José Manuel Noguera-Vivo
email: jmnoguera@ucam.edu

A journalistic approach to IDN when the user is the message: The JUC model for content strategy

Regarding the triad among environmental hypercomplexity, complex interactive narrative representations and complex audiences, underlined by Noam Knoller,1 this approach is related to the last element -audiences-and it is focused on the emergent trends around the called Creator Economy [START_REF] Schram | The state of the creator economy[END_REF], which it is happening because previously we had -and we are having right now in an increasing way-a Creator Communication Media Landscape (CCML). We develop here a model of content strategy for Interactive Digital Narratives (IDN) to deal with the growing complexity of the media audiences, by showing how professional content can coexist within digital ecosystems of mainly amateur content.

By rephrasing the well-known McLuhan´s paradigm [START_REF] Mcluhan | The medium is the message[END_REF]) where the medium is the message (and the massage), we apply it to the online media landscape in this last decade, where "the user is the message" [START_REF] Cardoso | Los medios de comunicación en la Sociedad Red: filtros, escaparates y noticias[END_REF]Scolari, 2008: 98;[START_REF] García-Avilés | Comunicar en la Sociedad Red. Teorías, modelos y prácticas[END_REF] but, what does it means? Traditional communication models (Lasswell, Gerbner, Shannon & Weaver, Schramm…) were created mainly by describing the effects of technology and content. Now it is different. Nowadays we have not just "prosumers revisited" [START_REF] Kotler | The prosumer movement[END_REF] or proactive audiences, but also a huge variety of user-led content creation [START_REF] Bruns | From prosumer to produser: Understanding user-led content creation[END_REF] which modifies in so many ways the original term of "prosumer" coined by [START_REF] Toffler | The third wave[END_REF] decades before of the arise of the social media. He had a futuristic glimpse about the horizontal digital scenarios where amateur and professional content would coexist at the same level.

Models created by digital networks are different than the previous ones to the internet. By one side, as Castells (2010) said, social networks are the contemporary social way of organization. By the other side, a network should be considered in a holistic way: any kind of network -especially digital ones-is much more than the simple aggregation of its individual members. Firstly, this holistic view is caused by internal factors (algorithms); secondly, the community component is a phenomenon developed by the social filtering (see Twitter, for instance). In this Network Society, journalism cannot be considered as a product anymore, but a service. Finally, we could add a third factor: the editorial filtering -no one like to read points of view against his/her "confirmation bias" [START_REF] Klayman | Varieties of confirmation bias[END_REF]-.

Media are not the final destiny for the users, now media are just a member of the network [START_REF] Hermida | Twittering the news: The emergence of ambient journalism[END_REF], (almost) just like the users. They both are not members of the news stock industry anymore, but members of the communication flows industry, where social platforms are leading the dissemination of news and "incidental news consumption" is one of the first consequences in this media landscape [START_REF] Boczkowski | News comes across when I'm in a moment of leisure": Understanding the practices of incidental news consumption on social media[END_REF]. This phenomenon shows us how the activity of looking for news is being replaced by the fact of finding news I was not looking for, so it is a challenge for any kind of professional digital content strategy.

The rise of social such Twitch, Tik Tok or Instagram Stories, as well as the new measures adopted by other one like Twitter for improving the experience of the "content creators" within the network (newsletters, tip button…) and relevance of youtubers for some audiences, are just some of the factors that helped to create the CCML mentioned before, which it is mainly an interactive digital narrative (IDN). When the user is the message, the journalism industry -as professional storytellersmust find its place inside this user-centered model, to solve some issues related mainly to authorship, revenues, content strategies and personal branding for journalists. A way to find this place is by considering any journalistic narrative as a potential IDN. In this context, the great disruption is not the interactivity journalist-user -which we had many years ago already-, but the inter-action among users, who are re-interpreting the content and the message in a daily basis (see the internet memes, for instances) and even contributing to the complexity growth instead of its reduction. For this reason, a professional filtering or edition is needed. With a new content strategy made in cooperation with community users, we can solve issues such cognitive reduction of complexity -see all the problems caused by misinformation and disinformation around COVID issues-.

In order to play a key role in this user-centered online market made by the Creator Economy, media can face this reality by using the tool we call here as JUC model (the triad of Journalists, Users and Community): just those narratives made from the horizontal perspective suggested by the JUC model -horizontal in terms of collaboration of different online actors without hierarchical borders: media, journalists, users…-can play at the same level. In other words, success comes when the Journalistic narrative is perceived by the Users as something made within the Community of each medium. Some key questions will be developed to clarify the role of each one of these spheres during the narrative process (journalist, user and community).

To sum up -but as starting point for further debates-, we claim here the JUC model as a content strategy for co-creations with the journalistic audiences, by considering also the so many different stages of the journalistic process: observation, selection, filtering, production, edition and dissemination. The co-creation can happens in any of these stages or in some of them at the same time. It depends how the JUC model helps to design the digital narrative in each particular case.

Personal communication, April 19,


Jacques Fontanel

Michael Ward

A Hard Look at the Costs of Peace

Keywords: Peace, disarmament, conversion, sovereignty, USA, leadership Paix, désarmement, conversion, souveraineté, USA, leadership

The end of the Cold War not only helps to end the destructive arms race, but also profoundly alters the major international balances. The United States was able to reap huge peace dividends, thanks to the acceleration of economic productivity, and Washington became the greatest economic and military power. However, for some regions (Africa) or countries (Russia), the human cost of the globalisation process has been very high, while the sovereignty of peoples has been indirectly questioned. Peace is both necessary and the conditions for its sustainable realisation requires major investments.

La fin de la guerre froide favorise l'extinction de la course aux armements destructrice, mais elle modifie aussi profondément les grands équilibres internationaux. Les Etats-Unis ont pu ainsi recevoir d'énormes dividendes de la paix, grâce à l'accélération de la productivité économique, et Washington est devenu la plus grande puissance économique et militaire. Cependant, pour certaines régions (Afrique) ou pays (Russie), le coût humain du processus de mondialisation s'est avéré très élevé, en même temps que les questions de souveraineté des peuples a été indirectement remise en question. La paix est à la fois nécessaire et les conditions de sa réalisation pérenne supposent d'importants investissements.

In 1988, Paul Kennedy surveyed the then current landscape of global politics and declared that what goes up must come down. In particular, f-great economic powers such as USA would be ineluctably seduced by an excessive and decadent investment in military might. As a result, le forecast a certain decline of American economics and military hegemony. Instead, it was the Soviet empire that quickly crumbled shortly thereafter. Ands cracks began to form in the foundations of putative Japanese economic invincibility, cracks that have expanded substantially since then. US military and economic mighty, far from waning, sere each enhanced significantly. The former was dramatically demonstrated by the stunning, rapid, and largely unpredicted victory in the Gulf war of 1990-91; the later by an explosive burst of productivity that expanded the breadth and scope of the post-industrial economy.

Indeed, the decade of the 1990s witnessed an enormous burst in new productivity in exactly the place it was least anticipated by Kennedy's flawed analysis. Instead of being replaced as a hegemonic power, the United States entered 21th century stronger than ever. While old enemies were primarily concerned with effecting a transition from failed socialism to hybrid capitalism, and as a result were devoting fewer resources to their military, the USA was able to effect a substantial reduction in its military sending programme, despite the fact that it continues to spend substantially more ion defence than most other countries. One plausible explanation is that the end of the cold war brought with it an enormous dividend-namely the acceleration of economic productivity-and that the largest beneficiary of that has quite naturally been the largest economic power, the United States.

The new economy and military leadership of the USA

It is important to take these twin developments into account, for their impact on the recent past has been very powerful. Yet, when historian historians write the chronology of the world politics in the 20 th century, the story will be dominated by three themes: military conflicts among states, economic development via capitalism, and the growth of political and economic institutions within and among states? Obviously, these themes are intertwined. The end of Cold War has important consequences.

One has been the embellishment of the US position as the pre-eminent global military power. Despite the fact that this was in reality the goal of the now defunct arms race, ironically it has been achieved in part as a result of disarmament that followed the end of the cold war. Not only did the Soviet Union disappear as a global military power, but also the US was able to slightly reduce its military spending while at the same time maintaining its lead through its advantageous technological position. Thus, militarily the hegemonic position of the US has been augmented by the peace dividend.

A second important consequence has been economic. Massive restructuring has brought with it enormous costs as well as opportunities. For Russia, the transformation from an inefficient command economy to a liberated market system (albeit with a troublesome legacy) presented itself as a series of deep crises for Russia and in part for its partners in the West [START_REF] Aganbeguyan | Un monde en transition. Les exemples de la Russie et de l'industrie d'armement[END_REF] In other words, these crises represented huge opportunities for transformation, but bore with them enormous costs and potential downside risks. Thus, the disinvestment and the reinvestment went hand in glove to produce a kind of peace investment that resulted directly from the necessities brought about the end of the Cold War [START_REF] Fontanel | [END_REF]. The most recent "Russian economic crisis of 1998 has been resolved by growth in Russian energy exports, but the economic is still struggling to find a stable growth path, with a huge human costs (Skharatan, [START_REF] Shkaratan | Conversion and personnel in the Russian military-industrial-complex[END_REF].

At the same time, US and Chinese economic power advanced at unprecedented rates. The Chinese economy has grown at rates of 10% per annum since the beginning of economic reform in 1978, has surpassed Japan as the fastest growing economy in Asia, and has had a stable currency; none of these trends have been affected by Asia's several economic Crisis. Us economy output was about $5,000 billion when Berlin wall fell; today it is worth about $10,000 billion [START_REF] Lau | The Chinese economy: Past, present and future[END_REF]. Most important has been increased productivity, much of it fuelled by the information economy, which in turn helped to generate sufficient taxes to eliminate budget deficits and bolster the capital accounts?? Moreover, globalisation could not have proceeded as quickly apace in the presence of the Cold War. The collapse of the USSR hastened the acceleration of local as well as global economic activity.

