The proximal tibial plane was calibrated by marking .35 points on the medial and lateral tibial compartments. The mechanical axis of the tibia was defined as the line connecting the center of the tibial spine and the center of the ankle joint. The MPPTA and LPPTA were measured as the angles subtended between the medial and lateral tibial plateaus, respectively, and the mechanical axis of the tibia in the sagittal plane (Figure 2).

To perform this study, we explored an anonymized database after obtaining local ethical committee approval of the research protocol (Aix-Marseille University, No. 2019-127).

Thresholds for ''Abnormal'' Morphometric Parameters

A literature search was performed on Medline. A preliminary screening of the articles was based on title and abstract analysis. A second screening was based on a full-text review. Cadaveric studies were excluded from the analysis. For relevant studies, the associations between ACL injury and femoral or tibial bony morphological factors were investigated. Established anatomic thresholds were searched in the ACL injury group. Values that were considered as ''at risk'' were intercondylar notch width \20.2 mm, [START_REF] Ireland | A radiographic analysis of the relationship between the size and shape of the intercondylar notch and anterior cruciate ligament injury[END_REF][START_REF] Zhang | The correlation between common 2D femoral notch parameters and 3D notch volume: a retrospective MRI study[END_REF] NWI \0.292, [START_REF] Hoteya | Association between intercondylar notch narrowing and bilateral anterior cruciate ligament injuries in athletes[END_REF][START_REF] Ireland | A radiographic analysis of the relationship between the size and shape of the intercondylar notch and anterior cruciate ligament injury[END_REF][START_REF] Souryal | Bilaterality in anterior cruciate ligament injuries: associated intercondylar notch stenosis[END_REF][START_REF] Zhang | The correlation between common 2D femoral notch parameters and 3D notch volume: a retrospective MRI study[END_REF] LFCI \0.67, [START_REF] Hodel | Introducing the lateral femoral condyle index as a risk factor for anterior cruciate ligament injury[END_REF] MPPTA \83.6°, 11 and LPPTA \81.6°4 ,10,11,13 (Table 3). According to these thresholds, we aimed to define the percentage of healthy participants who could be considered to be at a higher risk of ACL injury. Some bony factors have not been evaluated by CT scanbased modeling, such as the lateral femoral condylar ratio, [START_REF] Pfeiffer | An increased lateral femoral condyle ratio is a risk factor for anterior cruciate ligament injury[END_REF] the notch shape, [START_REF] Eck | Femoral intercondylar notch shape and dimensions in ACL-injured patients[END_REF] and the bony morphology of the femoral lateral condyle. [START_REF] Fernandes | Is the femoral lateral condyle's bone morphology the trochlea of the ACL? Knee[END_REF]

Statistical Analysis

Mean values and standard deviations were determined for each of the measured anatomic parameters. Normal (Gaussian) distributions were defined. Univariate analysis was performed using t tests to estimate differences between groups. Multiple linear regression models were developed to establish the determinants for each of the variables. For each model, variables with a P value \.1 were kept in the final model.

Sample size was calculated based on the estimated intercondylar notch width (notch width = 21.65 6 2.70 mm [START_REF] Zhang | The correlation between common 2D femoral notch parameters and 3D notch volume: a retrospective MRI study[END_REF] ). For a required level of statistical significance of a = .05 and a power of 1 2 b = 0.9, 50 lower limb pairs would be required in each group or subgroup to detect .2-mm difference between groups and subgroups. A trained statistician (M.O.) performed statistical analysis using SPSS software (Version 22; SPSS Inc). All calculations were based on 2tailed tests.

RESULTS

Mean values, dispersion, and range of morphometric parameters are reported in Table 2. Regarding the previously published thresholds (Figure 3), 25% of the healthy population had an intercondylar notch width \20.2 mm, 25% had NWI \0.292, 62% had LFCI \0.67, 54% had MPPTA \83.6°, and 15%-49% had LPPTA \81.6°-85.0°a nd therefore met the definition of being considered at risk for ACL injury (Table 3). Only 14.4% of participants exhibited no ACL bony risk factors, whereas 84.5% had between 2 and 4 bony risk factors and 1.1% had all bony risk factors in this healthy population (Figure 4).

Regarding sex subgroups, significant differences between men and women were found for medial (absolute difference [AD] = 2.8 6 0.17 mm; P \ .0001) and lateral (AD = 3.1 6 0.16 mm; P \ .0001) condylar width, intercondylar notch width (AD = 2.4 6 0.24 mm; P \ .0001), LCFCR (AD = 2.3 6 0.13 mm; P \ .0001), LCECR (AD = 2.9 6 0.30 mm; P \ .0001), LFCI (AD = 0.03 6 0.01; P = .034), LPPTA (AD = 1.23 6 0.32°; P \ .0001), and DPPTA (AD = 0.56 6 0.26; P = .031) (Table 4). For the previously published thresholds, 4.7% of men versus 20.4% of women had an intercondylar notch width \20.2 mm, 12% of men versus 13.1% of women had NWI \0.292, 25.1% of men versus 37.2% of women had LFCI \0.67, 23.6% of men versus 27.8% of women had MPPTA \83.6°, and 20% of men versus 4.7% of women had LPPTA \81.6°.

Regarding ethnicity subgroups, significant differences could be identified between White and Asian participants for lateral condylar width (AD = 0.74 6 0.23 mm; P = .001), intercondylar notch width (AD = 1.50 6 0.26 mm; P \ .0001), NWI (AD = 0.006 6 0.002; P = .015), LCECR (AD = 1.13 6 0.34 mm; P = .001), LFCI (AD = 0.03 6 0.02; P = .036), and MPPTA (AD = 2.63°6 0.35°; P \ .01) (Table 5). For the previously published thresholds, 9.4% of White versus 15.7% of Asians had an intercondylar notch width \20.2 mm, 8.9% of White versus 16.2% of Asians had NWI \0.292, 33.5% of White versus 28.8% of Asians had LFCI \0.67, 17.3% of White versus 34% of Asians had MPPTA \83.6°, and 6.3% of White versus 8.9% of Asians had LPPTA \81.6°.

