Giovanni Dosi
email: dosi@sssup.it.

Sébastien Lechevalier

Angelo Secchi

Interfirm heterogeneity: nature, sources and consequences for industrial dynamics. An introduction

Keywords: Interfirm heterogeneity: nature, sources and consequences for industrial dynamics. An introduction heterogeneity, firm growth, profitabilities, innovativeness, corporate organization, learning, selection, job creation and destruction

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Introduction

Contemporary economic analysis is largely subject to rather bizarre schizofrenic syndromes. On the one hand, over the last thirty years or so, macro theories have tried to squeeze the interpretation of whatever aggregate dynamics down to some sort of decision-theoretic framework in which the increasingly mythical "representative agent" was doing all the action. Whatever statistical properties of the time-series, being it productivity and GDP growth, fluctuations, employment, investment, had to be explained as the equilibrium outcome of some sophisticated inter-temporal maximization exercise by such an agent. Dynamic Stochastic General Equilibrium models are the dominant genre in this spirit. On the micro side largely the opposite has happened. Empirical analyses drawing upon an increasing ensemble of micro longitudinal datasets have powerfully highlighted the ubiquitous, large and persistent heterogeneity in all dimensions of business firms' characteristics and dynamics one cared to look at.

This Special Section of Industrial and Corporate Change adds both to the statistical evidence on the various dimensions of micro heterogeneity and on the ways diverse interacting entities make up for more aggregate dynamic profiles in variables such as productivity, output, sales, employment and the like.

Granted that (and also on that much more evidence is needed), the investigation is bound to ask what drives persistent asymmetries in performances and heterogeneity in corporate characteristics. This is a second major domain of analysis to which several of the papers which follow significantly contribute.

Third, a set of tricky and difficult questions regards precisely the relationships between corporate characteristics, performances and their dynamics. There are here both empirical challenges and tangled theoretical issues. For example, can one rationalize such relationships in terms of some underlying general equilibrium, albeit of a rather weird kind? What would that add to our interpretation of the evidence? Or, conversely, should one understand it as far from equilibrium evolutionary dynamics? In any case, what drives such processes? What is the balance in it between idiosyncratic and mistake-ridden innovation, learning, adaptation, on the one hand, and environmental selection amongst competing firms, but also products, technologies, patterns of organization, behavioral rules, on the other? Fourth, a crucial domain of analysis still at its infancy, concerns the investigation of the links "from micro to macro and back", as [START_REF] Bartelsman | Searching for the Sources of Productivity: from Micro to Macro and Back[END_REF] in this issue puts it. A few of the questions in this domain concern broadly speaking aggregation issues, basically involving the mapping between the features and dynamics of whatever distribution (productivities, profitabilities, rates of growth and so on) and their averages. Other questions bear more direct normative implications. How does the "macro", especially in terms of institutional conditions (e.g. in terms of effectiveness of competitive market selection, entry and exit conditions, labor hiring and firing rules, etc.), influence micro behaviors and performances? 1The papers in this Special Section improve, we believe, our knowledge in all the foregoing domains. In order to set such advancements in context, let us briefly map out the broad contours of the state of the art in these areas of investigation.

Heterogeneity wherever one looks

Thanks to massive infusions of micro-data (at plant and firm level levels ) into economic investigation over the last 20 years, economists have begun to identify a few robust statistical properties characterizing industrial structures, their changes, and performance indicators such as corporate growth and profitability.

A first, extremely robust, stylized fact regards the quite wide variability in firm size. Throughout industrial history, across all countries and irrespectively of the size proxy adopted, one observes unimodal highly right-skewed firm size distribution resemble quite closely a Power Law2 (within a large literature see [START_REF] Hart | The Analysis of Business Concentration: A Statistical Approach[END_REF][START_REF] Steindl | Random Processes and the Growth of Firms[END_REF]Bottazzi and Secchi, 2005;[START_REF] Bottazzi | Invariances and Diversities in the Evolution of Italian Manufacturing Industry[END_REF]Dosi, 2007). And skewness and large supports of the distributions themselves hold across all level of disaggregation. Independently of the precise form of the density function, the intuitive message is the coexistence of many relatively small firms with quite a few very large ones. In turn, of course, the robustness of this finding militates against any naive notion of optimal size and against any theory of production centered around some invariant U-shaped cost curve.

Moreover, a recent body of finer sectoral investigations suggests that sectoral firm size distributions (say at three digit level) are highly diverse in terms of shape: some sectors presents distributions rather similar to the aggregate one, others are unimodal but symmetric and yet others are bimodal or even multi-modal (cfr. for few examples [START_REF] Bottazzi | Invariances and Diversities in the Evolution of Italian Manufacturing Industry[END_REF].

All this evidence taken together, corroborating a conjecture put forward in [START_REF] Dosi | Learning, Market Selection and Evolution of Industrial Structures[END_REF], hints at the fact that near-paretian aggregate distribution may well be a puzzling outcome of sheer aggregation among firms belonging to different sectors characterized by different regimes of market interactions and of organizational and technological learning.

A somewhat similar message is conveyed by the empirical investigations regarding concentration ratios: confirming the older findings in [START_REF] Schmalansee | Inter-Industry Studies of Structure and Performance[END_REF] (and also the inter country comparison in [START_REF] Pryor | An International Comparison of Concentration Ratios[END_REF]) remarkable intersectoral differences are found in concentration ratios which, in turn, do not appear to be correlated with (sectoral) average firm size (cfr. [START_REF] Bottazzi | Invariances and Diversities in the Evolution of Italian Manufacturing Industry[END_REF].

Firm size distributions and their properties are by definition the outcome of the growth dynamics undergone by every firms in the industrial population together of course with entry and exit processes. 3It is handy to start the analysis of the statistical properties of firm growth by mean of a simple phenomenological model based on the classical [START_REF] Gibrat | Les inègalitès èconomiques[END_REF]. Let s t be the logarithm of firm size at time t. The simple integrated process s t = s t-1 + ǫ with iid shocks, known as the "law of proportionate effects" has been shown to yield a fairly good first order description of the observed dynamics of firm size (in a vast literature see Mansfield, 1962;[START_REF] Kumar | Growth, Acquisition Activity and Firm Size: Evidence from the United Kingdom[END_REF][START_REF] Hall | The Relationship Between Firm Size and Firm Growth in the Us Manufacturing Sector[END_REF][START_REF] Sutton | Gibrat's Legacy[END_REF][START_REF] Lotti | Does Gibrat's Law hold among young, small firms?[END_REF][START_REF] Bottazzi | Properties and Sectoral Specificities in the Dynamics of U.S. Manufacturing Companies[END_REF].

There are, however, significant deviations from this simple statistical benchmark. To synthetically account for them Bottazzi et al. (2010c) introduce a generalization of the original specification

s t -s t-1 = c + λ s t-1 + σ(s t-1 )ǫ t , (1)
where λ captures the autoregressive component in firm's size, σ is a function describing the heteroskedastic structure of the process while ǫ is a growth shock assumed independent from size. This extended framework allows to discuss the most relevant deviations from the benchmark represented by the "Law of Proportionate Effects".

First, in the vast majority of empirical investigations on firm and plant level data λ has been found to be negative, suggesting that smaller (surviving) firms grow faster than larger ones (see [START_REF] Lotti | Does Gibrat's Law hold among young, small firms?[END_REF], for an in-depth review of the empirical literature). Moreover, the relationship between size and growth is modulated by the age of firms themselves with age exerting negative effects on growth rates but positive on survival probabilities, at least beyond some post-infancy threshold [START_REF] Evans | The Relationship between Firm Growth, Size, and Age: Estimates for 100 Manufacturing Industries[END_REF].

Additional precious clues on the basic properties of the process of corporate growth are captured by the function σ which describes the dependence of the standard deviation of growth shocks on size. Since the early insights in [START_REF] Hymer | Firm Size and Rate of Growth[END_REF] a quite robust evidence shows that smaller firms experience more volatile growth patterns. This evidence has been recently refined showing that this relation robustly displays an exponential shape, with an exponent approximately equal to -0.2, in variety of different databases (cfr. [START_REF] Amaral | Scaling behavior in economics: The problem of quantifying company growth[END_REF]; [START_REF] Bottazzi | Properties and Sectoral Specificities in the Dynamics of U.S. Manufacturing Companies[END_REF] on US Compustat data, [START_REF] Bottazzi | Modes of Knowledge Accumulation, Entry Regimes and Patterns of Industrial Evolution[END_REF] on the international pharmaceutical industry and Bottazzi et al. (2010c) on a sample of limited Italian firms). A plausible interpretation of this stylized fact, put forward in Bottazzi and Secchi (2006b), is that the variance-scale relation is essentially a diversification-scale relation: business firms grow by both expanding within their incumbent lines of business and by diversifying into new ones. If market dynamics across activities are not perfectly correlated and if size goes together with an increasing number of lines of business in which a firm operate, then one should expect a lower variance of growth for bigger firm sizes. In turn, this diversification dynamics can be interpreted in terms of a branching process which appears intuitively consistent with a capability-driven pattern of diversification where the expansion into new activities build incrementally upon the knowledge and the complementary assets accumulated within the existing ones (see [START_REF] Teece | Understanding corporate coherence: Theory and evidence[END_REF], on the ensuing "coherence" in the diversification profiles).