The question of sovereignty

These changes fundamentally upset the uneasy equilibrium that characterised the international political economy during the latter half of the 20 th century. The modern international system grew largely as an outcome of the creation of modern states. Empires had of course ruled different parts of the globe for centuries. But as a way of ending the Thirty Years War -a horrific ethno-religious conflict between Catholics and Protestants-the Treaty of Westphalia established the principle of sovereignty, which correlated the legitimacy of governance with geography. In so doing, the notion of any supreme authority over the rulers of states was largely abandoned. This geographicallydefine sovereignty created and reinforced the power of the executive decision-makers of states and it created a system in which were largely all-powerful within their borders.

Neither the United Nations, not the Holy Roman Emperor, for example, could fundamentally constrain the actions of states, without the acquiescence of the states themselves. But states, through organised internally, can support anarchy. While all states were theoretically sovereign, they were not equal in other respects. Some states were richer, others more militarily aggressive, still others fiercely inward looking. If some states were able to conquer other states and incorporate them, why wouldn't such a system evolve into the types of empires that it replaced? The principle of sovereignty served to protect states from the interferences of other states. And, as such, most states developed strong interests in promoting and extolling the principle of sovereignty; it means that they were free to do as they wished inside their borders. Thus sovereignty as a principle introduced a great deal of predictability into diplomacy.

The French Revolution changed the rules of legitimacy and sovereignty. Prior to the revolution, most countries around the globe were ruled by a longstanding line of monarchs, sometimes propagated by heredity, but often established or renewed by force. The revolution suggested that legitimacy was to be established not necessarily by peaceful elections, but by drawing on popular will and popular enthusiasm for the policies of the state. The success of the French modern state in creating a large, modern and legitimate national organisation for governing its territory provided a huge challenge for the various political organisations that inhabited Europe at the time. In part as a result of France's demonstrated power, nationalist governments would result in political reorganization into what is now called Germany, Italy, Russia, and Austria-Hungary. France's huge success not only simulated organisation change in Europe, it also threatened the stability of Westphalia system and resulted in a violent European conflict as Great Britain, Prussia and Russia and Austria-Hungary were fearful of impending French hegemony in Europe. The resolution of that conflict led to the Concert of Europe, which amplified the notion of sovereignty even further. Sovereignty was reaffirmed, but dominance was viewed as inacceptable, and collective security was to be established by the use of military balance of power that would deter of overwhelm any potential violators. Thus, the organisation of the modern interstate system is one that underscores sovereignty, so much so that it enables nations to come together in war to protect it. A recent example of course was the Gulf War in 1991 fought to overturn the Iraqi invasion of Kuwait.

But what does the matter? Security dilemma is produced by an anarchic international system. This dilemma suggests that defensive behaviour such ass maintaining large military establishments or designing or deploying new military technologies will be threatening even is such behaviour has benign intentions. The security dilemma is based in the wellknown tendency -some would argue obligation -of leaders to view their own actions as prudent and defensive in character, but to perceive similar actions by others as threatening and offensive, even expansionist. As a result of this longstanding dilemma, two basic strategies have been envisioned and adopted.

One strategy develops overwhelming force, to either deter of decisively defeat potential belligerents. This strategy was responsible most recently for the US nuclear policy during the cold war. In another form it could be conceived of as the establishment of hegemony or empire. Yet the community has largely rejected this form as unacceptable. Indeed, if the major risk of hegemony is empire, then it too violates the basic mechanism of the western state system. The second major strategy is the implementation of substantial constraints and disincentives to the creation or maintenance of the so-called vicious cycle of international conflict that results from the security dilemma. These elements may be traced back to imaginative ideas that emerged in 18 th century liberal philosophy especially those of Kant. Three organisations or institutions systematically and symbiotically enhance the absence of war among modern nations: democracy, commerce, and international organisations [START_REF] Fontanel | Organisations économiques internationales[END_REF].

Ironically, the end of the cold war brought disequilibrium to the global political economy. As safe as Americans felt about this newfound stability, others around the globe began to worry whether a hegemonic future would fundamentally exclude them and lead to fundamental instabilities, as it had in the past. The tragedy of the terrorist attack on the World Trade Center and Pentagon on September 11, Ò2001, would puncture, but not eliminate these worries.

The military power of the USA

During the cold war, global military spending rose above $1 trillion level on the mid-1980s. This was a spike and it had fallen about 60% by 1996 as a result of considerable disarmament and demobilisation, following the end of the cold war. However, current levels have been growing by about two per cent per annum since 1987 largely owing to rising spending in North Africa, Asia and Latin America.

The military expenditures of the US were about $363 billion in 1989 and the projected spending (excluding war costs in Afghanistan) for 2002 rests at $343 billion, still more $20 billion less than the height of the cold war. To American politician and citizen used to an upward budget ratchet to government spending in general and military spending in particular., these numbers present themselves as substantial reductions in military spending. To others around the world, these numbers present a troubling trend. Despite the fact that pre-September 11 n US military spending was below 1994 levels, the US military budget dwarfs by a factor of six that if its competitor, Russia. Indeed the seven countries targeted by the Pentagon as potential enemies (Cuba, Iran, Iraq, Libya, North Korea, Sudan and Syria) spend a combined total on defence that is more than twenty times smaller than US military spending. Even adding Russia and China into the mix, still leaves the US spending twice as much? According to SIPRI database on military expenditures, the US spends almost 40 % of the global total? At the time of writing, it is clear that the US spending will be augmented by at least $30 billion annually in the near term.

The United States enjoys a crushing military supremacy today, in particular in the field of research and development applied to the military sector, despite its substantial reduction in level of spending. Globally, in 1998 spending on military R&D reached $60 billion (38 billion in the USA, 49 billion for NATO and 53 billion for all OECD countries). This reduction has come to an end. The US decided to increase its pending on R&D, in particular relating to a missile defence system? Even with a 25M% decline, the resources devoted to this aspect of US military policy are substantial. Some have argued that the crowding effect of military R&D will be detrimental to innovation in the private sector, so reductions should benefit private sector innovations.

However, it seems clear that there is greater synergy among these sectors and that the boundaries between them are purposely blurred by funding aimed at stimulating and exploiting civilian innovation by bringing to it sufficient resources so that it can be brought into the military arena cheaply and quickly.

Computers, networking and telecommunications are all good examples of areas in which miniaturisation was undertaken in part to meet defence requirement, but really adapted initially from the civilian sector with government/military funding? Theses technology transfers are sometimes serendipitous, but generally are predicated on a strategy priority that seizes on technological and commercial opportunities, as in the case of the unmanned surveillance aircraft, which eventually became fairly widespread and in smaller quantities armed.

Indeed US military research and development has focused on transformational technologies that take care advantage of (as well as initially fund) advances in civilian electronics and information technologies. Reduced by about 40% from all time highs, about $27 billion is projected for US military R&D in 2002. Most recent estimates suggest that the US has about 60% of the global military R&D and dwarfs its nearest competitor in this arena, France, which itself spends about one third of the European total on military R&D. That said, it is still only about 1% of the US military budget. Again, especially to Europeans, these numbers seem troubling for their size; to Americans they seem reassuring in their overall decline. It is the classic issue of whether to be concerned about the size of the part, or about who is getting the biggest piece of it. Indeed, one US senator penned in 1999 an essay about the "threat" to US military R&D in which he noted:

The armed Forces now risk losing one off their premier advantages, a technological edge. Past decision to counter numerically superior potential enemies with technological innovations have given the Nation the most formidable military in the world. But declining budgets combined with the legacy of the Cold War that pervades force structure and the R&D enterprise is degrading our ability to remain dominant in the technology of warfare… Military R&D must undergo an innovation revolution to maintain our technological dominance [START_REF] Lieberman | Techno Warfare: Innovation and Military R&D[END_REF].

However it is clear that the transformation of US forces is underway. Recent public revelations of some of the integration of electronics, avionics and satellite guidance provide a glimpse of this idea. The Global Hawk unmanned surveillance aircraft has a range of 14,000 nautical miles and prior to its crash in December 2001 proved to be especially useful to US and allied military commanders on the field of Afghanistan. But the Global Hawk is one of the sizeable number of similar, but much smaller unmanned aircraft, some of which are now armed. It seems clear that only the US is capable of mounting and stimulating such a recent programme (through its roots come from Israeli IDF initiatives). However, small hobby based versions of some of these aircraft are now publicly available for purchase over the Internet. An in early January 2002, Indian air defences shot down an unmanned Pakistani surveillance aircraft, demonstrating the diffusion of these revolutionary technologies.

Strategically, these conditions have changes the US policy. In particular, the absence of a nuclear threat renders a nuclear strategy largely devoid of immediate traction. The de-emphasis on nuclear strategy clearly facilitated the repeat nuclear force reductions of the past decade, as well as fuelled concerns of nuclear defence against a rogue state or agent with a missile guided chemical or biological weapons. Currently the US and Russia each have approximately 1,100-1,200 deployed ICBMs (including SLBMs and Heavy Bombers) down almost 45% from the levels in 1994 as a result of the START treaty reductions. At its height there were about 70,000 nuclear warheads in the world (1986); today, for example, the USA holds approximately 6,000. Thus, nuclear weapons stockpiles have been drastically pruned. Doubtless the world is a safer place for it. However, this too has generated considerable disagreement between the US ion the one hand and Europeans and Asians on the other. While the US sees this as a reason to withdraw from the 1972 ABM treaty and to begin anew with a missile defence system, Europeans, Russians and Asians see a disequilibrium in these changing arrangements, a disequilibrium which is viewed as threatening, even if these threats can be defused.