The multivariate regression analysis, including only the previously identified anatomic variables and controlling for confounding variables, confirmed the statistically significant relationship between sex and the medial and lateral condylar width (P \ .0001), the intercondylar notch width (P \ .0001), and the LCFCR and LCECR (P \ .0001). LPPTA, NWI, and LFCI were not significant, independent predictors according to sex (Table 6). Ethnicity was associated with significant differences between White and Asian participants for all parameters except for LPPTA and DPPTA in multivariate testing (Table 6). A significant correlation was found between femoral condylar width, AD, and BMI (respectively, P = .018 and P = .001). A weak relationship could be identified between medial and lateral condylar width and LCFCR with age (respectively, P = .001, P \ .0001, and P = .006) (Table 6).

DISCUSSION

The main finding of this study is the high proportion of healthy participants who should be considered at risk of ACL injury according to the previously published femoral and tibial anatomic morphological values. Substantial variations of these parameters were found according to sex (intercondylar notch width) and ethnicity (intercondylar notch width, LFCI, MPPTA).

Reported values for bony risk factors vary from one study to another, making it difficult to provide clinical recommendations for prevention or preventive treatments [START_REF] Dejour | Tibial slope correction combined with second revision ACL produces good knee stability and prevents graft rupture[END_REF] to reduce the risk of ACL injuries. In the present study, a high rate of healthy participants showed abnormal femoral and tibial bony morphological risk factors. This raises the question of their effective specificity and sensitivity in identifying which participants have a higher risk of sustaining an ACL injury or a graft rupture after ACL reconstruction.

A narrow notch is a recognized risk factor in patients sustaining an ACL injury. [START_REF] Smith | Risk factors for anterior cruciate ligament injury: a review of the literature, part 1: neuromuscular and anatomic risk[END_REF] Souryal et al [START_REF] Souryal | Bilaterality in anterior cruciate ligament injuries: associated intercondylar notch stenosis[END_REF] showed that the NWI was significantly smaller in patients with bilateral ACL (0.196) ruptures compared with those with unilateral ACL ruptures (0.225) or healthy controls (0.234). The reported mean NWI was higher in the present study (0.305) compared with the accepted threshold risk value (0.196).

Hodel et al [START_REF] Hodel | Introducing the lateral femoral condyle index as a risk factor for anterior cruciate ligament injury[END_REF] demonstrated an association between a decreased LFCI and ACL injury. This ratio indicates the normal spherical shape of the lateral condyle, which, when reduced, can be responsible for an abnormal pivoting mechanism. Hodel et al reported an LFCI of 0.67 in patients with ACL rupture and 0.76 in a control group. All P values were calculated using multiple analyses of variance. LCECR, lateral condylar extension circle radius; LCFCR, lateral condylar flexion circle radius; LFCI, lateral femoral condylar index; LPPTA, lateral posterior plateau tibial angle; MPPTA, medial posterior plateau tibial angle; NS, not significant; NWI, notch width index; DPPTA, difference between LPPTA and MPPTA.

have had degenerative changes that may have affected some parameters. Third, some bony factors were not evaluated in the present study given that the CT scan-based modeling and analysis system did not allow inclusion of all anatomic morphological parameters. Fourth, the results of this study cannot be generalized to the general population. Extreme age values were included, which are not representative of patients who have surgery for an ACL injury, but multivariate analysis showed that there was no correlation between the participants' age and the main bony risk factors for ACL injury. Some values were influenced by age and BMI of the participants, suggesting the dynamic contribution of these variables, but BMI and age did not influence the main ACL bony risk factors (NWI, LFCI, MPPTA, and LPPTA). The lack of inclusion of African descent participants, because of lack of data, also does not allow us to generalize the results of this study. This population is underrepresented in the literature, [START_REF] Kim | What differences in morphologic features of the knee exist among patients of various races? A systematic review[END_REF] and it has been demonstrated that White patients had narrower notches than African American men. [START_REF] Shelbourne | Intercondylar notch width measurement differences between African American and White men and women with intact anterior cruciate ligament knees[END_REF] The threshold values defined in this study may vary according to the ethnicity of the participants, and we did not perform the African and Middle Easterners subgroup analysis. Additional studies taking into account the ethnicity of the participants will have to be carried out before any conclusions can be made. The method of measuring bony values in this study was not strictly comparable with those used in the referenced studies, but there is no gold standard for such measurements. In addition, measurements derived from CT-scans are necessarily different from those derived from radiographs but have the advantage in this study of being reliable and reproducible.

The present study has some notable and relevant aspects. First, the reported values are clinically accepted and refer to a large demographic group in the published literature, which allowed for a secondary analysis with statistical power. Second, the study was based on 3dimensional CT analysis, which has been shown to be more accurate than 2-dimensional CT analysis for measurements of the lateral and medial tibial slopes and intercondylar notch width. The improved accuracy provided by this system allowed for improved reliability of the reported values.

Based on these findings, a significant proportion of healthy participants reached the thresholds considered to be at risk of ACL injury. Only 14.4% of participants had no ACL bony risk factor, and for some parameters, .50% of the population exhibited values exceeding defined normal values. Indeed, it seems to be difficult to correlate the clinical risk with bony morphological risk factors.

