Abdelkader Lahmadi
email: abdelkader.lahmadi@loria.fr

Laurent Delosière
email: delosieres@loria.fr

Olivier Festor
email: olivier.festor@loria.fr

Hinky: Defending Against Text-based Message Spam on Smartphones

Keywords: SMS, Spam, Collaborative, Filtering, Bloom Filters

We present a defense platform against text-based message spam on SmartPhones. We focus in particular on Short Message Service (SMS) based SPAM. Our solution relies on a social network based collaborative approach to filter this type of spam using Bloom filters and content hashing. We detail the design of the supporting framework and validate its efficiency in minimizing false positives and limiting the storage space. We show that a content hashing based approach provides better lookup than a bloom filter with the same storage space and false positive probability close to 10 -9 .

I. INTRODUCTION

Text based messaging services are very popular where 500 millions of SMS were sent in France to celebrate the new year 2011. These services are also widely used on emerging social networks like Twitter or the basic SMS service on mobile phones. Nowadays, the cost of SMS is decreasing and many providers offer unlimited texting plans. This cost cut makes mobile-phone users a more attractive target for spammers. SMS spam is declined through different threats. Simple spam advertising is the most known threat, but malicious SMS can also carry malicious content like malware. Phishing or fraud SMS also jeopardize users privacy. SMS spam has long been considered as a minor problem, mostly because email spam is cheaper and mobile phones have limited communication capabilities to infect other users or browse phishing or advertisement web sites. However, modern SmartPhones offer more capabilities than traditional mobile phones. They are able to compute and communicate using different communication means: WiFi, UMTS and GSM. These devices also come with different applications which use the communication capabilities. Focusing on these communication capabilities, spammers are interested in delivering abusive or malicious SMS content to smartphone users.

In France for example, operators have been encouraging subscribers to report SMS spam since October 2008. Phone users can forward offending messages to the Stop-Spam service via the short code 33700. An initial response prompts them to reply with the spammer's phone number, with a final SMS acknowledging the completed spam report. The service has received almost half a million spam reports in this way. This has resulted in the disconnection of only 300 phone numbers for spamming, although many more have received cease-and-desist orders. The operators can't just block offending SMS messages or shuffle them into a spam folder as many e-mail service providers do. For one thing, the senders have paid for the messages, so the operators are contractually obliged to deliver them unless they can prove that the sender has breached their terms of service. Also, creating an SMS spam folder would mean updating the firmware on millions of phones. We believe that SMS spam has to be considered as a global problem where mobile spam is generally originating from senders outside the receivers mobile network operators.

Text based spam, mainly mail target spam has been extensively investigated [START_REF] Cormack | Email spam filtering: A systematic review[END_REF], but little effort has been devoted to understanding their applicability on SMS spam. One of these defense techniques is the collaborative spam detection approach. In particular, this approach relies on exchanging black lists between users to block a detected spam on their own devices. This implies the usage of an efficient data structure to represent these black lists.

In this paper, we study a collaborative SMS spam filtering approach over smartphones using combined hashing and bloom filters techniques found in the literature. In section II we review the efficiency of these techniques regarding their false positive probabilities and storage space. Section III discusses the design of our defense solution against SMS spam using a collaborative approach and combining these techniques. We carried a series of experiments designed to test to what extent these techniques are effective in addressing SMS spam filtering. Section IV details the real implementation of the solution on Android based smartphones. Section V concludes with a summary of the contributions of this paper and presents future work.

II. BACKGROUND AND RELATED WORK

A. Collaborative spam detection

A spam filtering mechanism can be built manually by the mobile's user in which he tags an SMS message as spam and where the SMS sender is introduced in a blacklist. Next time, an SMS is received from this sender it is treated as spam and the SMS is discarded. This approach is limited since each user does not benefit from other user's black lists. A collaborative approach is based on simple and powerful insights. When a user tags an SMS as spam, then this human effort is shared among other users. When a message is identified as spam by somebody elsewhere, other users of the collaborative platform are protected from this undesired message. Our approach is similar to collaborative Anti-Spam services such as ALPACAS [START_REF] Li | Privacy-aware collaborative spam filtering[END_REF], [START_REF] Yan | Enhancing collaborative spam detection with bloom filters[END_REF], [START_REF] Cormack | Email spam filtering: A systematic review[END_REF] in that it employs a reporting and querying functions to identify if an SMS is a spam. However, these solutions were provided for spam email and designed to run over servers with important resources and connectivity.

B. Filters representation 1) Bloom filters: Bloom filters [START_REF] Broder | Network applications of bloom filters: A survey[END_REF] were designed as a space-efficient data structure for fast membership testing. A Bloom filter is a vector of m bits, each initially set to 0. The insertion of an element x in the filter requires to compute k hash functions. Each hash function provides a position in the range {0, 1, ..., m -1} to be set to 1 on the filter. The query of an element y also requires to compute k hash functions and to construct a mask which contains the k positions set to 1. Then, a bitwise AND operation between the mask and the Bloom filter is performed. If the result equals the mask, then the answer is Yes, else the answer is No. The major drawback of Bloom filters is false positives. A false positive occurs when an element x is not in the filter but its different positions computed by k hash functions are all set to 1 due to overlap with other entries. The probability of false positive (f p) can be calculated as follows after the insertion of n elements:

f p = (1 -(1 - 1 m ) nk ) k (1)
The minimum of the probability of a false positive is reached when:

k = m n × ln(2) (2)
In such case the minimum of false positive probability is estimated to f p min = ( 1 2 ) k . In section III, we validate this estimation using simulation to identify its limits regarding the filter size and the number of hash functions. Many network applications have used Bloom filters for routing table lookup, packet classification and peer-to-peer networks [START_REF] Broder | Network applications of bloom filters: A survey[END_REF]. Another major drawback of a Bloom filter is the difficulty of deleting inserted elements. A simple solution is the cold cache [START_REF] Chang | Approximate caches for packet classification[END_REF] where one removes all elements when the filter is full. The problem with this solution, is that no data remains in the filter and we loose useful information. In [START_REF] Chang | Approximate caches for packet classification[END_REF], authors propose the double buffering method for the deletion of old data. The Bloom filter is divided into sub filters: an active and a warmup filter. The active filter stores all the recent inserted elements and the warm-up filter is always a subset of the active filter. In [START_REF] Yoon | Aging bloom filter with two active buffers for dynamic sets[END_REF], the author proposes an enhancement of this approach through the use of two active sub filters. When one filter is full, the second is flushed and the two filters switch their roles. In our work, we adopted this approach for Bloom filter aging.

2) Hashing based filters: Instead of using a Bloom filter to query if a SMS is member of inserted spam messages in the filter, we may use a hashing based method. A hashing function is used to create a hashed value of the SMS reported as SPAM and insert it in a list. A first advantage of using a hashing method is to guaranty anonymity of the SMS content. The limit probability of a false positive within a list containing n hashed values is the probability to get at least a false positive. Therefore, we obtain:

f p = 1 -(1 - 1 2 b ) n (3)
Where b is the hashed value size.

III. DESIGN OF THE DEFENSE SYSTEM

A. Efficient Filtering Design

We first formulate the SMS filtering problem with both Bloom filters and hashing functions. We present the performance of each of them in terms of false positives, lookup time and storage size. The characteristics of mobile phones make the SMS filtering problem using signature matching unique: (i) the filtering system has to keep the spam signature as small as possible, because it needs to support a large number of spams. Storing undesired SMS PDUs is waste since the defense system's aim is to remove them and protect the user from their content. Moreover, we want to make a fast decision to match an incoming SMS against the set of available signatures instead of parsing the SMS and compare its content with the set of available SMSs. (ii) as stated before, the SMS service is critical and the removal of a legitimate SMS will be unacceptable. The filtering technique has to keep a null or a very low false positive rate; (iii) in a collaborative filtering approach, we have to handle multiple filters from different users. Thus, the raising issue is to merge them then perform matching or perform per-filter matching. (iv) Bloom filters were stated as a good candidate for filtering e-mail spam Fig. 2: The probability of a false positive in a Bloom filter of size 8KB.