Arms race and strategic equilibrium

Philip John Noël-Baker, a distinguished professor of international relations, UK Member of Parliament (Labour), Olympic medallist (Silver) and Nobel Laureate (1959) was among the first to write about arms race as threats for peace (Noël-Baker, P.J. (1926; 1958). Another Quaker who also served in France with Friends Ambulance Unit in World War I described the same dynamics in his own work on arms race. Lewis Fry Robertson was best known for his work on weather prediction, but developed a mathematical framework for evaluating the escalation involved in arms race using differential equations [START_REF] Richardson | Arms and Insecurity: A mathematical Study of the causes and the origins of war[END_REF]. Basically, he showed that arms races are comprised of three major factors (1) a competition in military expenditures, (2) the economic consequences of these expenditures and (3) the basic underlying hostility or grievances between the two competitors. Richardson showed that arms races would stabilise only if the fatigue and expense could outweigh the underlying hostility and sensitivity of one country's expenditures to another's. The major starting point and implication was the presumption that arms races were one of the major causes of war.

While it is clear that the old arms race is over, many have already warned of the resurgence of another, intensified arms race. If we follow Richardson's invocation to look empirically at the problem, it is evident that there is very little reactivity in terms of lock-step competitive arms budgeting, nor is there a substantial economic burden to new levels of military spending given the generally enhanced economic productivity across most of the parts of the globe. Neither are the old enmities between East and West, particularly between Russia and America, as easy to fan afire as many Thought. Indeed, Russia's calm and principal disagreement with the US notification of its withdrawal from the 1972 ABM treaty, seems very far from the predictions of a trenchant Russia rearmament that were made only a few months earlier.

The end of the cold war quickly swept away the assumptions on which major military procurement decisions had previously been based. However, this did not leave defence planning in total limbo. In spite of the downturn in world military spending, there are many plans for the construction of new weapon systems. Across the globe new cycles of weapon acquisitions will be required, and while arms exports and imports are continuing to fall, some growth can be seen. Russian exports are growing at a healthy pace (about 20% in 2000) as it continues to sell weapons to an expanding Chinese army, among others? In the USA, the initial contract for the new generation fighter bombers has been awarded to Lockheed-Martin and will amount to just under $18 billion. In France, the Rafale, which started in 1987 and will continue production into the foreseeable future ( 2004) will cost $7 billion to $8 billion in R&D. European governments, separately or together, are also looking at the requirements for a new jet aircraft for force protection similar to the JSF, which is planned for delivery by 2015. Indeed most of the new missile development and research is based on NATO countries, with Russia having abandoned this field almost entirely. The main point is that weapon system planners are still quite busy, and the resources that many countries will devote to military spending in the near future are substantial.

Despite the continued use of more traditional weapon systems, indeed their advancement and increasing sophistication, it may be that completely new technologies will transform not only how war is fought in the future, but also how peace is maintained as well. New weapon systems may be founded on information technologies, the infrastructure for which present even higher entry barriers than aircraft. As a result, smaller numbers of enterprises will control the production of these information laden new, weapons technologies, including, for example, cryptography. Further, those controlling these new technologies may gain even greater power over their putative enemies, as well as their allies. In any case, it is certain that there is substantial concentration of the production of weapon systems, at the same time that there is a wider and pore expansive diffusion of them across the globe. It should also be remembered that for most of the part, international commerce in these technologies falls outside the realm of normal trade relations as nations begin to use a wider swath of previously civilian technologies for national security, bringing under the guise of national security high technology trade.

This is likely to strengthen the commercial success of enterprises that are already dominant in electronics, avionics, software and telecommunications. These enterprises will be the major economic beneficiaries of future military spending around the world, in the same way that shipbuilding industry, to take one example, was in an earlier epoch. Whether American domination of there industries will continue is, however, an open question as the entry x-costs for new technologies are obviously lower than for older technologies, especially as these items become more labour intensive and highly qualified, technical labour become more labour intensive and highly qualified, technical labour becomes widely available in parts of the world where it heretofore was largely absent or not mobile among commercial enterprises [START_REF] Smith | Capital-labour substitution in defence provision[END_REF]. Indian and Chinese software engineers leap to mind as prime examples of this new reality.

So it is clear that we are in an area in which disarmament, demobilisation and reinvestment will characterise military policy more than arms races. Having jettisoned the arms race, we should not expect a future in which military costs are eliminated. Disarmament and demobilisation will not necessarily further reduce military expenditures, since in the one hand destruction of weapons stockpiles may incur substantial costs and, on the other hand, even remaining military stockpiles will either wear out or be consumed and as a result will need to be replenished and renovated, if not reinvented on a rather continuous basis? Indeed by retiring some weapons systems, such as many of the US nuclear attack submarines built in the 1960s, this may in fact engender greater costs as increased strategic requirements are imposed on replacement technologies. At the same time, economies of scale effects for smaller militaries may offset some of the costs efficiencies for smaller numbers of systems.

In short, the past decade provides ample evidence of massive economic, political and strategic changes, each in part a result of the end of the Cold War and the associated arms race. Yet the process of disarmament, demobilisation, and disengagement is temporary, caused by the failure of a security system to endure. The same may be said of armament. Often disarmament comes only after a conflict. In the past, this was after a violent war, but more recently after a war that was described as cold, rather than hot. But new weapons can help to create new strategic contexts in which the process of disarmament is replaced by one of armament.

Peace, Security, democracy and poverty

Today we face a dangerous situation in which we find new weapon systems that can modify the status quo. The possibly state-sponsored terrorist attacks on the USA in September 2001 illustrate that threats have not been eliminated to peace, and that security systems must evolve to meet new challenges, rather than addressing absent ones [START_REF] Fontanel | Le coût du terrorisme[END_REF]. Whatever the ultimate source of the Anthrax episodes, it seems clear that ignoring non-state actors in the military realms has had disastrous consequences. At the same time, the attacks served to stimulate a new tone to dialogue among important players in the global security regime, including the USA, China, Russia, France, Germany, the UK, Spain, Israel, Pakistan and India. Many potential problems still remain, yet the end of 2001 brought with it a renewed commitment to a cooperative security realm, and while it heightened the security concerns in many parts of the world, it also served to extinguish the last flames of the Cold War with it, and led to a broader global agreement on what a cooperative security regime might look like over the next fifty years.

The real goal problems remaining are not fundamentally problems of goals, but rather of implementation. Such a statement has not been possible during the Cold War and not very believable in the first decade thereafter. One goal is the further expansion democratic choice. Simply put and badly stated: democracy promotes peace. Democracies have different foreign policies than autocracies and monarchies in part simply because the political costs of fighting wars are higher for democratic leaders. If they lose the war, they almost certainly will lose power but even if they win, the domestic political costs may be quite high. As a result of the transparency of democratic choice, this will lead democracy to see a greater likelihood of successful negotiation with potential belligerents who will have to pay high costs if negotiation is unsuccessful, i.e. other democracies. The same logic suggests that democracies are likely to avoid conflicts that are likely to be risky or lengthy. At the same time, democracies are less likely to be dissatisfied with the status quo in part because they have historically tended to be among the richest countries. In short, leaders of democracies as well as citizens generally benefit from avoiding conflict, especially with one another. However, it now seems apparent that, at the extremes, democratic leaders who see this system threatened will band together, commit resources, and undertake these costs if necessary (Russel, Oneal, 2001).

At the same time, more extensive organisational connections involving a wider range of countries and other sectors help to promote security as well. They may not necessarily be economically efficient, but are necessarily nonetheless. International governmental and nongovernmental organisations also promote peace by fostering the basic ways in which countries peacefully resolve their conflicts while at the same time expanding the ways in which they view communalities among their interests with wide ranging sets of potential belligerents as well as potential allies. These mechanisms tend to convey private information to everyone involved, thereby further reducing uncertainty in the international realm.

Moreover, a continuing truth of world politics has been poverty in certain parts of the globe, especially Africa. The 2000/2001 World Development Report underscores the persistence of poverty in parts of the world while at the same time documenting some progress that has been made. Poverty has dropped in East Asia and in the Pacific, while it has continued to grow in South Asia and Sub-Saharan Africa, where hundreds millions of people live on less than $1 per day. It is estimated, for example, that over 40 % of the population in South Asia live on less than $1 per day. At the same time, the World Bank, along with other international organization such as World Health Organisation, has come to realise that material well being is only one, necessary, aspect of development and the elimination of poverty [START_REF] Fontanel | Disarmament for development in favour of the Developing Countries[END_REF]. Security has now taken a prominent place on the development agenda. The utter devastation of Afghanistan as a result of the former regime's policies and as a result of the subsequent war underscores this point with each broadcast of news.

Security is absolutely essential not only to maintain peace, but also to eliminate poverty. The standard answer in the recent past has been that economic development was the essential ingredient for a peaceful future. Doubtless there is independent merit in economic prosperity. But prosperity alone seems not to be sufficient. In the contemporary environment it is hard to imagine economic prosperity that is created in isolation from the international sphere. At the same time, the obvious toll in human suffering from the violent regime and ensuing conflict illustrates clearly the notion that the public health consequences of war and poverty are inexorably interwoven [START_REF] King | Rethinking Human Security[END_REF].