CONCLUSION

Precise definition of femoral and tibial anatomic risk factors for ACL injury is difficult. According to the thresholds that are usually reported in the literature, 15% to 62% of a healthy reference population should be considered as being at risk for an ACL injury. This rate is probably too In our study, a lower LFCI was observed (0.65) with a higher LCECR than the LCFCR. Conversely, Pfeiffer et al [START_REF] Pfeiffer | An increased lateral femoral condyle ratio is a risk factor for anterior cruciate ligament injury[END_REF] reported an increased posterior femoral condylar depth (corresponding to a less spherical femoral condyle) in patients with ACL injury. A meta-analysis showed that both medial and lateral slopes changes were associated with higher risk of ACL injury. Stijak et al, [START_REF] Stijak | Is there an influence of the tibial slope of the lateral condyle on the ACL lesion? A case-control study[END_REF] however, demonstrated an increased lateral tibial slope in patients with ACL injuries compared with control participants without substantial differences in the medial tibial slope. Hashemi et al [START_REF] Hashemi | Shallow medial tibial plateau and steep medial and lateral tibial slopes: new risk factors for anterior cruciate ligament injuries[END_REF] demonstrated similar results with a mean lateral tibial slope of 9° in the injured population. Similarly, Grassi et al [START_REF] Grassi | Patients with failed anterior cruciate ligament reconstruction have an increased posterior lateral tibial plateau slope: a case-controlled study[END_REF] found that lateral posterior tibial slope was a significant independent predictor for graft failure after ACL reconstruction. This may be because of the increased trend toward an anterior displacement of the tibia. More recently, some authors have shown that patients with posterior tibial slope .10° had a higher rate of subsequent graft tear, leading the investigators to consider osteotomy in these cases to prevent retear. [START_REF] Shelbourne | Posterior tibial slope in patients undergoing anterior cruciate ligament reconstruction with patellar tendon autograft: analysis of subsequent ACL graft tear or contralateral ACL tear[END_REF] All of these anatomic parameters may play a role in the pathogenesis of ACL tears; however, it should be noted that ''normal'' differences exist according to sex and ethnicity. For example, the intercondylar notch is wider in men than in women, [START_REF] Dienst | Correlation of intercondylar notch cross sections to the ACL size: a high resolution MR tomographic in vivo analysis[END_REF][START_REF] Ireland | A radiographic analysis of the relationship between the size and shape of the intercondylar notch and anterior cruciate ligament injury[END_REF][START_REF] Mahfouz | Three-dimensional morphology of the knee reveals ethnic differences[END_REF][START_REF] Shelbourne | Radiographic and intraoperative intercondylar notch width measurements in men and women with unilateral and bilateral anterior cruciate ligament tears[END_REF][START_REF] Shelbourne | The relationship of femoral intercondylar notch width to height, weight, and sex in patients with intact anterior cruciate ligaments[END_REF] which may explain the higher prevalence of ACL injuries in women. [START_REF] Hewett | Anterior cruciate ligament injuries in female athletes, part 1: mechanisms and risk factors[END_REF][START_REF] Myer | The effects of generalized joint laxity on risk of anterior cruciate ligament injury in young female athletes[END_REF][START_REF] Smith | Risk factors for anterior cruciate ligament injury: a review of the literature, part 2: hormonal, genetic, cognitive function, previous injury, and extrinsic risk factors[END_REF] Concerning ethnicity, it has been shown that African Americans have larger intercondylar notch width than White participants. [START_REF] Shelbourne | Intercondylar notch width measurement differences between African American and White men and women with intact anterior cruciate ligament knees[END_REF] In the present study, a wider intercondylar notch was reported in White compared with Asian participants.

In the present series, LPPTA was different between men and women on univariate analysis (84.1 6 0.2 vs 85.3 6 2.2, respectively) in keeping with previously reported results. [START_REF] Hashemi | Shallow medial tibial plateau and steep medial and lateral tibial slopes: new risk factors for anterior cruciate ligament injuries[END_REF] In healthy participants, Hashemi et al found a lateral posterior tibial slope of 5.40° in men (LPPTA = 84.6°) and 7.03° in women (LPPTA = 82.97°). However, multivariate regression analysis showed that lateral posterior tibial slope was not a predictive factor for differences according to sex. Our study identified LFCI as a positive predictive factor for significant differences between ethnicities. Trojian and Collins [START_REF] Trojian | The anterior cruciate ligament tear rate varies by race in professional women's basketball[END_REF] were the first to report different ACL tear rates in different ethnic and racial groups; those investigators found that Asian women had lower rates than White European American women. [START_REF] Trojian | The anterior cruciate ligament tear rate varies by race in professional women's basketball[END_REF] The results of the present study showed that only femoral anatomic features and specifically LFCI were slightly different between White and Asian participants, but the clinical effect may be small (absolute LFCI difference = 0.02).

The current study has several limitations that could affect the reported results. First, because of the retrospective nature of the database evaluation, it was not possible to incorporate any information regarding participants' behaviors such as sport and activity level. Second, only asymptomatic participants were included in this cohort, and they may not perfectly match patients with ACL-deficient knees in terms of anatomic parameters. This database excluded patients who had undergone ACL reconstruction but may have included participants who had an asymptomatic ACL injury or who sustained an ACL injury at a later stage. Some participants might high, and the generally reported thresholds may be misleading. Sensitivity and specificity analyses of large cohorts are therefore necessary to precisely define which participants with so-called bony abnormalities would really be at risk of sustaining ACL injuries and experiencing ACL reconstruction failures.

  yy

Figure 1 .

 1 Figure 1. The lateral femoral condyle index corresponds to the diameter of the flexion circle divided by the diameter of the extension circle, allowing an estimate of the sphericity of the lateral femoral condyle.

Figure 2 .

 2 Figure2. The lateral and medial proximal tibial planes are calibrated by marking .35 points on both compartments. The mechanical axis of the tibia is defined as the line connecting the center of the tibial spine and the center of the ankle joint. The medial posterior plateau tibial angle and lateral posterior plateau tibial angle were measured as the angles subtended between the medial and lateral tibial plateau, respectively, and the mechanical axis of the tibia in the sagittal plane.

Figure 4 .

 4 Figure 4. Number of anterior cruciate ligament (ACL) bony risk factors (RFs) per participant. Only 14.4% of the healthy population had no ACL bony risk factor according to the published thresholds; the threshold value of 81.6°was retained for the lateral posterior plateau tibial angle.

Figure 3 .

 3 Figure 3. Distribution of bony risk factors for anterior cruciate ligament (ACL) injuries in a healthy population. INW, intercondylar notch width; LFCI, lateral femoral condylar index; LPPTA, lateral posterior plateau tibial angle; MPPTA, medial posterior plateau tibial angle; NWI, notch width index.