Finally the extended model of firm dynamics in equation ( 1) suggests that other important features of the growth patterns of business firms might be found in the statistical properties of the growth shocks ǫ, i.e. of the firm growth rates s t -s t-1 once the autoregressive component and the heteroskedastic structure have been taken into account. Since the pioneer investigations in [START_REF] Stanley | Scaling behaviour in the growth of companies[END_REF] the evidence suggests an extremely robust stylized fact: the distribution of firm growth rates is characterized by tails fatter than in the Gaussian case and it is, in general, well approximated by the Laplace or by others distributions, like the Exponential Power, which posses an even fatter tail behavior. This property is among the most robust in the industrial organization literature: it holds across different levels of disaggregation, across countries and using different size proxies, even if one observes some diversity in shapes emerging across finer sectoral disaggregation (see [START_REF] Stanley | Scaling behaviour in the growth of companies[END_REF]; [START_REF] Bottazzi | Properties and Sectoral Specificities in the Dynamics of U.S. Manufacturing Companies[END_REF] on US Compustat data, [START_REF] Bottazzi | Modes of Knowledge Accumulation, Entry Regimes and Patterns of Industrial Evolution[END_REF] on the international pharmaceutical industry, [START_REF] Bottazzi | Invariances and Diversities in the Evolution of Italian Manufacturing Industry[END_REF] on Italian manufacturing industry and Bottazzi et al. (2010a) on the French manufacturing industry).

Such statistical property of growth rates -the generalized presence of fat tails in their distribution -implies the presence of much more structure in the growth dynamics than generally assumed. More specifically, ubiquitous fat tails are a sign of some underlying correlating mechanism which one would not observe if growth events were small and independent. In [START_REF] Bottazzi | Invariances and Diversities in the Evolution of Italian Manufacturing Industry[END_REF] and Dosi (2007) one puts forward the conjecture that such mechanisms are likely to be of two types. First, it seems plausible that the very process of competition induces correlation: a firm's gain in market share is some other firms' loss. Second, one could naturally expect "lumpy" growth events due to introduction of new products, the construction or closure of plants, entry/exit of firms in/from a particular market. In this vein, Bottazzi and Secchi (2006a) attempt to model an increasing returns dynamics able to reproduce the observed fat-tailed distribution.

A final important piece of evidence on the structure of firm growth processes concerns the possible autocorrelation over time of growth rates. A caveat is required. The investigation of this aspect of the growth process would require time series long enough to describe the properties of the sample path of each firm on the ground of the possibility that the evolutionary pattern of each firm may be specific to each entity in its interaction with the population of other firms with which it competes in that particular market in those particular times. Very often the available evidence falls well short of that. Interestingly, in an industry for which one has reasonable longitudinal panel data at different level of disaggregation, the international drug industry, one does find robust autocorrelation structures up to the 7 th lag [START_REF] Bottazzi | Modes of Knowledge Accumulation, Entry Regimes and Patterns of Industrial Evolution[END_REF]. In other investigations, pooling together firms belonging to the same (two or three digit) industrial sector, the autocorrelation structures in the growth dynamics appears to be weakened due to the aggregation of several different line of business each characterized by its own autoregressive profile [START_REF] Bottazzi | Properties and Sectoral Specificities in the Dynamics of U.S. Manufacturing Companies[END_REF][START_REF] Bottazzi | Invariances and Diversities in the Evolution of Italian Manufacturing Industry[END_REF][START_REF] Coad | A Closer Look at Serial Growth Rate Correlation[END_REF]. However, using bootstrap techniques [START_REF] Bottazzi | Corporate Growth and Industrial Structure. Some Evidence from the Italian Manufacturing Industry[END_REF] tend to confirm that there are systematic but idiosyncratic differences in autocorrelation structures, which are not captured by sectoral "average" autoregressive coefficients.

Together with growth in market shares, profitability is another crucial measure of revealed corporate performances. Irrespectively of diverse empirical proxies for profitability4 two robust finding have clearly emerged in the last three decades. First, the extent of the observed heterogeneity in profitabilities is wide irrespectively of the level of disaggregation considered: in the same sector coexist firms with large profit margins with firms incurring substantial losses (cfr. the recent evidence on two different samples of Italian firms in [START_REF] Bottazzi | Productivity, Profitability and Financial performance[END_REF][START_REF] Grazzi | Trade and Profitability: Is there an export premium? Evidence from Italian manufacturing firms[END_REF]. Second, given such a piece of evidence, a crucial issue regards the persistence of such differentials. Indeed a low persistence could simply mean that capitalism involves daring and heroic efforts by multitudes of firms which happen to make many mistakes as well as reap huge rewards, with markets there to help and quickly redress individual mistakes and wash away abnormal rents. It turns out that this view does not quite match the evidence. There is, on the contrary, a quite wide literature on the persistence of profitability differences across firms, with extremely high autocorrelation over time in profitabilities even at very narrow levels of disaggregation (cfr. [START_REF] Muller | Profits in the Long-Run[END_REF][START_REF] Cubbin | The Convergence of Profits in the Long Run: Inter-Firm and Inter-Industry Comparisons[END_REF][START_REF] Geroski | The Persistence of Profits: A European Comparison[END_REF]Muller, 1990;[START_REF] Goddard | The persistence of profit: a new empirical interpretation[END_REF][START_REF] Cefis | Is there any Persistence in Innovative Activities?[END_REF][START_REF] Gschwandtner | Profit Persistence in the "Very" Long Run: Evidence from Survivors and Exiters[END_REF]Dosi, 2007).

Summing up, we believe that there are two main messages coming from all the foregoing empirical evidence.

First, there is a rich statistical structure in the dynamics of business firms and industries that goes well beyond the ones identified simply focusing on average relations between corporate performance and corporate characteristics. Moreover, this revealed structure in the stochastic process describing industrial evolution bears clear signs common to all complex system dynamics including the fat-tailed distributions in the rates of changes of all the variable of interest. That, in turn, is likely to witness for the existence of some underlying correlation mechanism, which makes the system self-organized in its growth process. In these respects, all the evidence on industrial change corroborates the exciting conjecture that evolutionary phenomena tend to undergo non-gaussian lives influenced by persistent positive or negative interactions among agents within and across the relevant populations.

Second, the two key indicators of corporate performance , growth and profitability, reveal a widespread and profound heterogeneity across firms that persist over time notwithstanding the competition process. All this brings naturally the attention to the sources of such heterogeneities.

Behind heterogeneous performances: heterogeneous productivities, capabilities to innovate and organizational set-ups

The most plausible candidates for the explanation of the widespread and persistent heterogeneity in firm performances discussed in the previous section are, with little doubt, to be found in the diverse efficiencies with which firms turn input into output (i.e. different productivities) and in the (price-weighted) characteristics of outputs themselves. However, notwithstanding the relative simplicity of the concept, measuring productivity has shown to be not an easy task. As known, in the literature one finds two basic types of productivity measures, namely single factor and multi factor indexes. The former include ratios of some measures of output (total sales or value added) over the number of employees or, better, of worked hours. These single-factor measures do not require any assumption on the existence and form of underlying production functions but have the drawbacks of being affected by the intensity of use of the excluded inputs. Conversely, in order to overcome this limitation, many researchers willing to make many far from innocent assumptions on the form of the production function itself -including the absence of complementarities among production inputs and many others -have resorted to a multifactor productivity measures. This is not the place to discuss in details pros and cons of the choice between single and multi factor productivity measures (cfr. [START_REF] Dosi | Technological change and industrial dynamics as evolutionary processes[END_REF][START_REF] Dosi | Technologies as problem-solving procedures and technologies as input-output relations: some perspectives on the theory of production[END_REF][START_REF] Hulten | Total Factor Productivity: a Short Biography[END_REF], for discussion of different approaches underlying the choice). Here let us just warn the reader that, since data on output quantities are usually not available, almost any productivity measure used in the literature we are going to briefly review below will be a revenue-based measure, hence representing an accurate productivity index only in those cases where product quality differences are fully reflected in prices.

In any case, irrespectively of the proxy for productivity and of the highly diverse countries analyzed few, unambiguous results have emerged.

First of all, at any level of disaggregation we observe widespread differences in productivities which tend to persist over time. Moreover, higher productivity tend to be associated with higher survival probabilities. Hence, also at the level of input efficiencies the general picture is characterized by general, profound and persistent heterogeneity across plants and firms.