[3], however their performance compared to a hashing based signature for SMS is not assessed. In Hinky, architecture we are using different types of filters for local, group and global treatment. Each of them is different in terms of size and available resources on the hosting host. Choosing the right filter representation for each of them is our goal.

B. Bloom Filter numerical analysis

We have performed a numerical analysis of Bloom filters to identify their false positive probability and rate for filtering system level SMS messages.

1) Probability of a false positive: We are interested in the trade-off between the number of hash functions and the number of inserted elements in the best case where k is computed by the equation 2. We observe that k decreases when the number of inserted elements increases. However, when we increase the size of the filter, we need more k hash functions to insert the same number of elements and achieve the minimum false positive. Thus, a smaller bloom filter implies less hash functions and a bigger filter implies the use of more hash functions to achieve the minimum false positive. In a next step, we analyze numerically the probability of false positive while varying the number of hash functions k and the number of inserted elements. Figure 2 depicts their effect on the false positive probability. We observe that for a given bloom filter with a fixed size, increasing the number of hash functions or the number of inserted elements increases the probability of false positives. Moreover, increasing the size of the bloom filter decreases the probability of false positives.

2) False positive rate: In the previous analysis, we have assumed that n elements are already inserted in the filter to compute the false positive probability. However, we are interested in the number of false positive when inserting a new element. Therefore, we start with an empty filter and we insert one element at each step. Let p(n) = (1 -(1 -1 m ) nk ) k the probability of a false positive after inserting n elements with a fixed filter size m and k hash functions used per element. Let N B f p the number of false positive items after one element is inserted in the filter. Initially N B f p (0) = 0 where the filter Then the false positive rate after inserting n elements can be written as follows.

f pr(n) = N B f p(n) n (4)
This analysis tells us that bounding the number of false positives implies bounding the number of inserted elements in the Bloom Filter. Figure 3b depicts the effect of the number of inserted elements on the false positive rate. The circles marked plots present the false positive rate computed by the equation 4 and the square marked plots presents the estimation of the false positive rate according to the estimation ( 1 2 ) k proposed in [START_REF] Broder | Network applications of bloom filters: A survey[END_REF]. We observe that when the Bloom filter and the number of inserted elements are small, the estimation fits our formula. However, when the number of inserted elements is important or when the filter is large the lower bound of the false positive rate proposed in [START_REF] Broder | Network applications of bloom filters: A survey[END_REF] is overestimated. In our work, we use multiple bloom filters from different users. Thus, we are interested in analysing the probability of a false positive in case of merging N Bloom filters or keeping them disjoint to query an element.

3) Merging or not users Bloom filters: Let N=n 1 +n 2 +...+ n s where s is the number of users sharing their bloom filters in our defense system and n i is the number of elements inserted in each bloom filter. When merging different users Bloom filters, the probability of false positive is f p merge

(N ) = (1-(1-1 m ) N k ) k .
In the second case, where we keep the filters disjoint, the probability to get a false positive is the probability of a false positive in at least one user's filter. Hence, we obtain: 4 depicts the difference between the two probabilities while varying the number of inserted elements and the number of hashing functions. The merged filter has a size of 8KB and each of the separated filter has a size of 4KB. We observe that merging the filters has a

f p disjoint = 1 -(1 -p(n)) s . Figure

C. Analysis of hash based SMS filtering

An SMS filter is defined as a set of elements where each element represents one SMS. We have tried two hash functions to represents this set, where each SMS is hashed into k bits and stored into a list. We compared the performance of the two hashing algorithms MD5 and FNV [START_REF] Noll | Fowler/noll/vo (fnv) hash[END_REF] to create SMS hashes. In our experiment, we used 10 6 different SMS and we computed the number of false positive after inserting a new SMS hashed value in the list. Using a 16 bits hashed value of a SMS, empirical and theoretic results are close for both MD5 and FNV. The difference between empirical and theoretic results is around 0.01 for FNV and 0.05 for MD5. Therefore, our focus goes on the FNV based hashes which are dedicated to small messages like SMS. We found that FNV false positive probability is close to 10 -9 for a list of size 4000 entries and a 40 bits hashed value. This probability becomes close to 0 with 400000 entries and 48 bits hashed values. Thus, the FNV algorithm provides a lower false positive rate and it was shown that its throughput is acceptable [START_REF] Erdogan | Hash-av: fast virus signature scanning by cacheresident filters[END_REF].

D. Simulation study of Bloom Filter and Hash functions

While the above experiments look into the theoretical performance of hashing and bloom filters to create SMS filtering lists, their performance depends on their implementation within the target host. In [START_REF] Cloudmark | Taxonomy of current and potential mobile threats[END_REF], authors state that a person receives on average one SPAM per day. We evaluated hashing functions and bloom filters for the different required filters of the Hinky platform: local, group and global. We have assessed their filtering capacity in terms of number of stored SMS, their storage cost and lookup time. We fixed the number of inserted elements for each filter as follows: 4000 elements for the local filter, 400000 elements for the group filter and 50000000 elements for the global filter. We implemented the local filter on an Android simulator and it is persisted in a SQLite database. The group and global filters are located on a host with an 2.4Ghz Bi-processor CPU machine and 4GB of memory. The two filters are persisted in a MySQL database. 1) Local filter: Using Bloom filters the filter capacity varies between 2000 and 4000 elements. This is due to the aging mechanism which relies on two sub filters as explained in section II-B1. However, the hashing set contains mostly the 4000 elements. Each element is a 40 bits FNV hashed value. When we need to insert a new SMS the last element is removed and replaced by the new one. The two sub Bloom filters have a 20KB size to achieve the 10 -9 false positive rate. The hashing list requires the same storage with a 40 bits FNV hashed values. While inserting an element, we measured the time of its lookup and its insertion in the database if it does not exist. We found that by using the hashing method this time is around 0.3 seconds and 0.6 for a Bloom filter. The main reason for the difference is the cost to compute the k hash functions and access the k bits positions. Therefore, we observe that a hashing method is more performant than a Bloom filter for the local filter.

2) Group filter: For the same reason as above, the group filter capacity using the FNV hashing method is larger than a Bloom filter. That hashing list contains at most 400000 elements. The storage of these elements requires 2.06 MB using a Bloom filter and 2.3 MB using the FNV method with 48 bits hashed values. The false positive probability was fixed to 10 -9 for the two methods. The lookup and insertion time for the hashing method is 2 times faster than the bloom filter.

3) Global filter: For the global filter with Bloom filter, we fixed the number of hashing functions K=30. The hashing based filter uses an MD5 hashing method with a 128 bits hashed values. The capacity of a Bloom filter varies between 0 and 5×10 7 inserted elements. We used a Cold Cache strategy for the filter where we remove all elements when the filter is full. A hashing based method provides the maximum filtering capacity of 5 × 10 7 . To store the 5 × 10 7 elements in the filter with a false positive probability close to 10 -9 the Bloom filter requires 256 MB and a hashing method based on MD5 128 bits hashed values requires 762 MB. We found that the lookup and insertion time for the Bloom filter is around 0.01 seconds. For the hashing method this time linear and becomes greater than 0.01 seconds after inserting 4000 elements

The table I shows the required filtering methods for each filter in our defense system.

IV. IMPLEMENTATION

We have implemented our defense system according to the architecture described in Figure 1. We have developed a communication protocol between the mobile and the server components to register users, create filtering groups and to check an SMS. The different messages are the following:

• The register message: is used by the mobile user to register itself within the filtering service running on a dedicated server. The message carries the login and password provided by the user. • The join message: is used by a mobile user to join a filtering group of its choice. The user needs to provide the name of the group which is the login of a trusted user providing its filter. • The leave message: is used to leave a group by providing its credentials and the list of groups.