TABLE 1

 1

		Abbreviations Used
	Abbreviation	Definition
	ACL	Anterior cruciate ligament
	AD	Absolute difference
	BMI	Body mass index
	CT	Computed tomography
	INW	Intercondylar notch width
	LCECR	Lateral condylar extension circle radius
	LCFCR	Lateral condylar flexion circle radius
	LFCI	Lateral femoral condylar index
	LPPTA	Lateral posterior plateau tibial angle
	MPPTA	Medial posterior plateau tibial angle
	MRI	Magnetic resonance imaging
	NWI	Notch width index
	DPPTA	Difference between LPPTA and MPPTA

TABLE 2

 2 Demographic and Anatomic Parameters Evaluated in Our Global Series a

		Mean 6 SD Range (Min-Max)
	Demographic parameters
	Age, y	59.6 6 15.9	18-92
	Height, kg	164.1 6 8.6	140-189
	Weight, cm	67.2 6 15.9	39-110
	Body mass index	24.7 6 4.7	15.6-41.6
	Anatomic parameters
	Intercondylar notch width, mm 22.0 6 2.6	15.6-29.1
	Medial condylar width, mm	25.0 6 2.2	19.8-31.1
	Lateral condylar width, mm	24.0 6 2.2	18.2-29.8
	NWI	0.305 6 0.022	0.200-0.400
	LCFCR	20.3 6 1.8	16.4-26.3
	LCECR	31.1 6 3.3	21.4-40.1
	LFCI	0.65 6 0.15	0.50-0.96
	MPPTA, deg	83.3 6 3.7	72.8-94.1
	LPPTA, deg	84.7 6 3.3	74.3-92.8
	DPPTA	3.50 6 2.59	0.1-13.1
	a LCECR, lateral condylar extension circle radius; LCFCR, lat-
	eral condylar flexion circle radius; LFCI, lateral femoral condylar
	index; LPPTA, lateral posterior plateau tibial angle; MPPTA,
	medial posterior plateau tibial angle; NWI, notch width index;
	DPPTA, difference between LPPTA and MPPTA.

TABLE 3

 3 Comparison of Femoral and Tibial Risk Factors With the Published Data Sets a ACL, anterior cruciate ligament; LFCI, lateral femoral condylar index; LPPTA, lateral posterior plateau tibial angle; MPPTA, medial posterior plateau tibial angle; MRI, magnetic resonance imaging; NA, not assessed; NS, not significant; NWI, notch width index.

	Bony Risk Factors Analyzed

TABLE 4 Univariate

 4 Analysis Estimating Mean Distal Femoral Values and Absolute Differences Between Male and Female Participants a LFCI, lateral femoral condylar index; LPPTA, lateral posterior plateau tibial angle; MPPTA, medial posterior plateau tibial angle; NWI, notch width index; DPPTA, difference between LPPTA and MPPTA.

		Men (n = 184)	Women (n = 198)	Absolute Difference	P Value
	Intercondylar notch width, mm	23.2 6 2.5	20.8 6 2.2	2.4 6 0.24	\.0001
	Medial condyle width, mm	26.5 6 1.7	23.7 6 1.6	2.8 6 0.17	\.0001
	Lateral condyle width, mm	25.6 6 1.7	22.5 6 1.5	3.1 6 0.16	\.0001
	NWI	0.304 6 0.019	0.305 6 0.024	0.001 6 0.002	.509
	LCFCR, mm	21.5 6 1.5	19.2 6 1.2	2.3 6 0.13	\.0001
	LCECR, mm	32.6 6 3.1	29.7 6 3.0	2.9 6 0.30	\.0001
	LFCI	0.66 6 0.15	0.65 6 0.15	0.03 6 0.01	.034
	MPPTA, deg	83.6 6 3.5	83.1 6 3.7	0.48 6 0.37	.193
	LPPTA, deg	84.1 6 3.5	85.3 6 2.9	1.23 6 0.32	\.0001
	DPPTA	3.20 6 2.48	3.76 6 2.66	0.56 6 0.26	.031

a

Values are expressed as mean 6 SD. LCECR, lateral condylar extension circle radius; LCFCR, lateral condylar flexion circle radius;

TABLE 5 Univariate

 5 Analysis Estimating Mean Distal Femoral Values and Absolute Differences Between White and Asian Participants a Values are expressed as mean 6 SD. LCECR, lateral condylar extension circle radius; LCFCR, lateral condylar flexion circle radius; LFCI, lateral femoral condylar index; LPPTA, lateral posterior plateau tibial angle; MPPTA, medial posterior plateau tibial angle; NWI, notch width index; DPPTA, difference between LPPTA and MPPTA.

		White (n = 196)	Asian (n = 186)	Absolute Difference	P Value
	Intercondylar notch width, mm	22.7 6 2.7	21.2 6 2.3	1.50 6 0.26	\.0001
	Medial condyle width, mm	25.1 6 2.0	24.9 6 2.4	0.23 6 0.22	.290
	Lateral condyle width, mm	24.3 6 2.2	23.6 6 2.3	0.74 6 0.23	.001
	NWI	0.307 6 0.278	0.302 6 0.013	0.006 6 0.002	.015
	LCFCR, mm	20.4 6 1.8	20.1 6 1.8	0.31 6 0.18	.085
	LCECR, mm	31.6 6 3.5	30.5 6 3.0	1.13 6 0.34	.001
	LFCI	0.64 6 0.15	0.66 6 0.14	0.03 6 0.02	.036
	MPPTA, deg	84.6 6 3.3	81.9 6 3.5	2.63 6 0.35	\.01
	LPPTA, deg	84.8 6 3.0	84.8 6 3.3	0.07 6 0.32	.832
	DPPTA	3.39 6 2.44	3.53 6 2.60	0.14 6 0.26	.593

a

TABLE 6

 6 Results of Multivariate Analysis Regarding Factors That Influenced Absolute Differences a

	Confounding Factors for	Intercondylar	Medial Condyle	Lateral
	Absolute Difference	Notch Width	Width	Condyle Width NWI LCFCR	LCECR	LFCI MPPTA LPPTA DPPTA
	Sex	P \ .0001 P \ .0001	P \ .0001	NS P \ .0001 P \ .0001	NS	NS	NS	NS
	Age	NS	P = .001	P \ .0001	NS	P = .006	NS	NS	NS	NS	NS
			R 2 = 20.001	R 2 = 0.01		R 2 = 0.004
	Body mass index	NS	P = .018	P = .001	NS	NS	NS	NS	NS	NS	NS
			R 2 = 0.11	R 2 = 0.13
	Ethnicity	P \ .0001 P = .001	P \ .0001	NS	P = .001 P \ .0001 P = .012 P = .002	NS	NS
	a

received consulting fees from Stryker. S.L.