Before discussing, in the next section, if, how and on what time scales heterogeneous "identities" affect performances, let us try to offer a telegraphic overview of the main determinants of the persistent heterogeneity in productivities identified in the last decades by the empirical literature. A complete review of the full range of candidates to explain productivity dispersion clearly goes far beyond the scope of this introduction (more in [START_REF] Nelson | Research on Productivity Growth and Productivity Differences: Dead Ends and New Departures[END_REF][START_REF] Dosi | Technological change and industrial dynamics as evolutionary processes[END_REF][START_REF] Syverson | What Determines Productivity?[END_REF]. Here let us briefly recall three groups of factors that repeatedly appear in the interpretations of why firms display so diverse productivities, namely the quality of inputs, the R&D and innovation strategies and idiosyncratic organizational capabilities.

Characteristics of the workforce, management and capital inputs

As one might expect productivity appears to be positively correlated with the quality of labor as captured by personal characteristics of workers such as education, experience, training [START_REF] Abowd | The Relationship Between Human Capital, Productivity and Market Value: Bulding Up From Microeconomic Evidence[END_REF][START_REF] Fox | Does Input Quality Drive Measured Differences in Firm Productivity?[END_REF]. Moreover, similar evidence has recently emerged on the impact of managerial practices on productivity. [START_REF] Bloom | Measuring and Explaining Management Practices Across Firms and Countries[END_REF] document that higher "quality" management practices are positively correlated with various proxies of productivity, and the same seems to hold for "quality" of management itself (cfr. for example [START_REF] Shearer | Piece Rates, Fixed Wages and Incentives: Evidence from a Field Experiments[END_REF].

Together, as a good deal of technological advances is capital-embodied, other things being equal, one should expect firm's productivities to depend on the vintage distribution of its capital equipment.

That was also the conjecture put forward decades ago by [START_REF] Salter | Productivity and Technical Change[END_REF]. Unfortunately, the scarcity of data has largely prevented so far much empirical advance in this area. And similar considerations largely apply also to the role of intangible assets. On the contrary, over the last decade scholars have learned a great deal about the impact of that particular type of capital embodying various forms of ICT. Indeed information and communication technologies have shown to play an important role in accounting for the boom of productivity in the US in the last twenty years [START_REF] Jorgenson | A Restrospective Look at the US Productivity Growth Resurgence[END_REF] and, furthermore, the delay in their adoption seems also to have contributed to a European productivity gap vis-â-vis the USA [START_REF] Van Ark | The Productivity Gap between Europe and the United States: Trend and Causes[END_REF]. 5A recent literature has started to use micro-data in order to illuminate the impact of ICT technologies at the firm or even at the worker level. [START_REF] Brynjolfsson | Beyond Computation: Information Technology, Organizational Transformation and Business Performance[END_REF] review the two main strands of these micro-studies. First, a case-based literature provides evidence that the impact of ICT at the firm level goes together with changes in organizational practices, such as changes in authority relationships, decentralization of local decisions, shifts in task content and/or changes in reward schemes. Many of these studies (see for instance [START_REF] Brynjolfsson | The Matrix of Change[END_REF] show, however, that in the face of changes in organizational practice, many workers still remain trapped in old work practices. Inertial forces are at work, which explain the inability of firms to instantaneously exploit the potential of new technologies. Second, an econometric literature has also emerged, using large scale data recently becoming available from official sources. [START_REF] Pilat | The ICT productivity paradox: insights from micro-data[END_REF] provides an overview of these studies, available now for many countries. Let us briefly summarize the main results.

First, most of them find a positive relation between level of ICT and firm productivity. (Note that this is a correlation, more work needs to be done in understanding causality linkages).

Second, the evidence points at different factors moderating the impact of ICT at firm level, including the co-occurrence of matching skills of the workforce, appropriate organizational practice and other forms of organizational and technological innovation. Moreover, the size and age of the firm seem to influence the impact of ICT adoption upon productivity.

Third, while improvements in IT technology tend to be quickly available throughout the economy, the complementary organizational changes at the firm level rely on a process of 'co-invention' by individual firms [START_REF] Bresnahan | General purpose technologies 'Engines of growth'?[END_REF] suggesting co-evolutionary processes combining the adoption of information technology with complementary organizational changes and innovation in the form of new products and services [START_REF] Bresnahan | Information Technology, Workplace Organization, And The Demand For Skilled Labor: Firm-Level Evidence[END_REF]. Conversely there is some evidence that the sheer adoption of ICT without corresponding changes in organizational practices might be simply detrimental for the company. It is the combination of the three changes mentioned above that can drive productivity gains.

Fourth, some econometric works (cfr. [START_REF] Brynjolfsson | Beyond Computation: Information Technology, Organizational Transformation and Business Performance[END_REF][START_REF] Greenan | Information Technology and Research and Development Impact on Productivity and skills: Looking for Correlations on French Firm Level Data[END_REF], for US and France respectively) have used fixed effects models to estimate the impact of ICT on productivity in order to capture firm-specific determinants. The estimates controlling for fixed effects are substantially lower and indicate that much of the ability of firms to exploit gains from ICT relates to intrinsic pre-existent organizational somewhat capabilities. [START_REF] Bartelsman | Understanding Productivity: Lessons from Longitudinal Microdata[END_REF] also discuss insights coming from micro studies on the relationship between productivity and advanced technology. Use of the latest technology turns out to be highly correlated with other variables (such as human capital). A study by [START_REF] Doms | Workers, Wages, and Technology[END_REF] shows that plants that had above average productivity because of ICT, also had the same before the introduction of ICT because they consistently were the ones choosing the most advanced technologies. In this sense, also under an ICT-centered regime of technological change asymmetries across firms are the rule: some firms show a much higher performance and persistently so. In turn, this can easily be interpreted as an evolutionary story of path-dependence and persistent performance differentials among firms. [START_REF] Faggio | The Evolution of Inequality in Productivity and Wages: Panel Data Evidence[END_REF], in the present issue, add new evidence on the nature of the tie between ICT and productivity dispersion. Using a new panel of UK firms from both manufacturing and service sector they show that the observed increase in the wage dispersion, within groups of workers homogeneous in terms of experience, gender and skills, has been accompanied by an equally strong rise in productivity inequality among firms within the same industries. What matters most for the present discussion is that they reveal that those industries which adopted ICT more intensively are also those experiencing the highest increase in productivity dispersion.

Characteristics of R&D and innovation strategies

A second important set of plausible determinants of productivity dispersion regards R&D and innovation strategies. For the most part, the empirical literature in this domain has focused on the link between R&D expenditures and the residual part of firms productivity not accounted by other inputs, under the implicit assumption that this residual is the outcome of technical change induced by research and development efforts. Also in this case, despite the many measurement and econometric issues involved, a common result has emerged: elasticities of productivity to R&D expenditures are positive and rather large in most of the countries and sectors investigated and they are in general larger than those to ordinary capital (a complete review of the results on this issue is [START_REF] Hall | Measuring the Returns to R&D[END_REF].

Of course, R&D is only one, and in quite a few sectors not the most relevant aspect, of the firm overall innovative efforts. However, whether or not innovative search is undertaken via formal R&D activities, a crucial component, likely to impact on the observed dispersion of productivity levels, is to be found in the wide differences in the ability of firms to innovate and to adopt product and process innovation developed elsewhere. It should come as no surprise, at this point of the discussion, that also regarding firms' innovation strategies and outcomes the literature has identified wide and persistent heterogeneity (cfr. among many others [START_REF] Freeman | The Economics of Industrial Innovation[END_REF][START_REF] Dosi | Technological change and industrial dynamics as evolutionary processes[END_REF]. Innovative capabilities appear to be highly asymmetric with a rather small number of firm responsible of a good deal of innovation output, irrespectively of the country or of the sector analyzed.

These differential degrees of innovativeness are generally persistent over time, often revealing a small core of systematic innovators [START_REF] Cefis | Is there any Persistence in Innovative Activities?[END_REF]. Relatedly, while the arrivals of major innovations are rare events, they are not independently distributed across firms: rather recent evidence suggest they tend to arrive in firm-specific chunks of different sizes [START_REF] Bottazzi | Modes of Knowledge Accumulation, Entry Regimes and Patterns of Industrial Evolution[END_REF].

Similar considerations apply to the adoption of process innovations as robustly revealed by the major stylized facts on diffusion already reported by the early classic investigations including [START_REF] Griliches | Hybrid Corn: An Exploration in the Economics of Technological Change[END_REF]; [START_REF] Mansfield | Technical Change and the Rate of Imitation[END_REF]; [START_REF] Nasbeth | The Diffusion of new Industrial Processes[END_REF]; [START_REF] Rosenberg | Factors Affecting the Diffusion of Technology[END_REF]Rosenberg ( , 1976)). Telegraphically, diffusion is a time consuming process, whose speed varies widely across technologies and across countries. A good percentage of innovations never diffuses but when they do the diffusive processes follow S-shaped asymmetric profiles. This evidence is well in tune with the presence of ubiquitous heterogeneity among would-be adopters on nearly every dimension which one may think of as influencing adoption ranging from sheer size all the way to different absorptive capacities [START_REF] Cohen | Absortive Capacity: a New Perspective on Learning and Innovation[END_REF]) and abilities to use new techniques and pieces of equipment.