In summary, democracy, development and international commerce, and international organizations each reduce the risk of international conflict and at the same time enhance human security. This notion empowers individual as well as group of allied countries with considerable ability to affect the course of world politics, not just by avoiding war, but also by building international constraints and incentives. In one way, this idea is a grander version of the basic theories of economic integration that have slowly built the European Union over the past several decades. But, despite considerable globalisation, not everyone around the world shares this liberal ideal.

Conclusion

Indeed, even though the US was the primary target of the September 11 attack, a greater degree of democracy around the world, especially in the Middle East and South Asia, may serve to de-fuse conflict broadly and help to enhance human security. Further isolation from the political community and its general as well as specific international organisations removes further the constraints. So despite Huntington's fears, it is entirely plausible that even civilisations will benefit from representative choice of leadership, commerce and involvement in international network of various general and functional organisations [START_REF] Sen | Identité et conflit. Existe-t-il un choc des civilisation ?[END_REF].

The end of Cold War band the extinguishing of arms races, but it is indeed unbalancing. It seems clear that it also offers hope that institutions can be created within countries and among them that will change very much for the better our global history of violence as a means of conflict resolution and thereby enhance human security in the short as well as the long run. The only

viable alternative vision seems especially dire -a hegemonic superpower resented or despised by allies and enemies alike, who are faced with diminishing stakes in a peaceful status quo. We would not expect these opportunities to be inexpensive, nor should we short-change them.


Min Won Lee

Birgit Stiller

Jérôme Hauden

Hervé Maillotte

Carole Roch

Luc Thévenaz

Thibaut Sylvestre

Differential Phase-Shift-Keying Technique-Based Brillouin Echo-Distributed Sensing

Keywords:

In this letter, we experimentally demonstrate Brillouin echoes-based distributed optical fiber sensing with centimeter spatial resolution. It is based on a differential phase-shift-keying technique using a single Mach-Zehnder modulator to generate a pump pulse and a -phase-shifted pulse with an easy and accurate adjustment of delay. The results are compared to those obtained in standard Brillouin echo-distributed sensing system with two optical modulators and clearly show a resolution of 5 cm in a spliced segment between two fibers by applying a -phase-shifted pulse of 500 ps.

I. INTRODUCTION

O VER the last two decades, Brillouin scattering has widely been studied for distributed sensing applications using optical fibers [START_REF] Kurashima | Distributed-temperature sensing using stimulated Brillouin scattering in optical silica fibers[END_REF]- [START_REF] Song | High-resolution Brillouin optical time domain analysis based on Brillouin dynamic grating[END_REF]. Two main sensing analyses have been developed for this purpose: Brillouin optical correlation-domain analysis (BOCDA) and Brillouin Optical Time-Domain Analysis (BOTDA). BOCDA offers a very good spatial resolution [START_REF] Hotate | Distributed fiber Brillouin strain sensing with 1-cm spatial resolution by correlation-based continuous-wave technique[END_REF] down to 1 mm [START_REF] Song | Distributed strain measurement with millimeter-order spatial resolution based on Brillouin optical correlation domain analysis[END_REF]. Nevertheless, it is difficult to perform over a long distance using this technique. On the other hand, BOTDA has attracted particular attention for distributed sensing of temperature and/or strain in petrol and civil engineering industries. This analysis offers fast measurement and long-haul distributed sensing by measuring Brillouin frequency shift (BFS) produced by temperature and/or strain in optical fibers [START_REF] Rodríguez-Barrios | Distributed Brillouin fiber sensor assisted by first-order Raman amplification[END_REF], [START_REF] Soto | Long-range simplexcoded BOTDA sensor over 120 km distance employing optical preamplification[END_REF]. Recently, enhanced BOTDA systems have been reported such as vector [START_REF] Dossou | Vector Brillouin optical time-domain analyzer for high-order acoustic modes[END_REF] and simplex-coded BOTDA systems [START_REF] Soto | Simplexcoded BOTDA fiber sensor with 1-m spatial resolution over a 50-km range[END_REF]. Basically, the technique uses a pump-probe counter-propagative configuration with a pulse longer than 10 ns for pump. However, its spatial resolution is limited to 1 m due to the acoustic decay time of 10 ns. In order to overcome this limit, other techniques have been developed such as dark-pulse Brillouin scattering [START_REF] Brown | Dark-pulse Brillouin optical time-domain sensor with 20-mm spatial resolution[END_REF], differential pulse-width pair BOTDA [START_REF] Li | Differential pulse-width pair BOTDA for high spatial resolution sensing[END_REF] and Brillouin echo-distributed sensing (BEDS) [START_REF] Thévenaz | Brillouin distributed time-domain sensing in optical fibers: State of the art and perspectives[END_REF], [START_REF] Foaleng | High spatial and spectral resolution long-range sensing using Brillouin echoes[END_REF]. They all have neither physical nor technical limit down to 1-cm resolution sensing. However, in the dark-pulse sensing technique, residual peaks appear in the measurement spectra whereas the other two techniques suppress such peaks. Recently, it has been demonstrated that the BEDS approach offers a double contrast with respect to the other techniques [START_REF] Foaleng | High spatial and spectral resolution long-range sensing using Brillouin echoes[END_REF]. This technique uses an optical short -phase pulse in addition to a long intensity pulse and centimeter resolution sensing can be achieved by the short phase pulse with a very good quality. Despite of the advantage over high spatial resolution, the conventional BEDS systems exploit two modulators: a phase modulator for generating short -phase pulses and an intensity modulator for generating long intensity pulses. Besides, measurements can be undertaken using a differential gain approach taking the difference between two successive measurements with and without the -phase pulse. Therefore, a good accuracy sensing requires a sophisticated adjustment of the delay between the two pulses.

In this work, we propose a new concept to perform BEDS in which an optical -phase pulse is directly generated using a single intensity modulator by differential phase-shift keying (DPSK) technique. The system we propose in this letter is to implement BEDS with an optical scheme as simple as other high spatial resolution techniques, but with a double contrast. A long positive and a short negative electrical pulses are applied to the modulator to generate an optical -phase shift and centimeter resolution sensing is achieved in our DPSK-based BEDS system (DPSK-BEDS). Moreover, the pulse delay can easily be adjusted as the pulses are generated in intensity. For this purpose, we investigate a fiber section where two different fibers are spliced with a 5 cm-protection sleeve. The results will be compared with those obtained in a conventional BEDS system. Elongation measurements over a 5-cm fiber section will also be carried out using DPSK-BEDS.

II. -PHASE PULSE GENERATION BASED ON DPSK TECHNIQUE

DPSK technique is widely used in telecommunication industry to transmit bit-sequence messages in form of -phase shift using an intensity modulator, i.e. Mach-Zehnder interferometer modulator (MZI). In the principle of DPSK, optical phase can be shifted by modulating an MZI with an amplitude of double half-wave voltage . When the MZI is driven at its minimum bias point by a positive voltage and successively a negative voltage , the relative phase-shift between the optical fields at the two voltages is , or vice-versa [START_REF] Charlet | Progress in optical modulation formats for high-bit rate WDM transmissions[END_REF]. Therefore, when a negative pulse of (or a pulse of ) is applied to the modulator just after a positive pulse of at the minimum bias point as illustrated in Fig. 1(a), the output optical intensity remains unchanged whilst the phase of the optical field at the negative pulse part is shifted by with respect to the positive pulse part. In order to generate such an electrical pulse, the positive and negative electrical pulses are generated separately in this work as shown in Fig. 1(b). Their peak-to-peak amplitude is 7.6 V and applied to the MZI used in the work (Photline MXPE series, , 20-GHz bandwidth). The pulse durations are set to 30 ns and 500 ps, respectively. In telecommunication, such pulses are applied to a dual-drive MZI [START_REF] Wen | RZ/CSRZ-DPSK and chirped NRZ signal generation using a single-stage dual-electrode Mach-Zehnder modulator[END_REF]. In our work, these long and short pulses are applied to the direct current (DC) and radio-frequency (RF) inputs of the MZI, respectively. An impedance matching of 50 is made at the DC port and it provides a sufficient bandwidth for the 30-ns pulse. As the pulses are generated in intensity at the output of the MZI, the delay between the pulses is readily adjusted. Fig. 1(c) exhibits two intensity pulses at the modulator output, which are generated by the electrical pulses seen in Fig. 1(b). A 30-ns intensity pulse is followed by a 500-ps intensity pulse with -shifted phase. The rise/fall times of the long and short pulses are 700 ps and 200 ps, respectively. A short drop between the two pulses is seen due to the fast transition from the positive pulse to the negative pulse. The 500-ps duration of the short pulse defines a spatial resolution of 5 cm in our DPSK-based BEDS system.

III. EXPERIMENTAL SETUP

This dual-phase state intensity pulse is used as the pump wave in the experimental setup shown in Fig. 2 schematically. The setup is based on BOTDA system with an additional electrical pulse which is negative and applied to the MZI of the pump. The continuous wave (CW) emission of a distributed feedback (DFB) laser at 1550 nm is split into the pump and probe arms by a 50:50 tap coupler. In the pump side, an RF bias-T is used to combine the positive pulse and DC bias and the DC bias of the MZI is adjusted to be at the minimum bias point. The optical pulses in Fig. 1(c) are amplified by an Erbium-doped fiber amplifier (EDFA) with a peak power of 1.3 W. They are then polarization-scrambled by a polarization scrambler to average out polarization-sensitive Brillouin gain and injected into a fiber under test via an optical circulator. In the probe side, the Brillouin frequency-shifted probe is generated by the second MZI with a carrier suppression of 38 dB at 1550 nm by adjusting the DC bias. The probe power is set to 1 mW by another EDFA. The probe is then injected into the fiber through an isolator. At the fiber output, a fiber Bragg grating (FBG) enables to select the Brillouin gain obtained by the pump at the BFS. The gain is retrieved by a photodetector and then recorded as time traces by a digital oscilloscope. By sweeping the frequency of the optical probe, the gain along the fiber is mapped as a function of frequency. In this way, all BFS variations along the fiber caused by temperature or strain can be easily detected.