• The reportSpam: is used to report an SMS as a spam to the group filter. The message carries the user credentials and the hashed value of the SMS. • The isSpam: is used to check if an incoming SMS is a spam or not. The collaborative server will check firstly the group filter, then the global filter. A mode where the group filter is pushed regularly to the mobile is available as well. The different messages between the user and the collaborative server are carried over the HTTP/HTTPS protocols.

A. Mobile side implementation

On the mobile we implemented the local filter with the parameters identified in table I. The filter contains hashed values of SMS indicated as SPAM by the user. The mobile side application also provides a user interface to manage blocked SMS and the list of filtering groups. All the application data (filter, lists and groups) are stored in an SQLite data base.

B. Core Engine implementation

The collaborative server uses Jetty and MySQL to manage mobile clients requests to join groups, report spam as SMS and check SMS as spam or not. The server also maintains the global filter where an SMS identified as spam by many groups is inserted. The identification relies on a threshold function which computes the number of reports of a spam over existing groups. If the number exceeds a predefined value, the SMS hashed value is inserted in the global Bloom filter. To manage the global filter persistence, we use an approach close to the Prevayler project [START_REF] Prevayler | Objet persistence library for java[END_REF]. The Bloom filter is stored in a file which is loaded in memory as an object. The transactions are executed in memory over this object. Periodically, a snapshot is taken on the object to synchronize it to the system file.

C. A friendship mechanism for trust filtering

Users of the Hinky platform share their filters with the basic concept of friend. Each user can benefit from a local filter of another user by creating a friendship link with him. The link is created by sending a join message with the identifier of this friend. Therefore, when the mobile side application of Hinky checks if an SMS is a spam or not, it sends an isSpam request to the server. The server identifies the list of friendship links of the user. Then it does a lookup over their filters to identify if one of them contains the SMS to be checked. Therefore, each group is like a dynamic view over the set of users filters available on the server. When a user leaves a group (a friend), we only remove the identifier of his friend from the list of his friendship links. This mechanism has the advantage to be simple and it is driven by the user. It prevents from false reports since we only verify an SMS on trusted friends. A malicious user can not pollute a group filter since it need to be a trusted friend. We have to note that we used a direct friendship relation in our system. Each filter group viewed by a user contains only filters from his direct friends.

V. CONCLUSIONS

We have presented a solution to defeat SMS spam over smartphones using a user centric approach. Where users share their filters using a cooperative friendship mechanism. We believe that fighting SMS spam is a user problem rather than a telephony operator problem. The reason is that spammers are usually customers of the operator and they pay to get the SMS delivered to its destination. Therefore, operators have incentives, sometimes even contractual ones to provide the SMS service to all their customers including spammers. In our solution, we analyze two different methods to construct an efficient SMS filtering mechanism: Bloom filter and content hashing based lists. Our analysis targeted the rate of false positive which is an important metric due to the criticality of an SMS. We found that a hashing based approach provides better lookup time than a bloom filter and it supports the deletion operation which is missing in a Bloom filter. Therefore, a hashing list has a better capacity than a Bloom filter for this particular function. Currently, filtering users group's are created manually using a join mechanism. We are working on the automatic creation of these groups using social or business networks. We also plan to evaluate the energy consumption of our filtering approach on a smartphone.

Fig. 1 :

 1 Fig. 1: Hinky platform architecture.

Figure 1

 1 Figure 1 depicts the architecture of the Hinky platform. Our system relies on two components. The first component is located on the user's mobile phone. It contains a local filter maintained by the mobile user. The second component is the core engine. It is located on one or several collaborative servers. It contains the group filters shared by trustworthy users and a global filter shared by different groups.

Fig. 3 :

 3 Fig. 3: Impact of the number of inserted elements on the false positive rate.

Fig. 4 :

 4 Fig. 4: The difference of probabilities of a false positive between bloom filters merging and keeping them disjoint before querying.

TABLE I :

 I Different filters representation in the Hinky platform.


Nicolas Estrada
email: n.estrada22@uniandes.edu.co

Emilien Azéma
email: emilien.azema@univ-montp2.fr

Farhang Radjai

Alfredo Taboada

Identification of rolling resistance as a shape parameter in sheared granular media

Using contact dynamics simulations, we compare the effect of rolling resistance at the contacts in granular systems composed of disks with the effect of angularity in granular systems composed of regular polygonal particles. In simple shear conditions, we consider four aspects of the mechanical behavior of these systems in the steady state: shear strength, solid fraction, force and fabric anisotropies, and probability distribution of contact forces. Our main finding is that, based on the energy dissipation associated with relative rotation between two particles in contact, the effect of rolling resistance can explicitly be identified with that of the number of sides in a regular polygonal particle. This finding supports the use of rolling resistance as a shape parameter accounting for particle angularity and shows unambiguously that one of the main influencing factors behind the mechanical behavior of granular systems composed of noncircular particles is the partial hindrance of rotations as a result of angular particle shape.

Most numerical studies on the mechanical behavior of granular materials deal with model systems composed of disks in 2D or spheres in 3D. This is usually due to the technical difficulties that arise when dealing with particles of complex shapes in experiments or discrete element methods. However, real granular materials are rarely composed of spherical particles, and it has been shown that the nonspherical shape of the grains strongly influences the mechanical behavior of granular systems. This influence can be evidenced when characterizing the shear strength [1-4] and solid fraction [4][5][6][7], as well as microstructural properties such as the distribution of contact forces [8,9]. The effect of grain shape is thus a crucial aspect to be taken into account for a realistic description of granular systems.

One of the numerical "tricks" that can be used to obtain realistic values of strength and solid fraction while using only circular particles in simulations is to partially restrict the relative rotations between grains [10]. For example, several studies have shown that rolling resistance leads to shear strengths and solid fractions that are comparable to those observed in granular soils and rocks, e.g., [11][12][START_REF] Calvetti | Powders and Grains, 5th. International Conference on Micromechanics of Granular Media[END_REF][START_REF] Jiang | [END_REF]. However, the extent to which rolling resistance can actually be compared to angular shape in more general terms, or whether rolling resistance and angular shape lead to similar structures at the mesoscopic scale, are interesting issues that remain poorly understood.

In this Letter, we compare, by means of discrete element simulations, the effects of rolling resistance and angularity. We construct two sets of polydisperse 2D packings. In the first set, the packings are composed of disks with an increasing magnitude of rolling resistance, whereas in the second set, the packings are composed of regular polygonal particles of increasing number of sides. By comparing various properties extracted from the two sets, we find a remarkable matching of the data from the disk packings with those of the polygon packings for a rolling resistance expressed by a simple equation as a function of the number of sides. This one-to-one mapping between the two sets is based on energy dissipation considerations and might be generalized to other particle shapes.

All packings are made up of 7500 grains with diameters uniformly distributed by volume fractions between 0.6d and 2.4d, where d is the mean diameter. In all simulations, the coefficient of sliding friction µ s between particles is 0.4 and collisions are perfectly inelastic. The particles are initially placed in a semiperiodic box 100d wide using a geometrical procedure [15]. Next, the packing is sheared by imposing a constant shear velocity and a constant confining stress. To avoid strain localization at the boundaries, sliding and rolling are inhibited for the particles in contact with the walls. The samples are sheared up to a large cumulative shear strain γ = ∆x/h = 5, where ∆x is the horizontal displacement of the upper wall and h is the thickness of the sample. All measures are averaged over the last 50% of cumulative shear strain in order to guarantee that they characterize the behavior of the system in the steady state, also known as the "critical state" in soil mechanics. In all tests, the gravity is set to zero.

The simulations were carried out by means of the contact dynamics method [16][START_REF] Jean | Mechanics of Geometrical Interfaces[END_REF][START_REF] Jean | [END_REF][19], which assumes perfectly rigid particles interacting through mutual exclusion and Coulomb friction. For specific implementation of the contact dynamics method see [15,19].