Diverse organizational capabilities

The quality of the inputs, we suggest, does not exhaust the interpretation, paraphrasing [START_REF] Nelson | Research on Productivity Growth and Productivity Differences: Dead Ends and New Departures[END_REF], of why firms differ and how does it matter, while, at the same time, the differences in innova-tiveness, broadly defined, demand themselves an explanation. Here it is where the analysis of determinants of heterogeneous corporate performances links with a growing body of research addressing the nature and dynamics of organizational capabilities (more in [START_REF] Dosi | Organizational Capabilities, Patterns of Knowledge Accumulation and Governance Structures in Business Firms: An Introduction[END_REF]Dosi et al., , 2000;;[START_REF] Levinthal | Organizational Capabilities in Complex Worlds[END_REF][START_REF] Montgomery | Resource-Based and Evolutionary Theories of the Firm: Towards a Synthesis[END_REF][START_REF] Teece | Dynamic Capabilities and Strategic Management[END_REF]Winter, 2003). Such capabilities are grounded in those particular forms of organizational knowledge that account for organization's ability to perform and extend its characteristic "output" actions -particularly the creation of a tangible product or the provision of a service and the development of new products and services. In turns these capabilities involve to a good extent ensembles of organizational routines which account for the problem-solving abilities of the organization (Dosi et al., 2000).

The crucial research question here is the identification of robust and non-tautological proxies for capabilities. 6 While the search is far from over researchers are painstakingly pointing at an increasing number of (often sector-specific) indicators of capabilities (see for example [START_REF] Baldwin | Business Strategies in Innovative and Non Innovative Firms in Canada[END_REF][START_REF] Argote | Repositories of knowledge in franchise organizations: Individual, structural, and technological[END_REF][START_REF] Henderson | Measuring Competence? Exploring Firm Effects in Drug Discovery[END_REF][START_REF] Pisano | In Search of Dynamic Capabilities[END_REF] Firm characteristics and export performances An important consequence, and probably also cause, of heterogeneous productivities are diverse export performances. The issue has received a great deal of empirical attention after the theoretical contributions by [START_REF] Eaton | Technology, Geography, and Trade[END_REF] and [START_REF] Melitz | The Impact of Trade on Intra-Industry Reallocations and Aggregate Industry Productivity[END_REF] which attempt to formalize the link between firms with heterogenous productivities and their international trade involvement. Several investigations have documented a strong positive correlation between productivity levels and trade exposure suggesting that exporters are almost always more productive than their non-exporter competitors (cfr. the reviews in [START_REF] Wagner | Exports and Productivity: A Survey of the Evidence from Firm-level Data[END_REF][START_REF] Greenaway | Industry Differences in the Effect of Export Market Entry: Learning by Exporting?[END_REF]. That is, the vast majority of these studies support the idea that already more productive firms self-select themselves to access international markets (this is usually called the "self-selection into export" hypothesis: cfr. among many others [START_REF] Roberts | The Decision to Export in Colombia: An Empirical Model of Entry with Sunk Costs[END_REF][START_REF] Bernard | Exceptional exporter performance: cause, effect, or both?[END_REF]. On the other hand, some studies have found (less robust) support to the idea that firms increase their productivity after and because they start to export, through a sort of learning-by-exporting process which lead to subsequent improvements of their efficiencies (two examples are in [START_REF] Van Biesebroeck | Exporting raises productivity in sub-Saharan African manufacturing firms[END_REF][START_REF] De Loecker | Do exports generate higher productivity? Evidence from Slovenia[END_REF].

The relation between international exposure and productivity has been studied also in the older stream of literature analyzing the process of economic growth and development and, in particular, the process of productivity catching-up of "lagging behind" countries [START_REF] Gerschenkron | Economic Backwardness in Historical Perspective[END_REF][START_REF] Dosi | The Economics of Technical Change and International Trade[END_REF][START_REF] Fagerberg | Technology and the International Differences in Growth Rates[END_REF]. Traditionally the studies in this field have been focusing on aggregate units (such as countries, regions or at best sectors) neglecting the widespread firm heterogeneity and its impact on economic development largely due to lack of appropriate data. The explosion in the availability of micro evidence has substantially refocused the attention to sectors and firms(plants). Within the latter literature relying on multi-country micro data [START_REF] Bartelsman | Distance to Which Frontier? Evidence on Productivity Convergence from International Firm-level Data[END_REF] build measures of global and national technological frontiers and firms' distance from them highlighting the frequent possibility that firms characterized by big technology gaps vis-à-vis the international frontiers might well not be able to have a grasp of it and incrementally learn. However, even when this is the case [START_REF] Iacovone | Catching Up with Technological Frontiers: Micro-Level Evidence on Growth and Convergence[END_REF] find below on the ground of a large panel of Mexican manufacturing plants that learning just the domestic "best practice" might be somewhat easier . They explore the relative effect of internal R&D and export exposure upon catching-up with both the domestic and "global" frontiers. Not so surprisingly Mexican plants are much faster in catching-up vis-à-vis national technological best practice rather than with global one. Much more interestingly they provide evidence supporting the idea that plants making larger technological efforts, in terms of R&D and technology transfers, tend to catch up much faster to the global frontier but the same does not apply to catching-up to the domestic one. Conversely, increasing exposure to trade allows Mexican firms appears to speed up the adoption of best domestic technological practices but it does not affect to the same extent the convergence with the global technological frontier.

A final important point. Most often the determinants of differential efficiencies discussed above do not operate in insulation. Rather various complementarities are the norm. We have already mentioned the findings on the complementarities between ICT adoption and organizational change. Another example of such interactions is presented in [START_REF] Ito | Why Some Firms Persistently Out-Perform Others: About the Interactions of Innovation and Exporting Strategies[END_REF], below. Using a large Japanese administrative survey the authors show that innovation and exporting strategies are characterized by strong complementarities which define coherent productive models and patterns of learning. In turn, diverse combinations of innovation and export strategies affect persistently firms' productivities and survival probabilities.

Selection vs Adaptation and Idiosyncratic Learning

Different productivities, organizational setups, propensities to innovate and behaviors make up the distinct corporate identities which in turn should somehow influence firms' performances. A crucial empirical issue concerns the ways and the extent to which such influences actually operate.

Let us consider first the impact of different productivities upon profitability, growth, and survival probabilities.

Mainly North American evidence, mostly at plant level, does suggest increasing output shares in high-productivity plants and decreasing shares of output in low-productivity ones as drivers in the growth of average sectoral productivities, even if the process of displacement of lower efficiency plants is rather slow [START_REF] Baily | Productivity Dynamics in Manufacturing Establishments[END_REF][START_REF] Baldwin | The Dynamics of Industrial Competition: A North American Perspective[END_REF][START_REF] Ahn | Firm dynamics and Productivity Growth: A Review of Micro Evidence from OECD Countries[END_REF][START_REF] Baldwin | Plant turnover and productivity growth in Canadian manufacturing[END_REF].

In complementary efforts, a growing number of scholars has indeed began doing precisely what we could call evolutionary accounting (even if most do not call it that way; however for an early example of the genre, cfr. [START_REF] Nelson | An Evolutionary Theory of Economic Change[END_REF]. The fundamental evolutionary idea is that productivity distributions change as a result of learning by incumbent entities, differential growth(i.e., a form of selection) of incumbent entities themselves, death (indeed, a different and more radical form of selection), and entry of new entities. Favored by the growing availability of micro longitudinal panel data, an emerging line of research (cfr. [START_REF] Olley | The Dynamics of Productivity in the Telecommunications Equipment Industry[END_REF][START_REF] Foster | New Developments in Productivity Analysis[END_REF]Bottazzi et al., 2010c, and the discussion in [START_REF] Bartelsman | Understanding Productivity: Lessons from Longitudinal Microdata[END_REF]) investigates the properties of such decompositions, identifying the contribution to productivity growth of (i) firm-specific changes holding shares constant (sometimes called the within component), (ii) the changes in the shares themselves, holding initial firm productivity levels constant (also known as the between component), (iii) entry and (iv) exit. Of course, there is a considerable variation in the evidence depending on countries, industries and methods of analysis. However, some patterns emerge.

First, the within component generally is significantly larger than the between one: putting it another way improvement of productivity by existing firms dominates upon selection across firms as a mode of industry advancement at least concerning productivity (both labor and TPF). This emerges both from the foregoing evolutionary accounting exercises and from estimates of the relationship between efficiency and subsequent growth, allowing for firm fixed effects. Using data for France and Italy [START_REF] Bottazzi | Corporate performances and market selection. Some comparative evidence[END_REF], below, show that, in both countries, firms identified as more productive tend also to be more profitable than other firms. The impact on growth is, instead, much less clearcut. Both Italian and French data (cfr. again [START_REF] Bottazzi | Corporate performances and market selection. Some comparative evidence[END_REF], in the present issue) show a weak or nonexistent relationship between relative (labor) productivities and growth: more efficient firms do not grow more. Moreover even when some positive relation between efficiency and growth appears, this is almost exclusively due to the impact of few outliers (the very best and the very worst). And, this holds in both the short and the medium term. So, for example, in the analyses of Bottazzi et al. (2010c) on Italy and France, firm-specific factors generally account for almost an order of magnitude more than selection in the explained part of the variance in firm growth rates.