IV. EXPERIMENTAL RESULTS

In order to demonstrate the performance of the concept developed in this work, a 2-m single-mode fiber (SMF) is spliced to a 1-m fiber with high numerical aperture (HNA). The splice point is protected by a heat-shrinking sleeve of 5 cm. For comparison, distributed measurements of the splice segment have been done in two BEDS systems: conventional BEDS system using a phase and an intensity modulators for pump and DPSK-BEDS system using a single intensity modulator. Fig. 3(a) shows the distributed measurement obtained in the conventional BEDS system via a -phase shifted pulse with a pulse width of 500 ps. It clearly reveals the splice segment of 5 cm between the fibers at a frequency shift of 10.55 GHz. The BFS of the HNA and SMF are 10.67 GHz and 10.85 GHz, respectively. Fig. 3(b) displays the mapping using DPSK-BEDS developed in the work. It also manifests clearly the 5-cm splice segment and the 10.55-GHz frequency shift. Therefore, it is evident that our system manifests performances as good as the standard BEDS system. However, the contrast of the measurement in BEDS is slightly better than that in DPSK-BEDS. This is due to the peak-to-peak amplitude of 7.6 V which is only in DPSK-BEDS where is needed for the best performance. On the other hand, in BEDS a pulse amplitude of 5.1 V is applied to the phase modulator of which the is 5.9 V. In this case, only is required for the best operation and the amplitude meets almost this requirement . Nevertheless, Fig. 3(b) shows a good margin for improvement thanks to the good signal-to-noise ratio.

We have also tested our DPSK-BEDS system with centimeter resolution for strain monitoring. For that purpose, we have set up an elongation platform and applied three different elongations over a fiber section of 5 cm in the beginning of a 260-m long SMF. Fig. 4 exhibits the elongation measurements with 5-cm spatial and 1-MHz spectral resolutions. The elongations applied to the section are successively 0 ,3 0 and 60 .A s the elongation length increases, the BFS increases from 10.847 GHz to 10.865 GHz and 10.883 GHz. However, the figure reveals the elongation over more than 5 cm. We speculate that the pure fiber may slightly slip inside the fiber coating as a result of strain. The BFS is displaced by 18 MHz at 600 and 36 MHz at 1200 . Thus, the strain coefficient is obtained as 3 MHz per 100 with a strain accuracy of 33 . This accuracy can be further improved by using more frequency samples and higher pump and probe power. Since it is based on BEDS technique, our setup can potentially reach spatial resolution down to 1 cm if a faster pulse generator is used.

V. C ONCLUSION

We have successfully demonstrated a new concept for Brillouin echo-distributed sensing with centimeter resolution based on differential phase-shift keying technique. A -phase pulse with a pulse duration of 500 ps and an intensity pulse with 30 ns are generated for the pump using a single Mach-Zehnder modulator in our system. Our results clearly reveal the 5-cm splice segment between two fibers and its Brillouin frequency shift with a spatial resolution of 5 cm. The elongation test over a fiber section of 5 cm has also been performed with good results. Our new setup enables distributed measurements with centimeter resolution and a double contrast by simply adding a negative pulse into the pump in a Brillouin optical time-domain analysis system. Therefore it simplifies conventional Brillouin echo-distributed sensing systems by using a single modulator for pump rather than two modulators, and reduces the optical loss of the pump due to the modulators. Our setup also allows an easy adjustment of the delay between two pulses as they are generated in intensity. As such, our system may offer a great potential to fiber optic sensors with centimeter resolution for structural health and geotechnical monitoring.

  M. W. Lee, B. Stiller, H. Maillotte, C. Roch, and T. Sylvestre are with the Département d'Optique P. M. Duffieux, Institut FEMTO-ST, Université de Franche-Comté, CNRS UMR 6174, F-25030 Besançon Cedex, France (e-mail: thibaut.sylvestre@univ-fcomte.fr). J. Hauden is with PHOTLINE Technologies, F-25001 Besançon, France. L. Thévenaz is with the Institute of Electrical Engineering, Ecole Polytechnique Fédérale de Lausanne, CH-1015, Lausanne, Switzerland.

Fig. 1 .

 1 Fig. 1. (a) Schematic drawing of a positive/negative electrical pulse. (b) Positive (blue trace) and negative (red trace) electrical pulses are generated separately and applied to the MZI. The durations of the long and short intensity pulses are 30 ns and 500 ps, respectively. (c) The intensity pulses at the MZI output. The phase is shifted by for 500 ps at the pulse end.

Fig. 2 .

 2 Fig. 2. Experimental setup of DPSK-BEDS system using a single Mach-Zehnder interferometer (MZI) modulator for the pump. DFB: Distributed-feedback laser. EDFA: Erbium-doped fiber amplifier. FBG: Fiber Bragg grating.

Fig. 3 .

 3 Fig. 3. Distributed measurements of HNA/SMF fibers showing a splice segment of 5 cm (a) in standard BEDS system using a phase modulator and (b) in our BEDS system based on DPSK technique.

Fig. 4 .

 4 Fig. 4. Brillouin frequency shift versus the fiber length for three different elongations applied to a 5-cm fiber section.


Nicolas Bailly

; Diotalevi

; Beausejour

Wagnac

Éric

; Petit

Yvan Petit
email: yvan.petit@etsmtl.ca

Ph.D P Eng

Professor

Numerical investigation of the relative effect of disc bulging and ligamentum flavum hypertrophy on the mechanism of central cord syndrome

Keywords: Central cord syndrome, hyperextension, cervical spine, spinal cord, spondylosis

Background:

The pathogenesis of the central cord syndrome is still unclear. While there is a consensus on hyperextension as the main traumatic mechanism leading to this condition, there is yet to be consensus in studies regarding the pathological features of the spine (intervertebral disc bulging or ligamentum flavum hypertrophy) that could contribute to clinical manifestations.

Methods:

A comprehensive finite element model of the cervical spine segment and spinal cord was used to simulate high-speed hyperextension. Four stenotic cases were modelled to study the effect of ligamentum flavum hypertrophy and intervertebral disc bulging on the von Mises stress and strain.

Findings: During hyperextension, the downward displacement of the ligamentum flavum and a reduction of the spinal canal diameter (up to 17%) led to a dynamic compression of the cord.

Ligamentum flavum hypertrophy was associated with stress and strain (peak of 0.011 Mpa and 0.24, respectively) in the lateral corticospinal tracts, which is consistent with the histologic pattern of the central cord syndrome. Linear intervertebral disc bulging alone led to a higher stress in the anterior and posterior funiculi (peak 0.029 Mpa). Combined with hypertrophic ligamentum flavum, it further increased the stress and strain in the corticospinal tracts and in the posterior horn (peak of 0.023 Mpa and 0.35, respectively).

Interpretation:

The stenotic typology and geometry greatly influence stress and strain distribution resulting from hyperextension. Ligamentum flavum hypertrophy is a main feature leading to central cord syndrome.

Introduction

Central cord syndrome (CCS) is the most common type of incomplete traumatic cervical spinal cord injury and its incidence is increasing in older patients [START_REF] Mckinley | Incidence and Outcomes of Spinal Cord Injury Clinical Syndromes[END_REF][START_REF] Thompson | The changing demographics of traumatic spinal cord injury: An 11-year study of 831 patients[END_REF]. This syndrome is characterized by a greater motor impairment in the upper limbs than in the lower limbs. It was first described in 1954 by [START_REF] Schneider | The syndrome of acute central cervical spinal cord injury; with special reference to the mechanisms involved in hyperextension injuries of cervical spine[END_REF], and was attributed to hemorrhage damages and swelling, predominantly in the spinal grey matter and in the lateral corticospinal tracts. Later, MRI and histopathological studies substantiated this, showing a predominance of axonal injury in the lateral column [START_REF] Collignon | Acute traumatic central cord syndrome: magnetic resonance imaging and clinical observations[END_REF][START_REF] Jimenez | A histopathological analysis of the human cervical spinal cord in patients with acute traumatic central cord syndrome[END_REF][START_REF] Martin | MRI-pathological correlations in acute traumatic central cord syndrome: case report[END_REF][START_REF] Quencer | Acute traumatic central cord syndrome: MRI-pathological correlations[END_REF].

The pathogenesis of CCS was initially described as a compression of the spinal cord during hyperextension of the neck, usually combined with stenosis of the cervical spinal canal [START_REF] Molliqaj | Acute traumatic central cord syndrome: A comprehensive review[END_REF][START_REF] Schneider | The syndrome of acute central cervical spinal cord injury; with special reference to the mechanisms involved in hyperextension injuries of cervical spine[END_REF]. However, the main stenotic features of the spine contributing to CCS are still debated: the spinal cord is either compressed posteriorly from anterior bulging of the ligamentum flavum [START_REF] Schneider | The syndrome of acute central cervical spinal cord injury; with special reference to the mechanisms involved in hyperextension injuries of cervical spine[END_REF], anteriorly from marginal osteophytes, anteriorly from disc bulging [START_REF] Dai | Central Cord Injury Complicating Acute Cervical Disc Herniation in Trauma[END_REF], or by any combination of those three features. Histological and MRI studies suggested that axonal injury was mainly located in the lateral columns [START_REF] Collignon | Acute traumatic central cord syndrome: magnetic resonance imaging and clinical observations[END_REF][START_REF] Jimenez | A histopathological analysis of the human cervical spinal cord in patients with acute traumatic central cord syndrome[END_REF][START_REF] Martin | MRI-pathological correlations in acute traumatic central cord syndrome: case report[END_REF][START_REF] Quencer | Acute traumatic central cord syndrome: MRI-pathological correlations[END_REF], which may then be the location of maximal stresses in the spinal cord in the presence of CCS. Unfortunately, histological studies only present indirect evidence from a posteriori evaluations, with little understanding of the mechanism of injury.