In the first set of samples, composed of disks, the rolling resistance is introduced through a rolling friction law [20], analogous to the sliding friction law. Although rolling friction is introduced here as a numerical param-eter, it may reflect various material parameters such as hysteresis, micro-sliding when the elastic moduli are different, inelasticity (in particular for polymers) and surface roughness [START_REF] Johnson | Contact Mechanics[END_REF]. This law assumes that a contact can transmit a torque M not exceeding a limit value M max = µ r ℓf n , where µ r is the coefficient of rolling friction, ℓ is the magnitude of the branch vector joining the centers of the contacting particles, and f n is the normal force. The scaling of M max with ℓ is meant to make µ r dimensionless. Relative rotation between two grains in contact is allowed only if M = M max .

In the second set of samples, composed of regular polygonal particles, two types of contact may occur: (1) between a corner and a side, and (2) between two sides. Side/side interactions represent two constraints and are treated by associating two contact points along the common side and applying the volume exclusion and the sliding friction law to each of them. Thus, in practice, two contact forces are calculated at each side/side contact. However, only their resultant and application point are physically relevant, and the result is independent of the choice of the two contact points [START_REF] Saussine | [END_REF][START_REF]Polygonal particles are simulated with the LMGC90[END_REF].

The stress components can be calculated from the simulation data by the relation

σ ij = n c f c i ℓ c j ,
where n c is the number of contacts per unit volume and the average runs over the contacts c with contact force f c and branch vector ℓ c [START_REF] Radjai | [END_REF]. The mean stress is p = (σ 1 + σ 2 )/2, where σ 1 and σ 2 are the principal stress values, and the deviatoric stress is q = (σ 1 -σ 2 )/2. It is worth noting that in the presence of rolling resistance the stress tensor can be asymmetric and a couple-stress tensor may be added to the description. However, in all our tests the asymmetry is negligibly small (i.e., |(σ 12 -σ 21 )/(σ 12 + σ 21 )| ≤ 0.0002), suggesting that we do not need to consider the couple stress in the present study. Similar observations on the contribution of the couple stress tensor are reported in [25].

Figure 1 shows the shear strength q/p and solid fraction ν = V p /V , where V p is the volume occupied by the particles and V is the total volume, as functions of µ r for the disks and of 1/n s for the polygons, where n s is the number of sides of the polygons. It can be seen that both q/p and ν follow similar trends in the two sets as µ r and 1/n s increase. However, a direct comparison of the data between the two sets is not possible in this representation due to the different physical meanings of µ r and 1/n s .

The respective effects of rolling friction and angular shape can be compared by their roles in the hindering of relative rotation. Let us consider a particle (a disk with rolling friction and a regular pentagon) that rolls on a horizontal plane with a vertical force N exerted at its center of mass and that is not allowed to slide; see Fig. 2(a). Figure 2(b) shows the horizontal force T that must be applied at the center of mass in order to make the particle roll, as a function of the rotation angle θ. The work needed to displace the particle a distance equal to its perimeter is

W d = 4πµ r R d N (1)
for the disk with rolling friction, where R d is the radius of the disk and the magnitude of the branch vector ℓ (necessary to calculate M max ) has been replaced by the disk diameter, and

W p = n s (1 -cos(π/n s ))R p N (2)
for the polygon, where R p is the radius of its circumcircle. Assuming equal work, i.e. W d = W p , we arrive at the following mapping between µ r and n s

µ r = (1/4) tan ψ, (3)
where it has been assumed that both particles have the same perimeter (i.e., R p = R d (π/n s )/ sin(π/n s )), and ψ = π/(2n s ) is the mean dilatancy angle of the trajectory of the center of mass of the polygon (see Fig. 2(c)). For a similar attempt to quantify the role of grain shapes in hindering relative rotation, see [START_REF] Matsushima | Powders and Grains, 5th. International Conference on Micromechanics of Granular Media[END_REF].

Figure 3 shows the shear strength q/p and solid fraction ν as functions of µ r for the disks and of (1/4) tan ψ for the polygons. Remarkably, the shear strengths and solid fractions of the two sets of packings collapse, both increasing and decreasing, respectively, with µ r and (1/4) tan ψ and tending to a constant value at µ r = (1/4) tan ψ ≃ 0.1. In other words, from a macro-scale viewpoint, a packing of regular polygons of n s sides is equivalent to a packing of disks with a coefficient of rolling friction µ r given by Eq. 3. This result supports also the choice of the required energy for rolling as a relevant physical quantity for the rheology of granular materials.

The mapping evidenced in Fig. 3 hints at similar packing structures in the two sets. Figure 4 shows two snapshots: one representing a disk packing with µ r = 0.05 and the other representing a polygon packing with n s = 8 (note that 0.05 ≃ (1/4) tan(π/(2 * 8)) according to Eq. 3). The contact forces are represented by segments joining the particle centers, with a thickness proportional to the force magnitude. We observe that the force-carrying backbone is astonishingly similar in the two systems.

From the expression of the stress tensor, it can be shown that the shear stress q/p reflects the packing structure and force transmission via a simple relation [START_REF] Rothenburg | [END_REF]:

q/p ≃ (1/2)(a c + a n + a t ), (4)
where a c , a n , and a t , are the anisotropies of the angular distributions of contact orientations P n (θ), normal forces f n (θ), and tangential forces f t (θ), respectively, as a function of contact orientation θ, which are approximated by their lowest order Fourier expansions:

P n (θ) ≃ 1/π{1 + a c cos 2(θ -θ c )}, f n (θ) ≃ f n {1 + a n cos 2(θ -θ n )}, f t (θ) ≃ -f n a t sin(θ -θ t ), (5)
where f n is the mean normal fore, and θ c = θ n = θ t are the corresponding privileged directions, which, in the steady state, coincide with the principal stress direction. Equation 4 reveals distinct origins of the shear strength in terms of force and texture anisotropy. The empty symbols in Fig. 3 show q/p as predicted by Eq. 4. We see that this equation approximates well the shear strength for all raw data.

The anisotropies a c , a n , and a t are shown in Fig. 5 as functions of µ r for the disks and of (1/4) tan ψ for the polygons. It is remarkable that all anisotropies are almost identical between the two sets. This correspondence is only broken for polygons with small numbers of sides, i.e., for n s = 3 and 4. This happens because for these polygons the contact orientation is strongly influenced by the low rotational symmetry of the particles and the orientations of the sides rather than the relative positions of the particles.

The mapping between rolling friction and angular shape of particles is also reflected by the probability den- sity function (PDF) of normal forces displayed in Fig. 6. In this figure, we compare the PDFs of the two samples shown in Fig. 4. The two PDFs are almost identical. The PDF can be approximated by a power law (i.e., P DF ∝ (f n / f n )

-α ) in the range of small forces and by an exponential function (i.e., P DF ∝ e β(1-fn/ fn ) ) in the range of strong forces [28]. The inset in Fig. 6 shows the coefficients α and β as functions of µ r for the disks and of (1/4) tan ψ for the polygons, confirming that the similarity of the PDFs is maintained for the whole range of rolling frictions and numbers of sides studied in this work.

To sum up, the simulations presented in this Letter provide strong evidence for the mapping between the two studied parameters, i.e., rolling resistance and shape angularity. This correspondence was established by considering shear strength, solid fraction, force and fabric anisotropies, and the PDFs of normal forces in the steady state. A practical consequence of this finding is that rolling resistance may be employed to imitate the effect of angular shape in discrete-element simulations of granular materials. More importantly, it suggests that the hindrance of particle rotations is a major effect of angular particle shape. In this picture, the effect of rolling friction is to force the particles to rearrange as if they were glued to each other. In this way, the clusters of two or more particles behave as non-circular particles. This result may be tested in other loading conditions and it is potentially extensible to other particle shapes (in 2D and 3D), opening new scopes in modeling complex granular systems.

This work was financially supported by the France-Colombia Ecos-Nord project (Grant No. C08U01).

FIG. 2 :

 2 FIG.1:(color online) Shear strength q/p (Up) and solid fraction ν (Down) as functions of µr for the disks and of 1/ns for the polygons. Error bars indicate the standard deviation.