Second, relative efficiencies do influence survival probabilities, and it may well turn out that selective mechanisms across the population of firms operate much more effectively in the medium/long term at this level rather than in terms of varying shares over the total industry output.

In any case, the foregoing patterns hint at a sort of a puzzle, awaiting further research, in that such statistical evidence appears to be somewhat at odds with more qualitative reconstructions of industrial evolution whereby improvements in productivity (and in product characteristics), as induced by technological and organizational advances appear to be at the center of competitive advantages and ultimately a crucial driver toward corporate leadership: cfr. among others [START_REF] Dosi | Technical Change and Industrial Transformation -The Theory and an Application to the Semiconductor Industry[END_REF] on semiconductors and [START_REF] Murmann | Knowledge and Competitive Advantage[END_REF] on chemicals.

We have focused so far upon the linkages between admittedly rough proxies for productivity, on the one hand, and growth and survival, on the other. What about the relationships between profitability and the latter two variables? The evidence we are familiar with strikingly shows little or no link between profitability and firm growth of incumbents (cfr. again Bottazzi et al., 2010c, on Italian and French longitudinal data). However, other pieces of evidence suggest also systematic effects of profitability upon survival probabilities (cfr. the discussion in [START_REF] Bartelsman | Understanding Productivity: Lessons from Longitudinal Microdata[END_REF][START_REF] Foster | Reallocation, Firm Turnover, and Efficiency: Selection on Productivity or Profitability?[END_REF].

Certainly, there are other determinants of differential growth which have been neglected so far, largely due to lack of appropriate data. One ensemble of variables regards product characteristics which in market generally characterized by product differentiation (of both the "horizontal" and "vertical" kinds) ought to bear important consequences in terms of the growth potential of each firm. Another set of variables concerns the organizational characteristics and strategic orientations of firms themselves. In this respect, the evidence presented in [START_REF] Seo | Explaining Performances Changes of the Business Groups in Transition Economies: Three Hypothesis in the case of China[END_REF] in this volume highlights the importance of organizational forms (e.g. being a conglomerate or not) and ownership (e.g. stateowned or not) in terms of differential value of the firms. However, interestingly, there appear to be no unequivocally superior set-up. A lot seems to be contingent on the historical periods and on the stage of development.

The implications of all the empirical regularities identified so far are far-reaching. Certainly, the recurrent evidence at all levels of observation of interfirm heterogeneity and its persistence over time is well in tune with an evolutionary notion of idiosyncratic learning, innovation (or lack of it) and adaptation. Heterogeneous firms compete with each other and, given (possibly firm-specific or location-specific) input and output prices, obtain different returns. Putting it in a different language, they obtain different quasi-rents or, conversely, losses above/below the notional pure competition profit rates. Many firms enter, a roughly equivalent number of firms exits. In all that, the evidence increasingly reveals a rich structure in the processes of learning, competition and growth.

As mentioned, various mechanisms of correlation, together with the sunkness and indivisibilities of many technological events and investment decisions, yield a rather structured process of change in most variable of interest, for example size, productivity, profitability, also revealed by the fattailedness of the respective growth rates.

At the same time, market selection among firms -the other central mechanism at work together with firm-specific learning in evolutionary interpretations of economic change -does not seem to be particularly powerful, at least on the yearly or multi-yearly time scale at which statistics are reported. Conversely, diverse degrees of efficiencies seem to yield primarily relatively persistent profitability differentials. That is, contemporary markets do not appear to be too effective selectors delivering rewards and punishments in terms of relative sizes or shares, no matter how measured, according to differential efficiencies. Moreover, the absence of any strong relationship between profitability and growth militates against the naively Schumpeterian notion that profits feed growth (by plausibly feeding investments).

Selection among different variants of a technology, different vintages of equipment, different lines of production does occur and is a major driver of industrial dynamics. However, it seems to occur to a good extent within firms, driven by the implementation of better processes of production and the abandonment of older less productive ones.

Finally, the same evidence appears to run against the conjecture, put forward in the 1960s and 1970s by the managerial theories of the firm on a tradeoff between profitability and growth with managerialized firms trying to maximize growth subject to a minimum profit constraint.

In turn, the (still tentative) observation that market selection that winnows directly on firms may play less of a role than that assumed in many models of evolutionary inspiration [START_REF] Nelson | An Evolutionary Theory of Economic Change[END_REF][START_REF] Winter | Schumpeterian competition under alternative technological regimes[END_REF][START_REF] Silverberg | Long waves and 'evolutionary chaos' in a simple Schumpeterian model of embodied technical change[END_REF]Dosi et al., 1994a[START_REF] Dosi | Learning, Market Selection and Evolution of Industrial Structures[END_REF]Dosi et al., , 2006;;Iwai, 1984a,b;[START_REF] Silverberg | From the Artificial to the Endogenous: Modeling Evolutionary Adaptation and Economic Growth[END_REF][START_REF] Malerba | History-Friendly' Models of Industry Evolution: The Computer Industry[END_REF][START_REF] Bottazzi | Modes of Knowledge Accumulation, Entry Regimes and Patterns of Industrial Evolution[END_REF] demands further advances in the understanding of how markets work (or do not), and of the structure of demand (see the discussion in Nelson, 1991Nelson, , 2008)).

First, one measures productivity, supposedly a driver of differential selection, very imperfectly: we have mentioned above that one ought to disentangle the price component of value added (and thus the price effects upon competitiveness) from physical efficiency to which productivity strictly speaking refers. This applies to homogeneous products and even more so when products differ in their characteristics and performances: as this is often the case in modern industries, one ought to explicitly account for the impact of the latter upon competitiveness and revealed selection processes.

Second, but relatedly, the notion of sharp boundaries between industries and generalized competition within them is too heroic to hold. It is more fruitful in many industries to think of different submarket of different sizes as the locus of competition Sutton (1998). The characteristics and size of such submarkets offer also different constraints and opportunities for corporate growth. Ferrari and Fiat operate in different submarkets, face different growth opportunities and do not compete with each other. However, the example is interesting also in another respect: Fiat can grow, as it actually happened, by acquiring Ferrari.

Third, a growing microevidence highlights the intertwining between technological and organizational factors as determinants of Schumpeterian competition: [START_REF] Bresnahan | Schumpeterian Competition and Diseconomies of Scope: Illustrations from leading Historical Firms in Computing[END_REF] illustrate the point in the case of IBM and Microsoft facing the introduction of the PC and the browser, respectively. Both firms, the work shows, faced organizational diseconomies of scope precisely in the corporate activities where they were stronger.

Fourth, in any case, the links between efficiency and innovation, on the one hand, and corporate growth, on the other, are mediated by large degrees of behavioral freedom, in terms, for example, of propensities to invest, export, expand abroad; pricing strategies; patterns of diversification.

The other side of the process of "creative destruction" generated by industrial dynamics involving entry, exit and ever-changing market shares is a continuous process of job creation, destruction and relocation. Since the seminal works of John C. Haltiwanger and Steven Davis, at the beginning of 90s, an increasing attention has been devoted to the processes of job creation and job destruction which are pervasive in all capitalist economies. All the investigations in this tradition document the impressive amplitude of labour flows in and out and also the role of the idiosyncratic firm characteristics in explaining the emergence and the persistence of such job and worker flows (cfr. among many others [START_REF] Davis | Gross Job Creation, Gross Job Destruction, and Employment Reallocation[END_REF][START_REF] Davis | Job Creation and Destruction[END_REF]Davis and Haltiwanger, 1999).

However, the analyses in this stream of literature are often ridden with problems regarding the definitions of the variables which might severely limit the comparisons across countries(for two exceptions see [START_REF] Haltiwanger | Assessing Job Flows Across Countries: The Role of Industry, Firm Size, and Regulations[END_REF][START_REF] Wolfers | Measuring the Effects of Employment Protection on Job Flows: Evidence from Seasoonal Cycles[END_REF]. [START_REF] Bassanini | Inside the Perpetual-Motion Machine: Cross-country Comparable Evidence on job and Worker Flows and the Industry and Firm Level[END_REF] in this volume offers an attempt to overcome these difficulties exploiting a unique database built with homogeneously defined variables and under the same collection protocols. On the ground of this higher quality data, the paper confirms that firm characteristics such as industry, age and size are key factors in shaping gross job flows in all countries. Further, even after controlling for these idiosyncratic factors, cross countries differences appear large especially comparing US and UK with many continental European countries. Broad, country-specific, institutional arrangements do significantly modulate the processes of labour creation, relocation and destruction. The paper offers also further insight into the link between gross job flows and productivity. These investigations are the complement of the "evolutionary decomposition" mentioned above, seen in terms of labour relocation and churning -generally associated with relatively high flows of job creation and destruction. Inside this micro turbulence Bassanini (2010) also shows a basic asymmetry: in most of the countries, inefficient firms tend to destroy more jobs during contractions while, on the contrary, during expansions firms with higher productivity display relatively smaller rates of employment growth.