Keywords: Double level osteotomy, Patient Specific Cutting Guide, Accuracy, Joint line obliquity, Clinical Outcomes Double level osteotomy, Patient Specific Cutting Guide, Accuracy, Joint line obliquity, Clinical Outcomes

Purpose: Double level osteotomy (femoral and tibial) (DLO) is a technically demanding procedure for which pre-operative planning accuracy and intraoperative correction are key factors. The aim of this study was to assess the accuracy of the achieved correction using patient-specific cutting guides (PSCGs) compared to the planned correction, its ability to maintain joint line obliquity (JLO) and to evaluate clinical outcomes and level of patient satisfaction at a follow-up of 2 years.

Methods: A single-center, prospective observational study including 22 patients who underwent DLO by PSCGs between 2014 and 2018 was performed. Post-operative alignment was evaluated and compared with the target angular values to define the accuracy of the correction for the Hip-Knee-Ankle Angle (ΔHKA), Medial Proximal Tibial Angle (ΔMPTA), Lateral Distal Femoral Angle (ΔLDFA) and Proximal Posterior Tibial Angle (ΔPPTA). Pre-and post-operative JLO was also evaluated. At 2 years follow-up, changes in the KOOS sub-scores and patient satisfaction were recorded. The Mann-Whitney U test with 95% confidence interval (95% CI) was used to evaluate the differences between two variables, the paired Student t test was used to estimate evolution of functional outcomes.

Results:

The mean ΔHKA was 1.3±0.5°, the mean ΔMPTA was 0.98±0.3°, the mean ΔLDFA was 0.94±0.2°; ΔPPTA was 0.45±0.4°. The orientation of the joint line was preserved with a mean difference in the JLO of 0.4±0.2. At last follow-up it was recorded a significant improvement in all KOOS scores and 19 patients were enthusiastic, 2 satisfied and one moderately satisfied.

Conclusion:

Performing a DLO using PSCGs produces an accurate correction, without modification of the joint line orientation and with good functional outcomes at 2 years follow-up

INTRODUCTION.

Osteotomies around the knee rep an ideal joint preserving procedures for the treatment of early tibiofemoral osteoarthritis [START_REF] Conventry | Osteotomy of the upper portion of the tibia for degenerative arthritis of the knee. A preliminary[END_REF][START_REF] Ferner | Medial open wedge vs. lateral closed wedge high tibial osteotomy -Indications based on the findings of patellar height, leg length, torsional correction and clinical outcome in one hundred cases[END_REF] with extra-articular deformities [START_REF] Amendola | Results of high tibial osteotomy: review of the literature[END_REF][START_REF] Seil | The rapid evolution of knee osteotomies[END_REF]. When correcting large deformities in a single bone (tibia or femur), surgeons exposed them to the risk of creating abnormal joint line obliquity (JLO), which can compromise post-operative outcomes [START_REF] Saragaglia | Role of computer-assisted surgery in osteotomies around the knee[END_REF]. Double level osteotomy (femoral and tibial) (DLO) is a technically demanding procedure for which pre-operative planning accuracy and intraoperative correction is a key factor for achieving a corrected lower limb alignment [START_REF] Sharma | The role of knee alignment in disease progression and functional decline in knee osteoarthritis[END_REF][START_REF] Dugdale | Preoperative planning for high tibial osteotomy. The effect of lateral tibiofemoral separation and tibiofemoral length[END_REF]. The accuracy has been improved by the introduction of three-dimensional (3D) pre-operative assessment systems [START_REF] Sailhan | Differences in limb alignment and femoral mechanicalanatomical angles using two dimension versus three dimension radiographic imaging[END_REF], assisted surgery techniques such as computer assisted surgery [START_REF] Saragaglia | Role of computer-assisted surgery in osteotomies around the knee[END_REF] and 3D patient-specific cutting guides (PSCGs) [START_REF] Donnez | Are three-dimensional patient-specific cutting guides for open wedge high tibial osteotomy accurate? An in vitro study[END_REF][START_REF] Ke | Does patient-specific instrumentation increase the risk of notching in the anterior femoral cortex in total knee arthroplasty? A comparative prospective trial[END_REF].

The recent introduction of PSCGs using pre-operative computed tomography (CT) scan templating has raised the possibility of making instrumentation specific to each patient, which in turn could result in a more accurate correction of the bony misalignment with a decrease in operative time compared with conventional techniques during single level osteotomy procedure [START_REF] Thienpont | A systematic review and meta-analysis of patientspecific instrumentation for improving alignment of the components in total knee replacement[END_REF][START_REF] Haglin | Patient-Specific Orthopaedic Implants[END_REF][START_REF] Jacquet | Patient-specific high-tibial osteotomy's "cuttingguides" decrease operating time and the number of fluoroscopic images taken after a Brief Learning Curve[END_REF].

There are, however, potential difficulties when performing a DLO using PSCGs. One example is the inability to adapt the planned correction intra-operatively. The accuracy may also be compromised owing to the fact that the procedure requires a perfect match between the planned correction, the guide for the femoral correction and the guide for the tibial correction [START_REF] Jacquet | More accurate correction using "patientspecific" cutting guides in opening wedge distal femur varization osteotomies[END_REF][START_REF] Chaouche | Patient-specific cutting guides for openwedge high tibial osteotomy: safety and accuracy analysis of a hundred patients continuous cohort[END_REF] compared to a single level correction which simply requires a single accurate PSCG [START_REF] Gómez-Palomo | Double Level Osteotomy Assisted by 3D Printing Technology in a Patient with Blount Disease: A Case Report[END_REF].

To date, little has been published on the results and accuracy of DLO procedure using PSCGs. The aim of our study was to evaluate the accuracy of the achieved correction using PSCGs compared to the planned correction and its ability to maintain JLO in patients who suffered from knee pain, who had never undergone knee surgeries, in a context of important varus alignment with both tibial and femoral deformity. The second objective was to evaluate clinical outcomes and level of patient satisfaction at a follow-up of 2 years.

The hypothesis was that performing a DLO using PSCGs results in an accurate correction, similar to that seen in single level corrections, without adversely affecting the JLO (with an acceptable increase of JLO < 2°) and achieve satisfactory patient reported functional outcomes at 2 years follow-up.