FIG. 3 :

 3 FIG.3:(color online) (Up) Shear strength q/p as a function of µr for the disks and of (1/4) tan ψ for the polygons, both from raw simulation data (full symbols) and as predicted by Eq. 4 (empty symbols). (Down) Solid fraction ν as a function of µr for the disks and of (1/4) tan ψ for the polygons. Error bars indicate the standard deviation.

FIG. 4 :

 4 FIG. 4: Snapshots of the force network in (a) a system composed of disks with rolling friction (µr = 0.05) and (b) a system composed of octagonal particles. The line thickness is proportional to the normal force. The floating particles are represented in light grey.

2 FIG. 6 : 4 .

 264 FIG. 6: (color online) Probability distribution function of normalized normal forces fn/ fn for the two systems of Fig. 4. The inset shows the evolution of the exponents α and β (see text for definitions) with µr for the disks and with (1/4) tan ψ for the polygons.


Isabella Kardys

Jaap W Deckers

Bruno H Ch

Stricker

Wim B Vletter

Albert Hofman

Jacqueline Witteman
email: j.witteman@erasmusmc.nl

Á B H Ch

Á A Stricker

Á J Hofman

Witteman

Á W B Vletter

Distribution of echocardiographic parameters and their associations with cardiovascular risk factors in the Rotterdam Study

Keywords: Cardiovascular disease, Diastolic function, Echocardiography, Systolic function

Insight into echocardiographic parameters in the general population may facilitate early recognition of ventricular dysfunction, reducing the population morbidity and mortality of heart failure. We examined the distribution of structural, systolic and diastolic echocardiographic parameters and their associations with cardiovascular risk factors in the Rotterdam Study, a population-based cohort study in men and women aged C55 years. Participants with prevalent heart failure, myocardial infarction and atrial fibrillation and flutter were excluded. Echocardiographic parameters were assessed using two-dimensional, M-mode and Doppler echocardiography. Echocardiograms were available in 4,425 participants. Structural parameters were generally larger in men, and most consistently associated with age, body mass index and blood pressure in both sexes. Prevalence of moderate or poor left ventricular systolic function was 3.9% in men and 2.1% in women. Age, body mass index and blood pressure were most consistently associated with systolic function. E/A ratio was lower in women than in men. Age and diastolic blood pressure were most consistently associated with E/A ratio in both sexes. In conclusion, ventricular systolic and diastolic dysfunction is present in asymptomatic individuals. Selected established cardiovascular risk factors are associated with structural, systolic and diastolic parameters.

Introduction

Heart failure is an important health problem. Its prevalence is increasing, in part because of improved treatment of patients with heart failure and increased survival of patients with myocardial infarction [START_REF] Hunt | ACC/AHA 2005 guideline update for the diagnosis and management of chronic heart failure in the adult: a report of the American College of Cardiology/American Heart Association Task Force on Practice Guidelines (Writing Committee to Update the 2001 Guidelines for the Evaluation and Management of Heart Failure): developed in collaboration with the American College of Chest Physicians and the International Society for Heart and Lung Transplantation: endorsed by the Heart Rhythm Society[END_REF]. Since heart failure is primarily a condition in the elderly, the aging of the population also contributes to its increasing prevalence. Although in most patients, abnormalities of systolic and diastolic dysfunction coexist [START_REF] Hunt | ACC/AHA 2005 guideline update for the diagnosis and management of chronic heart failure in the adult: a report of the American College of Cardiology/American Heart Association Task Force on Practice Guidelines (Writing Committee to Update the 2001 Guidelines for the Evaluation and Management of Heart Failure): developed in collaboration with the American College of Chest Physicians and the International Society for Heart and Lung Transplantation: endorsed by the Heart Rhythm Society[END_REF], it has been shown that persons with normal ejection fraction can have impaired diastolic function [START_REF] Zile | Heart failure with a normal ejection fraction: is measurement of diastolic function necessary to make the diagnosis of diastolic heart failure?[END_REF]. Also of note is, that persons with a very low ejection fraction may be asymptomatic; this has been termed preclinical systolic dysfunction [START_REF] Redfield | Burden of systolic and diastolic ventricular dysfunction in the community: appreciating the scope of the heart failure epidemic[END_REF].

It has been recognized that therapeutic interventions introduced even before the appearance of left ventricular dysfunction or symptoms can reduce the population morbidity and mortality of heart failure [START_REF] Hunt | ACC/AHA 2005 guideline update for the diagnosis and management of chronic heart failure in the adult: a report of the American College of Cardiology/American Heart Association Task Force on Practice Guidelines (Writing Committee to Update the 2001 Guidelines for the Evaluation and Management of Heart Failure): developed in collaboration with the American College of Chest Physicians and the International Society for Heart and Lung Transplantation: endorsed by the Heart Rhythm Society[END_REF][START_REF]Effect of enalapril on mortality and the development of heart failure in asymptomatic patients with reduced left ventricular ejection fractions. The SOLVD Investigators[END_REF]. This underlines the importance of early recognition of preclinical ventricular dysfunction. Echocardiography, which has become a common method to assess ventricular function, may be useful to gain more insight into this matter. To its advantage, it is noninvasive and comprehensive. As a consequence, echocardiography has been used in several population-based studies to examine the prevalence and determinants of systolic and diastolic dysfunction in the community [START_REF] Redfield | Burden of systolic and diastolic ventricular dysfunction in the community: appreciating the scope of the heart failure epidemic[END_REF][START_REF] Benjamin | Determinants of Doppler indexes of left ventricular diastolic function in normal subjects (the Framingham Heart Study)[END_REF][START_REF] Devereux | A population-based assessment of left ventricular systolic dysfunction in middle-aged and older adults: the strong heart study[END_REF][START_REF] Devereux | Prognostic implications of ejection fraction from linear echocardiographic dimensions: the strong heart study[END_REF][START_REF] Gardin | Sex, age, and disease affect echocardiographic left ventricular mass and systolic function in the freeliving elderly. The cardiovascular health study[END_REF][START_REF] Xie | Left ventricular diastolic function in young adults: the coronary artery risk development in young adults study[END_REF] and to investigate the predictive value of echocardiographic parameters for heart failure, cardiovascular disease and mortality [START_REF] Redfield | Burden of systolic and diastolic ventricular dysfunction in the community: appreciating the scope of the heart failure epidemic[END_REF][START_REF] Devereux | Prognostic implications of ejection fraction from linear echocardiographic dimensions: the strong heart study[END_REF][START_REF] Aurigemma | Predictive value of systolic and diastolic function for incident congestive heart failure in the elderly: the cardiovascular health study[END_REF][START_REF] Bella | Mitral ratio of peak early to late diastolic filling velocity as a predictor of mortality in middle-aged and elderly adults: the strong heart study[END_REF][START_REF] Lauer | Prognostic implications of subclinical left ventricular dilatation and systolic dysfunction in men free of overt cardiovascular disease (the Framingham Heart Study)[END_REF][START_REF] Wang | Natural history of asymptomatic left ventricular systolic dysfunction in the community[END_REF].

The growing importance of insight into echocardiographic characteristics of the general population has prompted us to perform echocardiography in the Rotterdam Study, a population-based study in men and women aged 55 years and over. The purpose of the present report is to describe the distribution of structural, systolic and diastolic echocardiographic parameters in our study population and to examine the associations of established cardiovascular risk factors with these echocardiographic parameters.