"Restless capitalism", as Metcalfe puts it, entails persistent (mistake-ridden) learning and innovation by a (changing) population of heterogeneous firms, whose interactions also shape their opportunities, constraints and ultimately their fate in terms of survival. Together, the whole process leaves varying amount of "disruption" along the way, including, of course, labour disruption. Only recently researchers have begun to analyze in detail such processes, even if important advances in our understanding have already been achieved. And the works which follow importantly contribute to it.

Incidentally, note also that any answer to these questions is likely to bring our understanding of the political economy of different institutional set-ups much further than trying to answer questions like: how would an inter-temporally maximizing representative agent behave under institution x as compared to institution y?

A Power Law distribution is a relationship of the type: P r(X > x) = ax -b where P r(X > x) is the probability that a random variable X is greater than x, and a and b are constants.

The discussion which follows will not address explicitly the stylized facts on entry and exit dynamics. A fairly recent survey on the issue is[START_REF] Bartelsman | Distance to Which Frontier? Evidence on Productivity Convergence from International Firm-level Data[END_REF].

Among the most common we find ROS (Gross Operating Margins over Total Sales), ROI (Return on Investment) and a variety of other proxies capturing also results from extra operational activities such as financial and tax policies.

How big has been the gap and how much it is due to difference in ICT diffusion as compared to differences in the sectoral composition of output is, however, an issue beyond the scope of this introduction.

Obvious tautological measures are of course those performances that one tries to explain by means of organizational capabilities themselves

Acknowledgments

We gratefully acknowledge the support by Maison Franco-Japonaise, RIETI, and Waseda University which organized the conference "Organization and Performance: Understanding the Diversity of Firms" (Tokyo, November 2008) where some of the papers of this special issues have been originally presented. In particular we thank Masahisa Fujita, Marc Humbert, Hideaki Miyajima and Franoise Sabban for their invaluable support in the organization of the event.


Laurence Rouet
email: laurence.rouet@philips.com

Roberto Ardon

Jean-Michel Rouet

Benoit Mory

Cécile Dufour

Anne Long

Semi-automatic abdominal aortic aneurysms geometry assessment based on 3D ultrasound

This paper presents a new approach for improving the surveillance of the size of abdominal aortic aneurysms (AAA). Use of 3D ultrasound imaging combined with semi-automatic quantification provides automatic selection of the optimal plane for diameter measurement. Quantification parameters are defined to characterize the aneurysm with more accuracy. Volume imaging also provides 3D visualization of the AAA geometry and CT-like multi-planar reconstructions. Multiple volume registrations are proposed to overcome limited field of view issues. Quantification results show good correlation with 2D reference measurements and obtained Pearson correlation coefficients are significant for 30 patients.

I. INTRODUCTION

Abdominal aortic aneurysm (AAA) is clinically defined as a local enlargement of the aorta of more than 50% with a loss of walls parallelism. The prevalence of this disease is estimated to more than 5% in elderly subjects [START_REF] Lindholt | Screening for abdominal aortic aneurysm reduces overall mortality in men. a meta-analysis of the mid-and longterm effects of screening for abdominal aortic aneurysms[END_REF]. The main risk associated to AAA is rupture leading to mortality in up to 80% of the cases.

The standard surveillance of AAA consists in monitoring its maximum diameter using 2D ultrasound acquisitions. The main limit of such a monitoring is a lack of measurements reproducibility. Indeed, variability of measurements between successive exams may be comparable to the amount of aneurysm growth. Variability may be due to a combination of factors: various definitions of optimal selected diameter (for example true maximum diameter or maximum antero-posterior diameters), variability of AAA geometry and orientations leading to difficult identification of optimal diameter, various protocols of acquisitions and ultrasound image quality [START_REF] Ellis | Limitations of ultrasonography in surveillance of small abdominal aortic aneurysms[END_REF], [START_REF] Lederle | Immediate repair compared with surveillance of small abdominal aortic aneurysms[END_REF], [START_REF] The | The u.k. small aneurysm trial: design, methods and progress. the uk small aneurysm trial participants[END_REF], [START_REF] Sprouse 2nd | Is ultrasound more accurate than axial computed tomography for determination of maximal abdominal aortic aneurysm diameter?[END_REF] . Another limit is that 2D ultrasound provides a fixed single view of the AAA, which may not be the optimal view and the provided measurement can not be checked offline by another observer, such as the surgeon.

An alternative to 2D ultrasound imaging is CT scanning, considered as the gold-standard for AAA diameter assessment. However, this modality is mostly used to plan surgery or to monitor endovascular repair (EVAR) follow-up. In addition radiation dose, contrast injection and cost of exams are serious issues.

Our approach consists in using 3D ultrasound acquisitions in order to overcome the above limitations. The first objective is to provide a more reproducible measurement of the maximum AAA diameter for a given patient. A second objective is to provide a more complete assessement of the AAA geometry. In particular, more precise definition of the parameters extracted and longitudinal measurement of the diameters alongside the whole AAA length are presented. In addition, offline review of the exams and 3D visualization of the AAA are proposed in a comparable way with the CT workflow. Finally, in order to deal with limited field of view issues, multiple volume registrations are presented.

II. METHOD

A. Material

3D ultrasound aneurysm volumes are acquired using an IU22 system (Philips Ultrasound, Bothell, WA), and a 3D convex mechanical abdominal probe (V6-2). This probe is composed of a linear array of transducer elements that produce 2D slices. The mechanical angular scanning consists in a regular tilting of the transducer array in order to scan the volume. The slices are deflected by the same angle (tilt). The height of the acquired region is limited by the tilt amplitude of the transducers, controlled by the motor [START_REF] Long | 3D duplex scan for peripheral vascular applications: major progress or gimmick?" in Controversies and updates in vascular surgery[END_REF]. Standard field of view is about 10 cm in all directions.

Probe incidence influences image quality, as resolution of images is higher in 2D slices than in angular scanning direction. For comparison with standard 2D imaging, acquisitions were also made with a 2D convex abdominal probe (C5-2).

B. Acquisitions

30 patients, with 31 abdominal aortic or iliac aneurysms (13 AAA, 15 AAA after stenting, and 3 iliac aneurysms) were included in the study. For each aneurysm, 4 acquisitions were performed. Aneurysm was imaged in 2D in axial and longitudinal orientations. Then, 3D acquisitions were performed using 2 incidences of the mechanical probe: axial (fig. 1a) and longitudinal scanning (fig. 1c) with respect to the vessel orientation.

C. Semi-automatic segmentation

In order to extract quantified information from the volume acquisitions, it is necessary to segment the aneurysmal structure. Since manual segmentation of an aneurysm in 3D is a lengthy and tedious procedure, an interactive algorithm introduced in [START_REF] Mory | Non-euclidean imageadaptive radial basis functions for 3D interactive segmentation[END_REF] was specifically designed to allow rapid 3D segmentations, optimally combining user interactions and image information. User interactions are as simple as clicks on the image, specifying whether a point in the image lies The segmentation method is based on an implicit representation of the aneurysm region as a linear combination of image dependent kernels (geodesic radial basis functions). The algorithm sequentially builds this representation as the user introduces points in the image. At the introduction of the n th point x n , the algorithm computes an apodized geodesic distance x → ϕ( xx n gn ) where g n is a metric function and ϕ is a decreasing non-negative kernel. The aneurysm segmentation is then obtained by the interior ({x, Φ(x) ≥ 0}) of a linear combination of the previous interactions and the n th apodized geodesic distance:

Φ λ i=1..n (x) = n i=1 λiϕ x -xi g i . (1)
The n coefficients {λ i } i=1..n are obtained by solving the constrained optimization problem:

min λ 1 ,...,λn E(Φ λ i ) = Ω H(Φ λ i )ra(I) + Ω (1 -H(Φ λ i ))r b (I) (2)
where I is the image intensity, H is the Heaviside function, ra(I) = -log PΩ a (I), r b (I) = -log P Ω\Ωa (I) are region terms, and PΩ a , P Ω\Ωa are probability distributions of pixels intensity within the aneurysm and the exterior, respectively. This problem is minimized under a set of linear constraints specified as the user imposes a control point to be inside (Φ(xn) ≥ 0) or outside the aneurysm (Φ(xn) < 0). Visual feedback of segmentation is real-time in 3D. The output of the semi-automatic segmentation is a surface S representing the walls of the aneurysm (fig. 2).