MATERIAL AND METHODS

Population

All patients undergoing a DLO using PSCGs between February 2014 and November 2018 were enrolled in this single-center, prospective continuous cohort, observational study. Indication for DLO included patients aged under 65 years old with important knee pain and isolated medial knee osteoarthritis (Ahlbäck ≤3), a preserved status of the patellofemoral and lateral tibiofemoral joints assessed using clinical and radiological examination, a stable knee in the sagittal and coronal planes, a significant varus alignment (Hip-Knee-Ankle angle (HKA) ≤ 170°) with concomitant tibial and femoral varus deformity (Medial Proximal Tibia Angle (MPTA) < 85° and Lateral Distal Femoral Angle (LDFA) > 90°) and the failure of all non-surgical treatments. The exclusion criteria comprised of previous ipsilateral knee surgery and hardware or bony abnormalities that would interfere with obtaining a high-quality CT scan.

Twenty three patients met the inclusion and exclusion criteria, 1 patient was lost to follow-up and finally twenty two patients (19 men and 3 women) were included in this study. Minimum follow-up was 24 months Patient consent was collected pre-operatively after they were informed of the procedure in accordance with the principles of the Declaration of Helsinki. Local Ethical Committee approval was obtained prior to study initiation.

Pre-operative planning

In the pre-operative planning stage, the planned correction was first calculated by the surgeon using conventional radiographs (calibrated weight-bearing long-leg, A/P, and lateral views). Subsequently, all patients underwent a CT scan. The CT scan protocol consisted of acquiring images centered on the femoral head, the knee (allowing the distal femur and 15 cm of the proximal tibia to be captured), and over the ankle. The slice thickness was 0.625 mm for the knee and 2 mm for the hip and ankle (GE Light Speed VCT64). The surgeon took measurements and filled out an order form for the engineer which specified the correction objectives in the frontal and sagittal planes through variations in the HKA, MPTA, LDFA and Posterior Proximal Tibia Angle (PPTA). Pre-operative angles are summarized in the table 1. Joint orientation was also evaluated by measuring the joint line obliquity (JLO) and joint line convergence angle (JLCA) to assess soft tissue laxity. As there were no sagittal femoral correction planned, the posterior distal femoral angle was not considered. Tibial and femoral osteotomy models were used to virtually position PSCGs (Figure 1) and Activmotion plates (Newclip Technics®, Haute-Goulaine, France) both on the tibia and the femur using the protocol defined by the manufacturer. The PSCG design takes into account the resection plane and the position of the screw tunnels relative to the virtual positioning of the plates. The objective behind PSCGs is to define the optimal plate position after osteotomy correction, and then to transfer this anatomical position to the pre-osteotomy guide position. When the final plate's position fits the drill holes using the PSCG, the osteotomy is performed according to the pre-operative plan.

Surgical technique

All surgical procedures followed the same surgical steps, starting off with the distal femoral closing wedge osteotomy [START_REF] Jacquet | More accurate correction using "patientspecific" cutting guides in opening wedge distal femur varization osteotomies[END_REF]. The distal femoral lateral surface was exposed and the anatomical cutting guide was positioned. When an optimal position was confirmed by fluoroscopy, the guide was secured to the bone by 4 to 7 pins. Additional pins (cutting and hinge pins) were positioned to secure the osteotomy cutting plane. The nine holes required for the plate were pre-drilled prior to performing the osteotomy. The valgus femoral osteotomy was then performed with the PSCG in place; the saw blade was guided utilizing a specific slotted capture. Next, the distal part of the PSCG was removed and a closing wedge (with a 4-5 mm lateral base) was removed to complete the osteotomy. The plate was secured using nine screws, the sizes of which were pre-determined during the pre-operative planning.

The second stage consisted of performing the opening wedge high tibia osteotomy following a previously published method [START_REF] Chaouche | Patient-specific cutting guides for openwedge high tibial osteotomy: safety and accuracy analysis of a hundred patients continuous cohort[END_REF][START_REF] Munier | Can three-dimensional patient-specific cutting guides be used to achieve optimal correction for high tibial osteotomy? Pilot study[END_REF]. The medial aspect of proximal tibia was exposed. The eight holes needed for the plate were pre-drilled prior to performing the osteotomy. The osteotomy was then performed with the PSCG in place and the proximal portion of the modular cutting guide was removed to finish the osteotomy in a single plane or two planes. This step was dependent on the planned correction and the position of the patellar tendon. The osteotomy was then gradually opened/distracted with a laminar-spreader until the pre-drilled screw holes were aligned with the holes in the plate. The bone defect was left empty or filled with a femoral head wedge allograft.

Post-operative management

Weight-bearing was not allowed for the first 3 weeks. Then, progressive partial weight bearing with the aid of 2 crutches was commenced after 3 weeks to reach a full weight bearing after 6 weeks. Range of motion was not restricted during the rehabilitation phase. All patients received thromboprophylaxis with low molecular-weight heparin pre-and post-operatively for 45 days.

After surgery, patients were reviewed at 1, 3, 6, 12 and 24 months for regular follow-up with radiographs (long-leg standing (Figure 2), A/P, and lateral) and KOOS score evaluation. Femoral and tibial bone union were systematically assessed by radiological evaluation at 1, 3, 6, 12 and 24 months: the bone repair process was considered complete when there was continuity in 3 out of 4 cortices in anterior and lateral projections (both femoral and tibial) after 5 months; delayed between 5 and 8 months and not completed (non-union) after 8 months [START_REF] Dijkman | When is a fracture healed? Radiographic and clinical criteria revisited[END_REF]. Post-operative alignment was evaluated and compared with the target angular values, by two independent observers, to define the correction accuracy. We reported an Intraclass Correlation Coefficient (ICC) of 0.79, 0.81, 0.87 and 0.85 for the Δ values (ΔHKA, ΔMPTA, ΔPPTA, ΔLDFA respectively) and an ICC of 0,80 and 0.82 for JLO and JLCA measurements. For all angular values both in the sagittal and coronal planes, the goal was to obtain a perfect coincidence between the planned and the obtained angular values (delta = 0) with a degree of tolerance of 2°.

Changes in the KOOS sub-scores were recorded, comparing pre-operative to the 24 months assessment: ΔKOOS Pain, ΔKOOS Symptoms, ΔKOOS ADL, ΔKOOS Sport/Rec, and ΔKOOS QOL were defined this way. Ability to return to work and sport were also recorded. At 24 months followup, patient satisfaction was ranked upon 5 items questionnaires (disappointed, not-satisfied, moderately satisfied, satisfied, and enthusiastic).