Methods

Study population

The study was performed within the framework of the Rotterdam Study, a population-based cohort study aimed at assessing the occurrence of and risk factors for chronic diseases in the elderly [START_REF] Hofman | The Rotterdam Study: 2010 objectives and design update[END_REF]. Baseline visits of the Rotterdam Study took place in 1990-1993. All inhabitants of a suburb of Rotterdam aged 55 years and over were invited and 7,983 agreed to participate (response 78%). Follow-up visits took place in 1993-1994[START_REF] Oh | The noninvasive assessment of left ventricular diastolic function with two-dimensional and Doppler echocardiography[END_REF]-1999. In 2000-2001, the cohort was extended with 3,011 participants from the same suburb (response 67%), also aged 55 years and over. For the present study, data collection took place from 2002-2005. Within this period, the participants from the original cohort completed their fourth center visit (n = 3,550), and the participants of the extended cohort completed their second center visit (n = 2,389). Of these, 3,052 and 2,235, respectively, underwent cardiac echocardiography. The large majority of missing echocardiograms was explained by incidental absence of echocardiographers. Participants with prevalent heart failure (n = 304), prevalent myocardial infarction, (n = 561), and atrial fibrillation (n = 124) or atrial flutter (n = 13) at the time of echocardiography were excluded from the analysis. This led to the exclusion of a total of 862 persons and consequently resulted in a total of 4,425 participants available for analysis. The medical ethics committee of Erasmus Medical Center, Rotterdam, approved the study. Participants gave written informed consent and permission to retrieve information from treating physicians. The investigation conforms with the principles outlined in the declaration of Helsinki.

Assessment of cardiovascular risk factors and prevalent disease

A trained interviewer visited all participants at home and collected information on current health status, medical history, drug use, and smoking, using a computerized questionnaire. Participants were categorized as current, past and never smokers. Clinical measures were obtained during a visit at the study center. Height and weight were measured and the body mass index (BMI) was calculated (weight (kg)/ height (m) 2 ). Blood pressure was measured at the right brachial artery using a random-zero sphygmomanometer with the participant in sitting position. Serum total cholesterol and high-density lipoprotein (HDL) cholesterol were obtained using an automatic enzymatic procedure (Hitachi 911, Roche CHOD PAP). Diabetes mellitus was defined as the use of antidiabetic medication or a fasting glucose level of C7 mmol/l [START_REF]Report of the expert committee on the diagnosis and classification of diabetes mellitus[END_REF]. Presence of symptomatic heart failure at the time of echocardiography was assessed by using a validated score similar to the definition of heart failure of the European Society of Cardiology, as described previously [START_REF] Bleumink | Quantifying the heart failure epidemic: prevalence, incidence rate, lifetime risk and prognosis of heart failure the Rotterdam Study[END_REF], and the information needed was obtained by screening of all medical records of general practitioners (GPs) in retrospect for the occurrence of heart failure and obtaining letters and discharge reports from medical specialists when a case was found. A history of myocardial infarction was considered present when myocardial infarction was detected by screening GP medical records and reviewing letters and discharge reports from medical specialists, or when an ECG characteristic of prior myocardial infarction was detected during a follow-up visit. Presence of atrial fibrillation or atrial flutter at the time of echocardiography was assessed with electrocardiography by applying the Modular ECG Analysis System (MEANS), which has been extensively evaluated [START_REF] Van Bemmel | Methodology of the modular ECG analysis system MEANS[END_REF][START_REF] Willems | The diagnostic performance of computer programs for the interpretation of electrocardiograms[END_REF], and is characterized by a high sensitivity (96.6%) and a high specificity (99.5%) in coding arrhythmias [START_REF] Kors | Validation of a new computer program for Minnesota coding[END_REF]. For a small sample of participants, ECGs were not available at the time this report was written because of logistic problems and were approximated by using ECGs from the previous examination (year [2000][2001].

Echocardiography

For each participant, an echocardiogram was obtained. The first 2,188 echocardiograms were performed with a commercially available ultrasonography system (AU3 Partner, Esaote Biomedica, with a 3.5/2.5 MHz transducer). The following 3,099 echocardiograms were performed with another commercially available system (Acuson Cypress, with a 3V2c transducer). A standardized protocol was used, including two-dimensional scanning in the parasternal long axis view, parasternal short axis view, apical view and subcostal view, M-mode scanning in the parasternal long axis view, and pulsed wave Doppler scanning in the apical four chamber view [START_REF] Henry | Report of the American society of echocardiography committee on nomenclature and standards in two-dimensional echocardiography[END_REF]. Echocardiograms were recorded onto VHS tape and assessed at the reading center, which was located at Erasmus Medical Center.

Several structural parameters were assessed [START_REF] Schiller | Recommendations for quantitation of the left ventricle by two-dimensional echocardiography. American society of echocardiography committee on standards, subcommittee on quantitation of two-dimensional echocardiograms[END_REF]. Left atrium diameter, left ventricular end systolic dimension (LVES), left ventricular end diastolic dimension (LVED), end diastolic interventricular septum thickness (IVST) and end-diastolic left ventricular posterior wall thickness (PWT) were measured in the parasternal long axis view using M-mode with two-dimensional guidance. Left ventricular mass (grams) was calculated as 0.80(1.04* (IVST ? LVED ? PWT) 3 -(LVED) 3 ) ? 0.6, according to Devereux et al [START_REF] Devereux | Echocardiographic assessment of left ventricular hypertrophy: comparison to necropsy findings[END_REF]. Fractional shortening at the endocardium was calculated as (LVED-LVES)/LVED*100% [START_REF] Schiller | Recommendations for quantitation of the left ventricle by two-dimensional echocardiography. American society of echocardiography committee on standards, subcommittee on quantitation of two-dimensional echocardiograms[END_REF]. Global left ventricular systolic function was qualitatively assessed, without quantitative measurement, from the twodimensional echocardiogram and classified as normal, fair, moderate or poor. Furthermore, diastolic parameters were measured [START_REF] Quinones | Recommendations for quantification of Doppler echocardiography: a report from the Doppler quantification task force of the nomenclature and standards committee of the American society of echocardiography[END_REF]. Pulsed Doppler recordings of transmitral filling velocity were performed in the apical 4-chamber view, with the sample volume placed in the mitral valve orifice near the tips of the leaflets. Doppler peak E and peak A velocities were averaged over three cycles. E/A ratio was computed by dividing Doppler peak E velocity by Doppler peak A velocity. Early mitral valve velocity deceleration time was measured as the time between the peak E wave and the upper deceleration slope extrapolated to the zero baseline.

Echocardiograms were made and read by four trained echocardiographers. To assess intra-reader and inter-reader agreement, 32 participants were examined in duplicate. For continuous variables, overall median percent intra-reader and inter-reader measurement variabilities were calculated as the absolute measurement difference divided by the average of the two measurements, multiplied by 100. Overall median intra-reader and inter-reader variabilities for left ventricular end-diastolic dimension were 3 and 4%, respectively. For left ventricular end-systolic dimension both variabilities were 6%, and for fractional shortening both were 8%. Overall median intra-reader and inter-reader variabilities for E/A ratio were 15 and 18%, respectively, and for deceleration time both were 16%. Finally, the percentage agreement for categorization of left ventricular systolic function as normal or other than normal was 82% within readers and 86% between readers.

Statistical analysis

We calculated means, medians and proportions of cardiovascular risk factors and echocardiographic characteristics in men and women. Differences between the sexes were tested with t-tests, chi square tests and Mann-Whitney tests where appropriate.

Subsequently, we investigated the association between cardiovascular risk factors and echocardiographic parameters. We performed linear regressions with age, BMI, systolic blood pressure, diastolic blood pressure, total cholesterol, HDL-cholesterol, diabetes mellitus and smoking as independent variables and structural echocardiographic parameters (diameter of left atrium, left ventricular endsystolic dimension, left ventricular end-diastolic dimension, interventricular septum thickness, left ventricular posterior wall thickness, left ventricular mass), systolic parameters (ejection fraction, fractional shortening) and diastolic parameters (mitral valve inflow peak E velocity, mitral valve inflow peak A velocity, E/A ratio and mitral valve inflow deceleration time) as dependent variables. Continuous independent variables were examined per standard deviation increase. For some of the dependent variables, the distribution of the residuals was skewed. After log-transformation of these variables, the residuals were normally distributed with a constant variance. To make the regression coefficients more informative, units of dependent variables were multiplied by 10 -2 . The analysis was performed separately in men and women. We adjusted for age and type of ultrasonography system used, and subsequently, we also adjusted the analysis of each risk factor for all other risk factors and also for use of diuretics, beta-blockers, ACE inhibitors, lipid lowering drugs and heart rate.