The latest advances in finite element (FE) analysis enable the replication of such injury mechanisms and the estimation of the strain and stress distribution in the spinal cord throughout traumatic events. [START_REF] Li | Acute Central Cord Syndrome: Injury Mechanisms and Stress Features[END_REF] simulated the extension, flexion and compression of the cervical spinal cord submitted to an anterior or posterior compressive force. [START_REF] Nishida | Biomechanical analysis of cervical spondylotic myelopathy: The influence of dynamic factors and morphometry of the spinal cord[END_REF] simulated extension with the cervical spinal cord submitted to posterior compression from a simplified hypertrophic ligamentum flavum model. These studies showcased peak stresses located in the grey matter and both anterior and posterior funiculi, as opposed to histopathological studies reporting the predominance of axonal injury in the lateral column [START_REF] Martin | MRI-pathological correlations in acute traumatic central cord syndrome: case report[END_REF][START_REF] Quencer | Acute traumatic central cord syndrome: MRI-pathological correlations[END_REF]. Therefore, the exact pathogenesis of traumatic central cord syndrome remains largely debated, although it affects an increasing number of patients [START_REF] Thompson | The changing demographics of traumatic spinal cord injury: An 11-year study of 831 patients[END_REF].

The goal of this paper is to investigate the injury mechanisms of traumatic CCS. Using a comprehensive cervical FE model, this study will specifically assess the relative contributions of intervertebral disc bulging and ligamentum flavum hypertrophy on the stress and strain distributions within the spinal cord during an hyperextension of the neck.

Methods

Finite element modelling of the cervical spine

A finite element (FE) model of the cervical spine (C2-T1) described in previous works [START_REF] Beauséjour | Comparison of two intervertebral disc failure models in a numerical C4-C5 trauma model[END_REF][START_REF] Fradet | Finite element study of cervical spinal dislocation with spinal cord injury preliminary results[END_REF][START_REF] Taso | Anteroposterior compression of the spinal cord leading to cervical myelopathy: a finite element analysis[END_REF] was adapted for this study. This model of a 50 th percentile adult male subject includes vertebrae, intervertebral discs, as well as six spinal ligaments: anterior and posterior longitudinal ligaments, zygapophyseal joint ligaments, ligamentum flavum, interspinous ligaments and nuchal ligament (Fig. 1(a)). Each vertebra was defined as a rigid body. Material laws for the ligaments were defined by tabulated, non-linear, strain-rate dependent, stress-strain curves derived from mean forcedeflection curves measured in experimental studies [START_REF] Mattucci | Strain rate dependent properties of younger human cervical spine ligaments[END_REF][START_REF] Mattucci | A method to characterize average cervical spine ligament response based on raw data sets for implementation into injury biomechanics models[END_REF]. The interspinous ligament force-deflection curve was applied to the adjacent nuchal ligament, as this ligament was not included in the experimental studies. Toe regions of the curves were calibrated in a previous study to account for the initial elongation of cervical ligaments [START_REF] Beauséjour | Comparison of two intervertebral disc failure models in a numerical C4-C5 trauma model[END_REF]. The intervertebral discs were divided into a nucleus pulposus (20% of the disk volume) and an annulus fibrosus ground substance. They were then associated with first-order Mooney-Rivlin hyper-elastic material laws. The annulus fibrosus was divided into three sections (anterior, posterior and lateral) reinforced with specific tension-only spring elements organized in concentric lamellae with a crosswise pattern at ±35° to represent the collagen fibers [START_REF] Wagnac | Calibration of hyperelastic material properties of the human lumbar intervertebral disc under fast dynamic compressive loads[END_REF]. The initial material properties of the discs were initially defined from [START_REF] Schmidt | Application of a new calibration method for a three-dimensional finite element model of a human lumbar annulus fibrosus[END_REF] and [START_REF] Shirazi-Adl | A finite element study of a lumbar motion segment subjected to pure sagittal plane moments[END_REF], and then modified and calibrated for dynamic flexion and extension, as described in section 2.2.

The FE model also includes a spinal cord model previously described by [START_REF] Fradet | Finite element study of cervical spinal dislocation with spinal cord injury preliminary results[END_REF][START_REF] Taso | Anteroposterior compression of the spinal cord leading to cervical myelopathy: a finite element analysis[END_REF] and [START_REF] Diotalevi | Dynamics of spinal cord compression with different patterns of thoracolumbar burst fractures: Numerical simulations using finite element modelling[END_REF]. It is composed of white and grey matter, denticulate ligaments, pia mater and dura mater (Fig. 1 (a)). Meshing was performed with pentahedral (6 nodes) 3D elements for the white and grey matter, and quadratic (4 nodes) shell elements for the ligaments, the pia and the dura mater. The proximal end of the spinal cord was attached to the C2 vertebra to simulate the connection with the brain stem and to guide the spinal cord movement. The rest of the spinal cord was left unrestrained. Material laws and properties of the FE model are summarized in Table 1.

Dynamic calibration of the discs

The dynamic calibration of the model was performed by adjusting the material properties of the annulus extracellular matrix and nucleus until the moment-rotation curves of each functional spinal unit (C2-C3 to C7-T1) fit with experimental results from [START_REF] Barker | High Rotation Rate Behavior of Cervical Spine Segments in Flexion and Extension[END_REF]. For each spinal unit, the lower vertebra was fixed, while a rotation of 500 deg.s -1 in flexion and extension was applied to the upper vertebra. The axis of rotation of each unit was determined as described in [START_REF] Amevo | Instantaneous axes of rotation of the typical cervical motion segments: a study in normal volunteers[END_REF] to replicate the experimental conditions of [START_REF] Barker | High Rotation Rate Behavior of Cervical Spine Segments in Flexion and Extension[END_REF].

Since the C7-T1 axis was not included in this study, the data for C6-C7 was used to set the axis of rotation.

To determine the goodness of fit between simulation and experimental results, three criteria were used: corridor rating, shape rating and size rating. For each data point, the corridor rating was set to 1 if the simulation results fit inside one standard deviation, and to 0 if the result was outside two standard deviations. For results between one and two standard deviations, a linear relation between 0 (outside 2 standard deviations) and 1 (equal to one standard deviation) was calculated. The final corridor rating value was obtained by averaging corridor rating values at every data point. The size rating and shape rating were measured as defined in [START_REF] Barker | Lower cervical spine motion segment computational model validation: Kinematic and kinetic response for quasi-static and dynamic loading[END_REF]. The size rating (equation ( 1)) is the ratio between the area below the simulation curve y(t) and the experimental curve x(t). The larger value is set as the denominator.

𝑆𝑖𝑧𝑒 𝑟𝑎𝑡𝑖𝑛𝑔

= ∑ 𝑦 2 (𝑡 𝑚𝑖𝑛 +𝑖 * ∆𝑡) 𝑛 𝑖=1 ∑ 𝑥 2 𝑛 𝑖=1 (𝑡 𝑚𝑖𝑛 +(𝑚+𝑖) * ∆𝑡) (1)
The shape rating (equation ( 2)) compares the slope and the change in the slope of the simulated curve y(t) against the experimental curve x(t). The phase-shifting m, representing the x-intercept shifting, was not enabled for the measure of the shape rating. Therefore, m was set to 0.

𝑆ℎ𝑎𝑝𝑒 𝑟𝑎𝑡𝑖𝑛𝑔 = ∑ 𝑥(𝑡 𝑚𝑖𝑛 +(𝑚+𝑖) * ∆𝑡) * 𝑦(𝑡 𝑚𝑖𝑛 +𝑖 * ∆𝑡) 𝑛-1 𝑖=0 √∑ 𝑥 2 (𝑡 𝑚𝑖𝑛 +(𝑚+𝑖) * ∆𝑡) * ∑ 𝑦 2 𝑛-1 𝑖=0 𝑛-1 𝑖=0 (𝑡 𝑚𝑖𝑛 +𝑖 * ∆𝑡) (2)
An average of these three criteria was calculated for the moment-rotation curves in flexion and extension, and an overall rating was measured as the average between the rate in flexion and extension. It was chosen to target a rating of between 0.65 and 1, based on a rating scale defined by [START_REF] Cesari | WorldSID prototype dummy biomechanical responses[END_REF].

Calibration of the disk material properties was performed by adjusting the parameters C10 and C01 of the Mooney-Rivlin hyper-elastic material laws used for the annulus and nucleus for each spinal unit. First, the dynamic flexion and extension of each unit were performed with the quasistatic material properties of the disk [START_REF] Schmidt | Application of a new calibration method for a three-dimensional finite element model of a human lumbar annulus fibrosus[END_REF]. If the ratings met our criteria, no calibration was performed. Otherwise, a scaling factor of 0.5 to 15 was applied to the annulus and nucleus rigidity (parameters C10 and C01 of the material law), while maintaining the C10 to C01 ratio. The range of 0.5 to 15 was chosen to vary the properties grossly between values determined in other studies for the lumbar disk in quasi-static [START_REF] Schmidt | Application of a new calibration method for a three-dimensional finite element model of a human lumbar annulus fibrosus[END_REF] and dynamic [START_REF] Wagnac | Finite element analysis of the influence of loading rate on a model of the full lumbar spine under dynamic loading conditions[END_REF] loadings. A C10-to-C01 ratio was maintained based on the results of a preliminary sensitivity study, which showed that this ratio had no significant impact on the FSU mobility. If no satisfying result was obtained, the rigidity of the nucleus and the anterior, lateral and posterior bulk annuli were independently iteratively scaled until the best overall rating (extension and flexion) was obtained.