Statistical analysis

Statistical analyses were performed with use of SSPS software (IBM; Armonk, New York). Means and standard deviations (SDs) were determined for each of the measured and desired anatomic parameters. Normal (Gaussian) distributions was verified to determine adequate statistical testing method (either parametric or non-parametric) to estimate difference between pre-operative, planned and post-operative parameters groups in an univariate analysis. The Mann-Whitney U test for two independent samples with 95% confidence interval (95% CI) was used to evaluate the differences between two variables, the paired Student t test was used to estimate evolution of functional outcomes during follow-up. Following the data collection, the statistical power was checked. Using the Δ angular corrections (planned corrections -obtained corrections) as a primary parameter with 80% of power, Alpha 0.05 and a value of Δ < 3.0°, it was estimated that the sample size should be 14.

Therefore, the sample size of 22 in the present study is reasonable in terms of statistical power.

RESULTS

Correction accuracy and radiographic results

The mean ΔHKA was 1.3±1.5 (p = 0.12), the mean ΔMPTA was 0.98±1.3 (p = 0.09), the mean ΔLDFA was 0.94±1.2 (p = 0.09); ΔPPTA was 1.05±1.4 (p = 0.2). For all the radiographic parameters, there were no statistically significant differences between the target values and the post-operative values (Table 2). A mean pre-operative JLO of 1.4±1.2° and a mean post-operative JLO of 0.9±1.2° were observed, thus the orientation of the joint line was preserved with a mean difference in the JLO of 0.5±0.90.

Mean consolidation time at radiographic control was 4.4±1.8 months for the femur and 5.1±1.5 months for the tibia. No case of non-union was reported.

Functional outcomes

At final follow-up assessment, 24 months after surgery, an improvement of 37±16 for the KOOS pain (5-75), 37±25 for the KOOS Symptoms (2-82), 37±32 for the KOOS ADL (4-92), 34±37 for the KOOS Sport/Rec (2-87) and 3625 for the KOOS QOL (7-73) (p < 0.0001) (Table 3) were observed.

The mean time to return to work and sports were 4.0±1.6 (3-12) and 4.9±1.2 (2-7) months, respectively. At 24 months follow-up 19 patients were enthusiastic, 2 satisfied and one moderately satisfied.

Complications

One minor complication (post-operative hematoma) and one major complications (deep wound infection) were observed in the cohort. No revisions to total knee arthroplasty or unicompartmental knee arthroplasty were observed at 24 months follow-up.

DISCUSSION

The main finding of this study was that performing a DLO with PSCG is an accurate procedure and preserves pre-operative joint line orientation. The results for achieving desired corrective accuracy are in keeping with those previously published for both single femoral and tibial osteotomies. Good functional outcomes at 2 years follow-up were observed in this cohort.

Conventional DLOs are highly demanding procedures and require a protracted learning curve. In 1969, Benjamin et al [START_REF] Benjamin | Double osteotomy for the painful knee in rheumatoid arthritis and osteoarthritis[END_REF] was the first to report a series of 57 DLO with indications of rheumatoid osteoarthritis and osteoarthritis. In this series, he reported a good level of patient satisfaction despite some complications including limited range of motion and six patients without reduced pain. Analyses of the pre-operative deformity and the post-operative correction (HKA angle or JLO) were not mentioned. Babis et al. [START_REF] Babis | Double level osteotomy of the knee: a method to retain joint-line obliquity. Clinical results[END_REF] reported on 24 patients (29 knees) operated on utilizing a conventional technique. A computer-aided analysis of the mechanical status of the knee was used for pre-operative planning. Their results showed a mean post-operative HKA angle of 176.9° (169.4-184.9°) with a residual varus in two cases (4.6-4.9°) and an over correction of more than 4° in ten cases and more than 6° in five. No information was available concerning the pre-operative and post-operative JLO.

Otherwise, a high level of post-operative alignment accuracy was reached in computer assisted procedures despite their cost and increased surgical time [START_REF] Saragaglia | Navigated osteotomies around the knee in 170 patients with osteoarthritis secondary to genu varum[END_REF][START_REF] Maurer | High tibial osteotomy: does navigation improve results?[END_REF]. Saragaglia [START_REF] Saragaglia | Results of forty two computer-assisted double level osteotomies for severe genu varum deformity[END_REF] reported a case series of 38 patients in which the pre-operative target was reached in 92.7% of patients for HKA and 88.1% for MPTA with 2° of accuracy. No information was reported concerning the pre-operative and post-operative JLO. The results of the present study are comparable with those of Saragaglia. Our study demonstrates that pre-operative targets were reached in all the patients with a slight difference between the planned correction and the post-operative values, which were not statistically significant and always within the gap of 2° of discrepancy. A lower accuracy in the correction was observed for the HKA angle compared to other parameters. This angle is influenced by both the bony and soft tissue status [START_REF] Lee | Effect of soft tissue laxity of the knee joint on limb alignment correction in open-wedge high tibial osteotomy[END_REF]. This is accounted for the joint line convergence angle (JLCA). HKA measurements include JLCA values; therefore, it is important to assess the accuracy of the system by evaluating only direct bone corrections (MPTA, mLDFA and PPTA).

Previous studies have analyzed the accuracy of the PSCG system, but have been restricted to single level knee osteotomy [START_REF] Predescu | Early experience using patient-specific instrumentation in opening wedge high tibial osteotomy[END_REF]. Nevertheless, a high level of precision has been demonstrated in single level osteotomies. Cerciello et al. in a systematic review analyzed 28 studies which focused on single level osteotomies performed by computer navigation and patient specific instrumentation. In their conclusions they stated that it had been observed a reduced rate of post-operative outliers for PSI instrumented osteotomies compared to conventional techniques [START_REF] Pérez-Mañanes | 3D Surgical Printing Cutting Guides for Open-Wedge High Tibial Osteotomy: Do It Yourself[END_REF][START_REF] Cerciello | CAS and PSI increase coronal alignment accuracy and reduce outliers when compared to traditional technique of medial open wedge high tibial osteotomy: a meta-analysis[END_REF]. Specific accuracy correction results of open-wedge high tibial osteostomy procedures using PSCGs have been published by Chaouche et al [START_REF] Chaouche | Patient-specific cutting guides for openwedge high tibial osteotomy: safety and accuracy analysis of a hundred patients continuous cohort[END_REF]. They observed that the mean ΔHKA was 1 ± 0.95°, the mean ΔMPTA was 0.54 ± 0.63°, and the mean ΔPPTA was 0.43 ± 0.8°. In all cases, the discrepancy between planned and achieved correction was less than or equal to 2°. Similar results were published in distal femoral osteotomies using PSCGs by Jacquet et al [START_REF] Jacquet | More accurate correction using "patientspecific" cutting guides in opening wedge distal femur varization osteotomies[END_REF]. The HKA target was also reached in 100% of case with 2° of discrepancy. Finally, the correction accuracy observed in the present study was similar to those previously described for both femoral or tibial single level osteotomies using PSCGs.