We used analysis of covariance to compare risk factors, structural echocardiographic parameters, and fractional shortening according to categories of qualitatively assessed left ventricular systolic function and categories of E/A ratio and diastolic function. Few men and women had poor left ventricular systolic function (n = 19 and n = 10, respectively), therefore we pooled moderate and poor systolic function for the analysis to make the results easier to interpret. We categorized E/A ratio according to cut points used in previous reports [START_REF] Redfield | Burden of systolic and diastolic ventricular dysfunction in the community: appreciating the scope of the heart failure epidemic[END_REF][START_REF] Ommen | A clinical approach to the assessment of left ventricular diastolic function by Doppler echocardiography: update 2003[END_REF].

All analyses were performed using SPSS 11.0. Values for cardiovascular covariates were missing in less than 3% of participants, except for BMI, which was missing in 5.5%. Missing values were handled by single imputation using the expectation-maximization algorithm in SPSS 11.0. All tests were two-sided. We ran several analyses in duplicate to compare the two ultrasonography systems we used.

Results

Table 1 shows the distribution of cardiovascular risk factors in men and women. Women were significantly older than men, although this was a clinically modest difference of 1.1 years. In Table 2, the distribution of echocardiographic characteristics is displayed in men and women. All characteristics showed significant differences across the sexes; in general, structural parameters were larger in men, systolic function was worse in men, and with regard to diastolic function, E/A ratio was lower in women.

For reasons of conciseness, only the multivariable results are presented. Overall, age, BMI, systolic blood pressure and diastolic blood pressure were significantly associated with most structural parameters in men and women (Supplementary Table 1). Age, BMI and systolic blood pressure generally showed positive associations, with the exception of an inverse association of age with left ventricular end diastolic dimension in women. Diastolic blood pressure showed inverse associations with left atrium diameter in men and women. Furthermore, total cholesterol showed associations with selected parameters (Supplementary Table 1). The age-and ultrasonography system adjusted results (data not shown) demonstrated additional associations between HDL-cholesterol and diabetes mellitus and most structural parameters (inverse and positive associations, respectively), which disappeared after further adjustment.

In Table 3, multivariable-adjusted associations with fractional shortening are displayed. Age, BMI and diastolic blood pressure showed inverse associations with fractional shortening, while systolic blood pressure showed positive associations. In men, the association of systolic blood pressure with fractional shortening did not reach statistical significance. However, the magnitude of the regression coefficient was comparable to that of the significant regression coefficient in women. The results were similar when models were adjusted for age-and ultrasonography system only (data not shown). Table 4 shows associations of risk factors with left ventricular systolic function. Overall, the results were in accordance with Table 3. Age was higher in men and women with fair and moderate/poor function than in those with normal function. BMI was also significantly higher in men and women with fair function. Systolic blood pressure was lower in men with fair function than in men with normal function. In women, systolic blood pressure decreased and diastolic blood pressure increased according to systolic function categories. In Table 5, structural echocardiographic parameters are displayed according to categories of left ventricular systolic function. In general, left ventricular end-systolic and end-diastolic dimensions increased with worsening systolic function, as did interventricular septum thickness, left ventricular posterior wall thickness and left ventricular mass. As expected, fractional shortening significantly decreased with worse qualitative systolic function.

Subsequently associations between cardiovascular risk factors and diastolic echocardiographic parameters were examined. Age and diastolic blood pressure were inversely and significantly associated with E/A ratio in men and women, whereas systolic blood pressure showed no association (Supplementary Table 2). BMI was positively and significantly associated with E/A ratio in women; in men, the regression coefficient was of similar magnitude but did not reach significance. Age-and ultrasonography system adjusted analyses also showed inverse associations between BMI and systolic blood pressure and E/A ratio in both sexes; however, these did not persist after additional adjustment. Categorization of E/A ratio confirmed the associations of lower E/A ratio with higher age and diastolic blood pressure in both sexes (Table 6). Of note is that it also showed significantly lower systolic blood pressure in women with E/A ratio \0.75. All above-mentioned analyses were adjusted for ultrasonography system to account for any possible differences. When running analyses in duplicate using the two systems separately, the associations were similar in direction and magnitude, but were more likely to reach statistical significance using the Acuson system.

Discussion

Summarizing, in this study, we have examined structural, systolic and diastolic echocardiographic parameters and their associations with cardiovascular risk factors in a population-based cohort. Structural parameters were generally larger in men, and larger values were most consistently associated with higher values of age, BMI and systolic blood pressure in both sexes. Although we had excluded participants with prevalent heart failure, myocardial infarction, and atrial fibrillation and flutter, moderate or poor left ventricular systolic function was found to be present in the participants, albeit with a modest prevalence (a total of 3.9% of men and 2.1% of women). Higher age, higher BMI, lower systolic and higher diastolic blood pressure were most consistently associated with worse systolic function. Furthermore, persons with worse systolic function had larger ventricular dimensions and larger left ventricular mass. With regard to diastolic parameters, we found that Doppler peak E and peak A velocities were larger in women than in men, but that E/A ratio was lower in women than in men. Higher age and higher diastolic blood pressure were most consistently associated with lower E/A ratio in both sexes.

Strengths of the present study include its populationbased nature, its large size, and its standardized assessment of risk factors and echocardiographic characteristics. Nevertheless, several issues warrant consideration. First, we used global left ventricular function assessed qualitatively from two-dimensional images. This approach is easily obtainable and reflects the routine procedure in echocardiography All models are adjusted for ultrasonography system, age, BMI, systolic and diastolic blood pressure, total and HDL cholesterol, diabetes mellitus, smoking, use of diuretics, beta-blockers, ACE inhibitors, lipid lowering drugs and heart rate * 0.01 \ P \ 0.05, 0.001 \ P \ 0.01, à P \ 0.001, compared to normal left ventricular systolic function § Geometric mean because of skewed distribution laboratories. Prior studies have reported that the reproducibility and accuracy of visual assessments are as good as those of quantitative methods [START_REF] Amico | Superiority of visual versus computerized echocardiographic estimation of radionuclide left ventricular ejection fraction[END_REF][START_REF] Jensen-Urstad | Comparison of different echocardiographic methods with radionuclide imaging for measuring left ventricular ejection fraction during acute myocardial infarction treated by thrombolytic therapy[END_REF], and similar visual assessments have also been used in other studies such as the Framingham Study [START_REF] Wang | Natural history of asymptomatic left ventricular systolic dysfunction in the community[END_REF]. Associations of risk factors with qualitative left ventricular function and with quantitatively measured fractional shortening showed similar patterns, and this suggest that assessment of left ventricular systolic function was performed appropriately in our study. Second, we used E/A ratio as an indicator of diastolic function, while measures such as pulmonary venous flow or Doppler tissue imaging are needed to further categorize diastolic function [START_REF] Garcia | New Doppler echocardiographic applications for the study of diastolic function[END_REF][START_REF] Wang | Current perspectives on cardiac function in patients with diastolic heart failure[END_REF]. We were not able to assess such additional measures because of constraints in examination time available per participant, inherent to large-scale population-based research. Several different recommendations have been issued for categorization of diastolic function based on E/A ratio [START_REF]How to diagnose diastolic heart failure. European study group on diastolic heart failure[END_REF][START_REF] Oh | The noninvasive assessment of left ventricular diastolic function with two-dimensional and Doppler echocardiography[END_REF]. E/A ratio is usually categorized according to absolute cut-points based on its physiology. We based our categorization of E/A ratio on absolute cutpoints used in recent reports [START_REF] Redfield | Burden of systolic and diastolic ventricular dysfunction in the community: appreciating the scope of the heart failure epidemic[END_REF][START_REF] Ommen | A clinical approach to the assessment of left ventricular diastolic function by Doppler echocardiography: update 2003[END_REF].