Finite element modelling of the spondylotic stenosis

The original geometry of the vertebral canal was modified from C4 to C7 to simulate a stenotic canal area. First, the canal diameter was reduced by 3 mm, corresponding to the average reduction seen in patients with spondylosis [START_REF] Shedid | CERVICAL SPONDYLOSIS ANATOMYPATHOPHYSIOLOGY AND BIOMECHANICS[END_REF]. Two spondylotic features were also included: linear disc bulging and hypertrophic ligamentum flavum. Four cases were modelled, based on the presence or absence of these two features (Fig. 1 (b)).

As canal stenosis associated with cervical spondylosis typically occurs at several levels, these features were inserted at three intervertebral levels: C4-C5, C5-C6 and C6-C7 (displayed in red in Fig. 3) [START_REF] Stevenson | Traumatic central cord syndrome: neurological and functional outcome at 3 years[END_REF]. Hypertrophic ligamentum flavum and linear disk bulging idealized geometries (Fig. 1 (b)) were defined based on MRI measurements of typical cases found in our institution database [START_REF] Thompson | The changing demographics of traumatic spinal cord injury: An 11-year study of 831 patients[END_REF], and were consistent with the literature [START_REF] Muhle | Classification system based on kinematic MR imaging in cervical spondylitic myelopathy[END_REF][START_REF] Song | Clinical evaluation of traumatic central cord syndrome: emphasis on clinical significance of prevertebral hyperintensity, cord compression, and intramedullary high-signal intensity on magnetic resonance imaging[END_REF][START_REF] Tani | Cervical spondylotic myelopathy in elderly people: a high incidence of conduction block at C3-4 or C4-5[END_REF][START_REF] Yu | Cord shape and measurements in cervical spondylotic myelopathy and radiculopathy[END_REF]. Idealization of these features is also in accordance with the literature [START_REF] Kim | Biomechanical effects of spinal cord compression due to ossification of posterior longitudinal ligament and ligamentum flavum: a finite element analysis[END_REF]. These features were meshed with hexahedral (8 nodes) 3D elements and defined as rigid bodies.

Modelling of the ligamentum flavum hypertrophy and disc bulging was performed in a preliminary simulation, with the neck placed in an upright position, and a normal C2-C7 lordosis angle of 22.7° according to [START_REF] Gore | Roentgenographic findings of the cervical spine in asymptomatic people[END_REF]. The spondylotic features were moved alongside the anteroposterior axis into the canal at the three affected levels to compress the cord and reach 40% reduction of the sagittal canal diameter, which corresponds to a typical degree of compression in cervical spondylosis, according to [START_REF] Ogino | Canal diameter, anteroposterior compression ratio, and spondylotic myelopathy of the cervical spine[END_REF]. Then, the disk bulging features were fixed to the lower vertebra while the hypertrophic ligamentum flavum features were fixed to the upper vertebra of each segment. These altered geometries were then used in the neck hyperextension simulation. Both spondylotic features had frictionless contacts with the dura mater.

Loading and boundary conditions

Hyperextension was achieved by fixing T1 in space and applying 60 degrees of rotation in the median plane to C2 at 500 deg.s -1 , around a mobile axis located at the center of the vertebral foramen of C2. This rotational speed of 500 deg.s -1 has been observed during typical car crash scenarios [START_REF] Panzer | Cervical spine response in frontal crash[END_REF] and a 60° magnitude of rotation approximates the maximal amplitude, without soft-tissue injury, as reported by [START_REF] Barker | High Rotation Rate Behavior of Cervical Spine Segments in Flexion and Extension[END_REF].

Analysis

Model outcomes were von Mises strains and stresses in the grey and white matter. Both outcomes were extracted at every node of the FE model. A simple averaging of their values was performed by summing the studied tensor equivalent invariant measured at the finite element corner adjacent to the studied node, and then dividing them by the number of finite element corners adjacent to this node. This method was used to avoid mathematical aberrations on the results.

Results

Dynamic calibration

Goodness of fit scores between the model's FSU kinematics and experimental results from [START_REF] Barker | High Rotation Rate Behavior of Cervical Spine Segments in Flexion and Extension[END_REF] varied from 0.82 to 0.90 (Fig. 2). The resulting C01 and C10 parameters for the annulus and nucleus are presented in Appendix 1. The moment-rotation curves generally lie within one standard deviation of the experimental results (overall corridor ratings between 0.76 and 1) (Fig. 2).

2. Stress and strain distribution during hyperextension

Figure 3 presents a sagittal cross-section of the cervical spine during hyperextension and the strain distribution in the cord. During hyperextension, the rotation of the upper adjacent vertebra induced a downward displacement of the ligamentum flavum: at the C5-C6 level, the ligamentum flavum, initially located above the disk, ended up below it at the end of hyperextension (Fig. 3). This was associated with a reduction of the minimal spinal canal anteroposterior diameter (up to 17% decrease at C5-C6). The location of this canal reduction also shifted downward during the hyperextension: it is above the disk at 30°, but below the disc at 60° of extension. The highest stress and strain were observed at C5-C6 (Fig. 3).

Fig. 3. Strain distribution in a sagittal cross-section of the spinal cord during hyperextension with a stenotic case presenting a narrowed canal, hypertrophic ligamentum flavum and linear disk bulging (both displayed in red)

In the transverse plane, stress and strain at C5-C6 increased gradually throughout extension, with different patterns depending on the stenotic cases (Fig. 4 and5). We observed that the stress distribution did not exactly match the strain distribution due to the higher rigidity of the grey matter compared to white matter. In the normal column (reference case), the peak stress and strain were located in the posterior funiculi, and were respectively equal to 0.0017 kPa and 0.08 at 30 of extension, and 0.0045 kPa and 0.17 at 60 (Fig. 4 and5). In the presence of linear disk bulging alone, stress and strain were initiated in the anterior and posterior funiculi and increased gradually in both areas. At 30 extension, the peak stress and strain were respectively 9 and 4.2 times higher than in the normal column (respectively 6.5 and 3.2 times higher at 60°).

The peak stress was observed in the anterior horn while the peak strain was located in the anterior and posterior funiculi. In the presence of hypertrophic ligament flavum alone, the peak stress and strain first appeared in the posterior and medial parts of the lateral funiculi, where they increased gradually, as well as in the posterior horn. At 30, the peak stress and strain were respectively 4.1 and 2.62 times greater than in the normal column (respectively 2.5 and 1.5 times higher at 60°). In the presence of both linear disk bulging and hypertrophic ligament flavum, stress and strain initiated in both the posterior and medial parts of the lateral funiculi and in the anterior funiculi. At 30 extension, the peak stress and strain were mainly located in the posterior and medial parts of the lateral funiculi and in the posterior horn, and were respectively 9.4 and 3.8 times higher than in the normal column (respectively 5.2 and 2.1 times higher at 60°) (Fig. 4 and5).

In every simulation, the presence of a hypertrophic ligamentum flavum was associated with high stresses and strains in the medial part of the lateral funiculi at the early stage of the extension, which corresponds to the main damaged region in CCS [START_REF] Martin | MRI-pathological correlations in acute traumatic central cord syndrome: case report[END_REF][START_REF] Quencer | Acute traumatic central cord syndrome: MRI-pathological correlations[END_REF] and to the location of the corticospinal tract. The addition of a linear disk bulging into the canal in the presence of hypertrophic ligamentum flavum increased the overall level of stress in these areas during extension.

Discussion

This FE method study is the first to investigate the spinal cord dynamics with different cases of cervical canal stenosis leading to CCS. The results demonstrate that the geometry and position of the stenotic feature greatly influence the stress and strain distributions throughout the hyperextension movement of the neck. In particular, the presence of hypertrophic ligamentum flavum induced specific stress and strain distributions that are consistent with histologic findings related to CCS [START_REF] Jimenez | A histopathological analysis of the human cervical spinal cord in patients with acute traumatic central cord syndrome[END_REF][START_REF] Martin | MRI-pathological correlations in acute traumatic central cord syndrome: case report[END_REF][START_REF] Quencer | Acute traumatic central cord syndrome: MRI-pathological correlations[END_REF]. This provides important insights into the physiopathology of CCS.

The mechanism of CCS is described as a transverse compression of the spinal cord, during an hyperextension of the neck, due to a reduction of the cervical spinal canal size induced by the bulging of the ligamentum flavum [START_REF] Schneider | The syndrome of acute central cervical spinal cord injury; with special reference to the mechanisms involved in hyperextension injuries of cervical spine[END_REF]. A reduction of the canal diameter was indeed observed by [START_REF] Muhle | Classification system based on kinematic MR imaging in cervical spondylitic myelopathy[END_REF] in some spondylotic patients performing a neck extension in a kinematic MRI. In the present study, up to a 17% canal reduction was observed at the C5-C6 intervertebral level, but this was also associated with a downward displacement of the ligamentum flavum (Fig. 3). This combined phenomenon modifies the pinching zone of the cord: it was above the disc in the neutral position, but below the disc at 60° of extension. This might explain the significant strain increase in the cord (>25% at 60 of extension) despite the small reduction in the canal diameter (6% at 60 of extension).