D. Cross-sections extraction

It has been shown in [START_REF] Han | Ultrasound-determined diameter measurements are more accurate than axial computed tomography after endovascular aortic aneurysm repair[END_REF] that for 2D ultrasound acquisitions, the operator usually optimizes the acquisition incidence in order to provide an image showing the maximal size of the aneurysm. However, such a manual estimation of the best imaging plane does not ensure that the optimal incidence for measurement is selected. The principle of our approach is to provide an automatic selection of the optimal plane, avoiding to underestimate the aneurysm size.

After 3D aneurysm segmentation, the user is asked to click on proximal and distal extremities of the aneurysm. Clicks are used to generate a centerline of the surface S. The centerline is used as a referential for further quantification. We note l the length of the aneurysm centerline and s the curvilinear abscissa of a point on this centerline. By convention, s = 0 at the proximal extremity of the aneurysm and s = l at its distal extremity. For each s, a cross-section normal to the centerline is extracted, and the intersection of S with the cross-section provides a 2D contour C s of the aneurysm. Quantification of the aneurysm from 3D volumes is based on the analysis of the set of contours {C s }.

E. Parameters definitions

Selection of appropriate quantification parameters is essential to improve the accuracy of aneurysm assessement. In addition to providing a method to extract automatically the plane providing the largest aneurysm size, we propose to clarify the notions of measurement referential and of "diameter".

In 2D, there is often an ambiguity between maximal diameter and diameters measured with anatomical referentials (such as antero-posterior and lateral). In our 3D approach, quantifications are made with respect to the centerline referential. Maximum diameter is the usual descriptor of aneurysm. However, this is based on the assumption that the cross-section of the aneurysm is circular. In many patients, the aneurysm can present an irregular geometry making the definition of the maximum diameter less relevant. We introduce the use of an elliptic model to characterize more accurately non circular cross-sections.

From each contour C s , we extract 3 parameters :

• Real maximum diameter corresponding to the maximum distance between any couple of points on a contour. • Short and long axes lengths obtained from the fitting of an elliptic model onto the contour, based on the method described in [START_REF] Halíř | Numerically stable direct least squares fitting of ellipses[END_REF]. Each parameter being obtained for each cross-section, the output results in three functions f real (s), f major (s) and f minor (s) (fig. 3).

For each function, the real maximum diameter, major and minor diameters are defined by DX real , DX major and DX minor (eq. ( 3), ( 4), ( 5)), where A and L represent respectively an axial or a longitudinal acquisition. For comparison with 2D measurements, the following quantification is extracted from 2D acquisitions (fig. 1b and1d):

DX real = max s∈[0,l] (f real ) with X ∈ {A, L} (3)
DX major = max s∈[0,l] (f major ) ( 4
)
DX minor = f minor (s = argmax(f major )) (5
• in axial acquisition, maximal antero-posterior dA AP and transverse diameters dA T • in longitudinal acquisitions, maximal antero-posterior diameter dL AP The 2D minimum and maximum diameters used for quantification are defined in eq. ( 6) and ( 7):

d max = max (dA AP , dA T , dL AP ) (6) d min = min (dA AP , dA T , dL AP ) (7)
III. RESULTS

A. 3D Visualization and CT-like reconstructions

3D ultrasound acquisitions provide a 3D visualization of the aneurysm geometry in space. Such a feature was previously limited to CT or MRI acquisitions (fig. 2). In addition, it is also possible to provide multi-planar reconstructions of the cross-sections, as is provided in CT workstations (fig. 4) for better assessement of the aneurysm geometry, making offline review possible.

B. Quantification validation

A first step towards the validation of the 3D quantification is to compare results with the conventional 2D measurements. For each patient, the 8 parameters (DA real , DA major , DA minor , DL real , DL major , DL minor , d max and d min ) were computed. Correlations between 2D and 3D parameters are plotted in figure III-B. Minimum diameter in 2D is compared with the minor axis of the fitted ellipse. Maximum diameter in 2D is compared with the real diameter and the major axis of fitted ellipse. In order to assess the correlations, statistical analysis of the results was performed and Pearson correlation coefficients were calculated (table I). All statistical tests were significant (p < 0.0001) with very strong correlation coefficients (> 0.95).

IV. LIMITS

Presented approach has intrinsic limits due to both ultrasound image quality and AAA physical size and geometry.

A. Image quality limitations

Quality of 3D ultrasound imaging of the aneurysm can be limited by presence of bowel gaz, depth, or complex geometries. Ultrasound beams may be tangent to the structures of interest. Regarding the segmentation, aneurysm walls identification can be difficult in presence of calcifications, or for obese patients.

B. Limited field of view

Depending on the geometry of the aneurysm with respect to the patient, the field of view can be too limited. In particular, very long or large aneurysms, or close to patient skin might not fit into a single volume. Two patients of the cohort present an aneurysm so large that it would not fit within the field of view of the probe. To overcome this difficulty, we propose to acquire multiple volumes in order to cover the full geometry of the aneurysm and then stitch together those volumes so that the whole geometry of the aneurysm is recovered.

In an attempt to validate this scheme, we performed an offline registration. A rigid 3D registration relying on the minimization of a simple distance (SSD) and taking data anisotropy into account was used to estimate the translation and rotation of the probe displacement between different views. Registrations were made between consecutive pair of images, and composed with respect to the central view. A panoramic volume was obtained, combining motion compensation, and data fusion. Visual inspection of final volume (fig. 6) showed good continuity of the data in all dimensions, despite the presence in some views of shadows and/or specular reflectors.

V. CONCLUSION 3D ultrasound imaging of the AAA or iliac aneurysms and associated dedicated quantification has the potential to overcome some limitations of 2D imaging. In particular, automatic definition of the optimal imaging plane for measurement of the AAA size is a major input. Characterization of the aneurysm Fig. 6. Result of 3 volumes registration for a AAA too long to fit into a single acquisition geometry using more advanced and precise descriptors such as elliptic model fitting was proposed to refine the geometric assessement of the aneuryms. Providing a full 3D visualization of the aneurysm geometry is also a major improvement for practicians, since offline review and measurements were previously reserved to CT acquisitions. The present evaluation has shown that 2D and 3D measurements are comparable, however, further validation is necessary in order to assess the improvement provided by 3D quantification in longitudinal follow-up of patients. More precisely, evaluating the variability of 3D measurements versus the 2D variability remains to be done.

Fig. 1 .

 1 Fig. 1. 3D probe orientations and 2D reference acquisitions

Fig. 2 .

 2 Fig. 2. 3D AAA visualization, centerline and cross-sections (green)

Fig. 3 .

 3 Fig. 3. Longitudinal quantification of diameter measurements

Fig. 4 .

 4 Fig. 4. Multi-planar reconstructions for assessement of AAA in a CT-like viewing mode

Fig. 5 .

 5 Fig. 5. Parameters correlations between 2D and 3D acquisitions, compared with y = x function

TABLE I PEARSON

 I COEFFICIENTS FOR 2D/3D CORRELATIONS

		DA real	DA major	DL real	DL major
	dmax	0.97471	0.97612	0.98050	0.98229
		-	DA minor	-	DL minor
	d min	-	0.97788	-	0.97254


Professor Jerome Roncalli
email: roncalli.j@chu-toulouse.fr

PhD Patricia Lemarchand

Autologous bone marrow cells and ischemic cardiomyopathy

Keywords: Heart failure, Ischemic cardiomyopathy, MRI, Cardiac cell therapy, Mesenchymal stem cells

Evaluation of: Intramyocardial stem cell injection in patients with ischemic cardiomyopathy: functional recovery and reverse remodeling.

3

This article reviews the recent paper by Williams et al.1 showing that transcatheter intramyocardial injections of autologous bone marrow progenitor cells may improve regional contractility of a chronic myocardial scar, and that these changes predicted subsequent reverse remodeling. Heart failure (HF) is a disease of increasing concern around the world. Fifty percent of all hospital admissions in patients over 65 years of age in the United States are for cardiac failure. It has a significant economic burden, and therapies today for these patients are limited. Stem cell therapy in this population has shown enormous promise to provide benefit to patients.A variety of adult stem and progenitor cells from different sources have already been examined for their potential to promote cardiac repair and regeneration after acute myocardial infarction (AMI). Although early, small-scale clinical studies underscored the potential effects of cell-based therapy largely by using bone marrow cells, subsequent randomized-controlled trials have revealed mixed results that might relate, at least in part, to differences in study design and techniques, e.g. differences in patient population, cell sources and preparation, and endpoint selection. Recent meta-analyses 2 have supported the notion that administration of bone marrow mononuclear cells (BMCs) may improve cardiac function on top of standard therapy after AMI and our group recently showed the effect of BMCs on myocardial viability 3. Among the next steps, patients with chronic ischemic HF are potential targets for cell therapy because of the limits of available treatments and a lack of emerging therapies. Cardiac cell-based therapy currently also lacks clinical comparison studies of cell types, a situation of increasing concern given the growing number of cell types contemplated for therapy4. Focusing on these issues, Williams et al.1 initiated a program of cell therapy using two types of bone marrow-derived stem cells, in which the pilot study is presented here.