Double level osteotomies have been introduced to avoid joint line obliquity [START_REF] Schröter | Development of the double level osteotomy in severe varus osteoarthritis showed good outcome by preventing oblique joint line[END_REF][START_REF] Micicoi | Osteotomy around the knee is planned toward an anatomical bone correction in less than half of patients[END_REF]. Nakayama et al.

reported that a JLO >5° (medial proximal tibial angle of 95°) determines detrimental stress to the articular cartilage, so they proposed that DLO should be indicated for varus knees with a preoperatively anticipated MPTA of >95 [START_REF] Nakayama | Large correction in opening wedge high tibial osteotomy with resultant joint-line obliquity induces excessive shear stress on the articular cartilage[END_REF]. Our study highlights the benefits of this technique [START_REF] Akamatsu | Joint line obliquity was maintained after double-level osteotomy, but was increased after open-wedge high tibial osteotomy[END_REF],

with preservation of the joint line orientation in cases where there is extra-articular varus deformity arising from both the tibia and femur. An acceptable difference of 2°, as recommended by most studies, was found in this study [START_REF] Nakayama | Large correction in opening wedge high tibial osteotomy with resultant joint-line obliquity induces excessive shear stress on the articular cartilage[END_REF][START_REF] Song | What Is An Acceptable Limit of Joint-Line Obliquity After Medial Open Wedge High Tibial Osteotomy? Analysis Based on Midterm Results[END_REF].

Finally, the second main outcome was to investigate clinical results at 24 months follow-up. A consistent improvement in all sub-categories of the KOOS score was observed and 86.6% of patients were enthusiastic regarding the results of their surgeries. Comparing these clinical results to previously published DLO results, they were comparable [START_REF] Saragaglia | Results of forty two computer-assisted double level osteotomies for severe genu varum deformity[END_REF] or even superior [START_REF] Nakayama | Physiologic knee joint alignment and orientation can be restored by the minimally invasive double level osteotomy for osteoarthritic knees with severe varus deformity[END_REF].

The present retrospective study has several limitations. Firstly, this is a non-comparative study; even if data exist on the accuracy and recurrence of JLO in conventional techniques, a control group of conventional DLO would have been interesting for doing a direct comparison. Secondly, the surgeons who performed these procedures, were familiar with osteotomy surgeries and had already used PSCGs during femoral or tibial single level osteotomies. Their results may not be directly transferrable to other less experienced surgeons. Thirdly, follow-up time was limited to two years following surgery and so long-term data on functional outcomes, revision rates, total knee arthroplasty conversion rates were not available.

CONCLUSION

Performing a DLO using PSCGs produces an accurate correction, without modification of the joint line orientation and with good functional outcomes at 2 years follow-up. The use of PSCGs in the execution of DLOs guarantees very high levels of precision comparable to those obtained through the use of the same instrumentation for single level osteotomies. Therefore, it represents a useful tool in the hands of surgeons with less experience in this complex surgery, with the assumption of correct planning and adequate indications.

HKA (°)

165 ΔKOOS pain, ΔKOOS symptoms, ΔKOOS ADL, ΔKOOS sport/rec, ΔKOOS QOL: difference between the value obtained in the pre-operative questionnaire and that obtained at 24 months followup

Fig. 1 :Fig. 2 :

 12 Fig.1: Planification of ideal cutting guides positioning using a 3D-CT Based corrected femoral and tibial models. A: Femur frontal view/ B: Femur sagittal view/ C: Tibia frontal view/ D: Tibia sagittal view

Table 1

 1 Radiological parametersHKA hip-knee-ankle angle; MPTA medial proximal tibial angle; PPTA posterior plateau tibial angle; JLO joint line obliquity; JLCA joint line convergence angle; LDFA mechanical lateral distal femoral angle; Δ accuracy of the post-operative alignment correction was defined by the difference between the desired corrections defined pre-operatively and the correction obtained post-operatively measured on Ct scan; N/E: Not evaluated

		.7 ± 4.4°	179.7 ± 1.2°	1.3 ± 1.5°
	MPTA (°)	81.1 ± 1.2°	86.9 ± 2.8°	0.98 ± 1.3°
	PPTA (°)	80.8 ± 4.3°	81.5 ± 3.7°	1.05 ± 1.4°
	LDFA	92,8 ± 0.2°	88.7 ±0.2°	0.9 ± 1.2°
	JLO (°)	1.4 ± 1.2°	0.9 ± 1.2°	N/E
	JLCA	2.8 ± 2.3°	1.7 ± 2.3°	N/E

Table 2

 2 Functional outcomes.

The authors did not receive support from any organization for the submitted work.

No funding was received to assist with the preparation of this manuscript.

No funding was received for conducting this study.

No funds, grants, or other support was received. MO is educational consultant for New-Clip, Stryker and Arthrex KK is educational consultant for New-Clip CJ, RK, FG, PM, GM, LH have no relevant financial or non-financial interests to disclose.

Ethics approval and consent to participate and to publish

Patient consent was collected pre-operatively after they were informed of the procedure in accordance with the principles of the Declaration of Helsinki. Local Ethical Committee approval was obtained prior to study's initiation (Comité Informatique et Liberté (CIL) / Assistance Publique des Hopitaux de Marseille (AP-HM) / Registration Number 2019-127)).

Conflicts of interest

MO is educational consultant for New-Clip, Stryker and Arthrex KK is educational consultant for New-Clip CJ, RK, FG, PM, GM, LH have no relevant financial or non-financial interests to disclose