In the presence of the hypertrophic ligamentum flavum, the peak stress and strain were observed in the posterior and medial parts of the lateral funiculi, close to the posterior horn of the grey matter. This area matches those where most of the axonal damage and Wallerian degeneration are found in histological studies of CCS [START_REF] Jimenez | A histopathological analysis of the human cervical spinal cord in patients with acute traumatic central cord syndrome[END_REF][START_REF] Martin | MRI-pathological correlations in acute traumatic central cord syndrome: case report[END_REF][START_REF] Quencer | Acute traumatic central cord syndrome: MRI-pathological correlations[END_REF]. Conversely, stress patterns with linear disk bulging alone were mostly distributed in the anterior and posterior funiculi. These results suggest that the presence of hypertrophic ligament flavum is an important factor in the pathogenesis of CCS, as proposed by [START_REF] Schneider | The syndrome of acute central cervical spinal cord injury; with special reference to the mechanisms involved in hyperextension injuries of cervical spine[END_REF] and discussed by many others [START_REF] Dai | Central Cord Injury Complicating Acute Cervical Disc Herniation in Trauma[END_REF][START_REF] Li | Acute Central Cord Syndrome: Injury Mechanisms and Stress Features[END_REF][START_REF] Quencer | Acute traumatic central cord syndrome: MRI-pathological correlations[END_REF]. The concomitant presence of hypertrophic ligamentum flavum and linear disk bulging further increases the stresses and strains in the lateral funiculi by inducing an additional pincer effect from combined anterior and posterior compression of the spinal cord during extension, as suggested by previous authors [START_REF] Morishita | The pincers effect on cervical spinal cord in the development of traumatic cervical spinal cord injury without major fracture or dislocation[END_REF][START_REF] Nishida | Biomechanical analysis of cervical spondylotic myelopathy: The influence of dynamic factors and morphometry of the spinal cord[END_REF].

The differences in stress and strain distributions induced by hypertrophic ligamentum flavum and disk bulging may be explained by their geometry and their location of contact with the cord.

In the present study, disk bulging applies a linear compression to the anterior part of the cord, resulting in strain concentrations at the contact area decreasing toward the center of the cord.

Conversely, the hypertrophic ligamentum flavum applies two lateral contact forces converging toward the center of the spinal cord, forming a pincer movement between contralateral segments of the ligamentum flavum. This induces centralized stresses and strains in the cord. In previous FE method studies, [START_REF] Nishida | Biomechanical analysis of cervical spondylotic myelopathy: The influence of dynamic factors and morphometry of the spinal cord[END_REF] used other simplified geometries to model the pinching force applied to the cord during hyperextension: the ligamentum flavum was modelled with a linear shape, and three types of anterior compression were used (central, lateral or diffuse type). Each of these configurations also presented a unique stress pattern, mainly located in the grey matter and in the anterior and posterior funiculi. However, none led to high levels of stress in the corticospinal tracts, as observed in the present study. This confirms that different stenotic configurations lead to different stress and strain distributions, which is consistent with the great variability of syndromes and outcomes associated with hyperextension injuries without instabilities [START_REF] Mckinley | Incidence and Outcomes of Spinal Cord Injury Clinical Syndromes[END_REF]. Future FE method studies may need to consider patient-specific model geometry to understand their unique injury mechanism.

The area of highest stress and strain concentrations generally observed in the presence of hypertrophic ligamentum flavum is located in the lateral corticospinal tract, which is associated with motor control, and is strongly linked with hand dexterity [START_REF] Courtine | Can experiments in nonhuman primates expedite the translation of treatments for spinal cord injury in humans?[END_REF]. According to [START_REF] Foerster | Symptomatologie der Erkrankungen des Rückenmarks und seiner Wurzeln[END_REF] and [START_REF] Schneider | THE SYNDROME OF ACUTE CENTRAL CERVICAL SPINAL CORD INJURY[END_REF], the lateral corticospinal tracts have a somatotopic arrangement in which the medial part is associated with upper extremity function, while the lateral part is associated with lower extremity function. Based on this somatotopy, greater motor impairment in the upper limbs observed in CCS would be explained by higher damage in the medial part of the corticospinal tract than in the lateral part. However, this hypothesis has been challenged by histologic findings showing uniform damage to the lateral corticospinal tract [START_REF] Quencer | Acute traumatic central cord syndrome: MRI-pathological correlations[END_REF]) and by [START_REF] Nathan | LONG DESCENDING TRACTS IN MANI[END_REF], who demonstrate that the lateral tracts are not laminated into functional units, but rather, that the motor fiber involved in upper and lower limb function were interlaced. This hypothesis was reinforced by several studies on monkeys showing that sectioning of the entire corticospinal tract lead to greater dysfunction in the upper limbs than in the lower limbs [START_REF] Bucy | Destruction of the Pyramidal Tract in the Monkey: The Effects of Bilateral Section of the Cerebral Peduncles[END_REF][START_REF] Nathan | LONG DESCENDING TRACTS IN MANI[END_REF]. The results of the present study are compatible with a CCS in the two theories. On the one hand, in the presence of the ligamentum flavum, high stresses were mostly distributed in the corticospinal tracts, suggesting that the entire lateral corticospinal tract was affected [START_REF] Quencer | Acute traumatic central cord syndrome: MRI-pathological correlations[END_REF][START_REF] Jimenez | A histopathological analysis of the human cervical spinal cord in patients with acute traumatic central cord syndrome[END_REF]. On the other hand, peak stress in the white matter was mainly seen in the medial part of the lateral funiculi, next to the posterior horn, which is the zone associated with upper extremity function in the somatotopic arrangement described by [START_REF] Foerster | Symptomatologie der Erkrankungen des Rückenmarks und seiner Wurzeln[END_REF]. To further correlate the stress pattern in the cord with neurological damage and discriminate these two theories, future FE method studies should consider reproducing patient-specific geometry and injury dynamics and compare them with clinical observations. This study presents some limitations associated with assumptions and simplifications. First, the cerebro-spinal fluid was not included because it was absent in the stenotic zone of most cases of CCS with severe spinal stenosis found in our institutional database [START_REF] Thompson | The changing demographics of traumatic spinal cord injury: An 11-year study of 831 patients[END_REF].

Secondly, disks and ligament behaviour in the current model were calibrated based on data from non-pathological spine segments [START_REF] Barker | High Rotation Rate Behavior of Cervical Spine Segments in Flexion and Extension[END_REF], but a stenotic spine is expected to be more rigid and less likely to sustain a 60 hyperextension. However, this does not challenge our conclusions since high stress and strain appeared at less than 30of extension, which is a normal range of extension for the elderly, according to [START_REF] Muhle | Classification system based on kinematic MR imaging in cervical spondylitic myelopathy[END_REF]. Thirdly, the mechanical behaviour of white and grey matter was defined by isotropic strain rate-dependent tabulated laws derived from experiments reported in the literature [START_REF] Fradet | Geometrical variations in white and gray matter affect the biomechanics of spinal cord injuries more than the arachnoid space[END_REF].

Nevertheless, these materials are possibly anisotropic as they are notably composed of neurones, myelin, glial cells, etc. In order to further study the local stress concentrations and the affected axonal tracts, future studies should be performed to supplement the understanding and characterization of the local behaviour of the spinal cord white and grey matter and to refine finite element models. Finally, no direct link could be established between the results of this study and neurological injury because no accepted stress and strain thresholds have been defined for neurological injury of the spinal cord and because the model was not associated with the specific geometry and injury dynamic of a patient with identified neurological evaluation.

Future work should focus on reproducing patient-specific injuries and establishing a neurological injury threshold.

Conclusions

This study is the first, to the authors' knowledge, to examine the dynamics of a detailed osteoligamentous spine and spinal cord model for a typical traumatic event associated with central cord syndrome. The hypothesis suggesting a pinching of the spinal cord by hypertrophic ligament flavum and linear disk bulging during a hyperextension was investigated in this study. It was found that only ligamentum flavum hypertrophy was associated with high stress and strain in the corticospinal tracts, which is consistent with the histologic pattern of the central cord syndrome. The presence of a linear disk bulging alone was not associated with such a pattern, but when combined with hypertrophic ligament flavum, increased the overall level of stress and strain in the corticospinal tract.

Fig. 1 .

 1 Fig. 1. (a) Finite element model of the cervical spine and (b) Stenotic scenario at C5-C6 levels in the 4 tested cases. Abbreviation: DM, dura mater; PM, pia mater; DL, denticulate ligament; WM, white matter; GM, grey matter.

Fig. 2 :

 2 Fig. 2: Cervical FSU moment-rotation diagrams at rotational velocity of 500 deg.s -1

Fig. 4 .

 4 Fig. 4. Stress distributions in a transversal cross-section of the spinal cord at the C5-C6 intervertebral level at 5 extension angles for the 3 different stenotic cases

Table 1 : Finite element model material properties Type of elements Material law Material parameters (units: g, mm, ms) References Spinal cord:

 1

	Grey matter	Pentahedral Brick Stress-strain tabulated	Curves in Fradet et al.	(Fradet et al., 2016)
				2016
	White matter	Pentahedral Brick Stress-strain tabulated	Curves in Fradet et al.	(Fradet et al., 2016)
				2016
	Pia mater	Quad	Linear elastic	ρ = 0.001; ν = 0.45; E = 2.3 (Fradet et al., 2016)
	Dura mater	Quad	Linear elastic	ρ = 0.001; ν = 0.45; E = 5	(Fradet et al., 2016)
	Dentate ligament Quad	Linear elastic	ρ = 0.001; ν = 0.45; E = 10	(Fradet et al., 2016)
	Ligaments:
		Quad	Stress-strain nonlinear curves Curves derived from	(Mattucci	and
		Except capsular		Mattucci and Cronin 2015	Cronin, 2015)
		ligament (tria)