Methods

In the study, eight patients with ischemic cardiomyopathy (4 months to 11 years after an AMI) received transendocardial injections in left ventricular (LV) scar and border zone of autologous bone-marrow-derived cells that had been harvested from iliac crest. Four patients were treated with BMCs and four with cultured mesenchymal stem cells (MSCs). The investigators used magnetic resonance imaging (MRI) to evaluate cardiac structure and function at baseline and at three, six, and 12 months after cell therapy. Only 4 patients had longitudinal assessment of scar size because of the presence of implantable cardioverter defibrillators. Thus, this study does not have a placebo nor control comparison group and lacks the power to identify any superiority between MSCs or BMCs.

Results

The primary outcome of this phase 1 study was to assess the safety of transendocardial administration, and none of the patients experienced a serious adverse event. Secondary endpoint analyses performed with MRI in 4/8 patients showed at 1-year follow-up a decrease in end-diastolic volume (p=0.03) and a trend toward decreased in end-systolic volume (p=0.06) after cell administration compared to baseline. Authors stated a strong correlation between changes in end-systolic volume and end-diastolic volume with a parallel decrease in chamber volume. However, ejection fraction and left ventricular mass did not significantly change, but there was a significant decrease in infarct size of 18.3% (p<0.05). The authors conclude that human autologous bone-marrow progenitor cells may increase regional contractility of injected myocardial scar tissue within three months of treatment, and these functional changes are associated with later reverse remodeling. Several limits are pointed out, including the small patient number and the lack of placebo or control group.

Discussion

In preclinical porcine studies, Hare's group previously demonstrated that transcatheter, intramyocardial injection of bone marrow-derived progenitor cells to chronically scarred myocardium improves LV regional function, reduces scar size, and creates reverse remodeling 5. The translation of basic research described in this clinical trial occurs relatively early on in the evolution of this new field of research. What has been lost in translation is our understanding of the value of surrogate end points in cardiac cell therapy clinical trials 6. Surrogate end points are useful ways of looking for effects that may have clinical relevance.

Cardiac MRI represents a promising modality for a tissue characterization of AMI, beyond traditional morpho-functional indexes. Moreover, cardiac MRI parameters may in the future be used with greater frequency as surrogate imaging end points of morbidity and mortality for testing novel therapeutic strategies as in the case of cellular-based therapies7, 8. However, electronic devices such as pacemakers, defibrillators, infusion pumps, and others are still considered as contraindications in most of the patients, therefore preventing the use of MRI in patients at risk of having such devices, including patients with defibrillator because of low ejection fraction and HF (ESC guidelines 2010). Alternative methods for exploring myocardial viability also include nuclear imaging modalities9(SPECT and PET), and low-dose dobutamine stress echocardiography.

The clinical relevance of small changes in surrogate measures with respect to their overall consequence is poorly understood. The literature is now full of similar small trials (Table 1) that were designed to test for safety but report effects despite a lack of statistical power. Although these trials demonstrated significant improvements in clinical outcome, they were associated with very small changes in cardiac function4, 10. MRI provides a unique opportunity to image the in vivo structural and functional changes after bone-marrow stem-cell therapy for the heart. Although, the infarction zone improvements were evident as early as 3 months and persisted out to 1 year and strongly correlated to the improvements in end-diastolic volume and end-systolic volume, the main limit of this study is the extrapolation of benefits with only 4 patients.

Comparing cell type administration

BMCs have already been administered in patients with ischemic cardiopathy 11,12. Adult mesenchymal stem cells (MSCs) have shown promise for heart repair and have been explored for possible cardiac regeneration. The advantage of this cell population is the ease of acquisition and expansion in culture.

However, their use in cardiac repair, as compared to bone marrow mononuclear cells is still at early stage. To date only two clinical trials have assessed the therapeutic potential of autologous MSCs for AMI 13,14. In both studies, MSCs were selected by culture and have shown that intracoronary MSC administration is safe and feasible. So far, there is no available publication on intramyocardial administration of MSCs for chronic HF but only one study in the setting of refractory angina 15.

Future Perspectives

The study by Williams et Results: All patients tolerated the procedure with no serious adverse events.

CMR at 1 year demonstrated a decrease in end diastolic volume (208.7±20.4 versus 167.4±7.32 mL; p=0.03), a trend toward decreased end systolic volume (142.4±16.5 versus 107.6±7.4 mL; p=0.06), decreased infarct size (p<0.05), and improved regional LV function.

Discussion: These data suggest that transcatheter, intramyocardial injections of autologous bone marrow progenitor cells may improve regional contractility of a chronic myocardial scar, and these changes predict subsequent reverse remodeling.

Future perspectives: The findings support the potential clinical benefits of this new treatment strategy and ongoing randomized clinical trials.

  al.1 is the pilot phase of the Transendocardial Autologous Cells in Ischemic Heart Failure (TAC-THF) study (NCT00768066), aimed at evaluating the safety of cells administered via the BioCardia Helical Infusion Catheter (BioCardia, San Carlos, CA). TAC-HFT study will be the first study to compare BMCs and MSCs in humans in a phase II, randomized, doubleblinded, placebo-controlled study. The end points will be hospitalization plus death as well as the MRI end points used in the pilot study. Development of new systems for cell therapy product administration is of high interest since the number of patients with ischemic HF is increasing. Most often used in clinical trials (as referred to previous publications and referenced ongoing trials in clinicaltrials.org website), the NOGA mapping system has already been evaluated in humans but suffered from a long time period data acquisition allowing the 3D reconstruction of the left ventricle. However, in conjunction with the new NOGA® XP mapping system, new multi-electrode QwikStar® catheters (Biosense Webster) enable the sampling of several points simultaneously. This feature may allow the construction of maps with more points while decreasing manipulation of the LV cavity, resulting in shorter mapping times and greater mapping accuracy 16 to guide injections into viable zones. The TAC-HFT trial is built on the previous experience obtained in this Phase I, and the Phase I Transendocardial Autologous Bone Marrow in Myocardial Infarction (TABMMI) trial that treated ten patients and supported the safety of the procedure with patients showing sustained benefits 17. As of April 27, 2011, only a few clinical trials currently recruiting patients with ischemic HF dedicated to treatment by autologous MSCs are ongoing and have been registered in clinicaltrials.org website. While the TAC-HFT trial is designed to compare BMCs and MSCs, the POSEIDON trial (NCT01087996) is comparing autologous and allogenic MSCs. However, there is still a need to compare MSCs versus placebo in order to show an effect of MSC therapy in ischemic HF. In this process, we are currently leading the phase I of the MESAMI (MESenchymal cell therapy And Myocardial Ischemia with decreased left ventricular function) program evaluating the safety of injecting MSCs directly into the heart to repair and restore heart function in patients who have chronic myocardial ischemia with HF (clinicaltrials.org NCT01076920). The multicenter randomized MESAMI phase 2 will be dedicated to evaluate versus placebo the effects of MSCs and preconditioned MSCs with melatonin following our recent findings 18. Executive summary Backgroung: Transcatheter, intramyocardial injections of bone marrow-derived cell therapy produces reverse remodeling in large animal models of ischemic cardiomyopathy. Methods: Eight patients received transendocardial, intramyocardial injection of autologous bone marrow progenitor cells (mononuclear or mesenchymal stem cells) in left ventricular (LV) scar and border zone.

Table 1 :

 1 Published clinical trials of cardiac cell therapy using bone marrow-derived cells in patients with chronic ischemic heart disease associated or not with decreased left ventricular function.

	Study	Design Patient	Disease	Cell	Follow-Up	Primary End Point	Imaging
			number		type	(months)		Modalities
	IACT19	NonRCT	18	Chronic MI	BMC	3	LVEF	LV angio,
								SPECT, PET
	Tse et al.11 NonRCT	8	Severe ischaemic heart	BMC	3	safety	LV angiography
				disease
	Perin et al.20 RCT	21 Severe, chronic ischemic heart	BMC	2-12	myocardial perfusion	LV angiography
				failure
	TOPCARE-	RCT	75	Stable ischemic heart disease BMC	3	LVEF	LV angiography,
	CHD21							MRI
	TOPCARE-	Registry 121 Stable ischemic heart disease BMC	18	NTpro-BNP, NTpro-	LV angio, SPECT
	CHD						ANP
	registry22
	Fuchs et al.12 nonRCT	27	Refractory angina	BMC	3-12	safety
	van Ramshorst	RCT	50	Chronic myocardial ischemia BMC	6	myocardial perfusion	MRI
	et al.23
	Diederichsen et	NonRCT	32	Congestive heart failure	BMC	4	LVEF	MRI
	al.24
	Friis et al.15 NonRCT	31	Refractory angina	MSC	6	changes in perfusion	Echocardiography
							defects
	Ang et al.25 NonRCT	63	Chronic MI	BMC	6	LV segmental wall	MRI
							motion
	TABMMI17 NonRCT	10	Chronic MI	BMC	12	LVEF	Echocardiography
	Losordo et	RCT	24	Refractory angina	CD34+	6	safety