Furthermore, we should bear in mind that some of the echocardiographic measurements displayed considerable variability. Inter-reader and intra-reader measurement variabilities for E/A ratio and deceleration time reflect the practical difficulties involved in estimating Doppler peak E velocity and Doppler peak A velocity. In contrast, intrareader and inter-reader variability of structural and systolic parameters was in a much lower range. Finally, when analyzing the Esaote and Acuson ultrasonography systems separately, similar results were found, but associations were more likely to reach statistical significance in the group where the Acuson system was used. Higher numbers of participants in the Acuson group may partly explain this. However, precision may have also played a part, since the Acuson system provided images of somewhat better resolution. In the latter case, the associations we found may in reality be even stronger.

Previously, fractional shortening has been measured in a subset of 2,267 participants of the Rotterdam Study [START_REF] Mosterd | Prevalence of heart failure and left ventricular dysfunction in the general population; the Rotterdam Study[END_REF]. In accordance with the present study, fractional shortening was found to be somewhat higher in women (40 ± 7%) than in men (38 ± 8%). However, no significant association was found with age.

In the present study, women on average had better left ventricular systolic function than men, and E/A ratio was found to be lower in women. This is in accordance with known gender differences in heart failure; systolic dysfunction is more common in men and diastolic dysfunction tends to occur more often in women. This is explained by the fact that men have coronary artery disease as an underlying factor for heart failure more frequently than women, while women are more likely to have hypertension as an underlying factor [START_REF] Hussey | Sex-related differences in heart failure[END_REF][START_REF] Petrie | Failure of women's hearts[END_REF]. Heart failure that occurs after myocardial infarction is characterized by profound ventricular dilation, wall thinning, increased heart size, eccentric hypertrophy and systolic dysfunction. Heart failure that occurs due to long-standing hypertension is characterized by (concentric) left ventricular hypertrophy, increased myocardial mass and diastolic dysfunction, especially in the early stages. The distribution of echocardiographic parameters and their associations with cardiovascular risk factors have previously been examined in several population-based studies. Table 7 provides an overview of the main findings of several large studies and compares them to the current study. It shows that prevalence of systolic and diastolic dysfunction varies across studies, probably in part due to differences in population characteristics and definitions of ventricular dysfunction. Nevertheless, associations of age, sex, and blood pressure with ventricular dysfunction appear to be rather consistent across studies.

In conclusion, we have found that moderate and poor left ventricular systolic function was present in asymptomatic men and women participating in the Rotterdam Study. With regard to diastolic parameters, we found that E/A ratio was on average lower in women than in men. Higher age, BMI and diastolic blood pressure and lower systolic blood pressure were most consistently associated with worse systolic function in both sexes. Higher age and diastolic blood pressure were most consistently associated with lower E/A ratio in both sexes. Further research is warranted to investigate the value of echocardiography in identification of individuals with preclinical ventricular dysfunction.

Table 1

 1 Population characteristics

		Variable		Men (n = 1,736)	Women (n = 2,689)	P-value
		Age (years)		70.8 ± 7.0	71.9 ± 7.5	\0.001
		Body mass index (kg/m 2 )		27.2 ± 3.4	27.7 ± 4.5	\0.001
		Systolic blood pressure (mmHg)	148 ± 20	151 ± 22	\0.001
		Diastolic blood pressure (mmHg)	81 ± 11	79 ± 11	\0.001
		Total cholesterol (mmol/l)		5.4 ± 0.9	5.9 ± 0.9	\0.001
		HDL-cholesterol (mmol/l)		1.3 ± 0.3	1.6 ± 0.4	\0.001
		Diabetes mellitus (%)		13.4	12.7	0.49
		Smoking
		Never (%)		13.4	43.1	\0.001
		Former (%)		68.2	42.8
	Categorical variables are	Current (%)		18.4	14.0
	expressed as percentage. Continuous variables are expressed as mean ± standard	Use of diuretics (%) Use of beta blockers (%)		5.4 11.9	11.8 15.6	\0.001 \0.001
	deviation. T-tests and chi square	Use of ACE-inhibitors (%)		11.2	11.0	0.79
	tests were used where appropriate	Use of lipid-lowering drugs (%)	11.2	11.9	0.52
	Table 2 Echocardiographic characteristics
	Variable		Men (n = 1,736)	Women (n = 2,689)	P-value
	Structural parameters
	Left atrium diameter (mm)		42 ± 5		3 9 ± 5	\0.001
	Left ventricular end systolic dimension (mm)	32 (29-36) a		29 (27-32) a	\0.001
	Left ventricular end diastolic dimension (mm)	53 ± 5		4 9 ± 5	\0.001
	Interventricular septum thickness (mm)	8 (8-10) a		8 (7-9) a	\0.001
	Left ventricular posterior wall thickness (mm)	8 (7-8) a		7 (7-8) a	\0.001
	Left ventricular mass (g)		157 (135-187) a	130 (110-151) a	\0.001
	Systolic parameters
	Ejection fraction (%)		0.77 (0.71-0.82) a	0.79 (0.74-0.83) a	\0.001
	Fractional shortening (%)		38 ± 7		4 0 ± 6	\0.001
	Left ventricular systolic function (qualitative)
	Normal (%)		55.0		64.9	\0.001
	Fair (%)		41.0		33.1
	Moderate or poor (%)		3.9		2.1
	Diastolic parameters
	Mitral valve inflow peak E (m/s)		0.63 ± 0.15		0.66 ± 0.16	\0.001
	Mitral valve inflow peak A (m/s)		0.72 ± 0.16		0.80 ± 0.17	\0.001
	Mitral valve inflow deceleration time (ms)	219 ± 47		211 ± 45	\0.001
	E/A ratio		0.86 (0.71-1.00) a	0.81 (0.70-1.00)

a \0.001 Categorical variables are expressed as percentage. Continuous variables are expressed as mean ± standard deviation. T-tests, chi square tests and Mann-Whitney tests were used where appropriate a Median and inter-quartile range because of skewed distribution

Table 3

 3 Multivariable adjusted regression coefficients for risk factors, describing the increase in fractional shortening (% *10 -2 ) per (sex-specific) standard deviation increase of the risk factors

	Variable	Fractional shortening (% *10 -2 )
	Men
	Age (years)	-125 (-163, -87.1) à
	Body mass index (kg/m 2 )	-39.4 (-74.4, -4.34)*
	Systolic blood pressure (mmHg)	34.3 (-4.94, 73.6)
	Diastolic blood pressure (mmHg) -54.3 (-93.9, -14.6)
	Total cholesterol (mmol/l)	6.11 (-27.7, 39.9)
	HDL-cholesterol (mmol/l)	20.0 (-14.0, 53.9)
	Diabetes mellitus	-51.8 (-148.6, 45.0)
	Current smoking	-41.8 (-124, 40.6)
	Women
	Age (years)	-77.5 (-106, -49.6) à
	Body mass index (kg/m 2 )	-26.1 (-52.0, -0.13)*
	Systolic blood pressure (mmHg)	36.4 (5.52, 67.3)*
	Diastolic blood pressure (mmHg) -47.6 (-77.3, -17.8)
	Total cholesterol (mmol/l)	10.3 (-14.3, 34.9)
	HDL-cholesterol (mmol/l)	3.59 (-21.2, 28.3)
	Diabetes mellitus	9.65 (-63.1, 82.4)
	Current smoking	-32.9 (-99.5, 33.7)

All models are adjusted (where appropriate) for ultrasonography system, age, BMI, systolic and diastolic blood pressure, total and HDL cholesterol, diabetes mellitus, smoking, use of diuretics, betablockers, ACE inhibitors, lipid lowering drugs and heart rate * 0.01 \ P \ 0.05, 0.001 \ P \ 0.01, à P \ 0.001

Table 4

 4 Population characteristics according to left ventricular systolic function, multivariable adjusted

	Variable	Left ventricular systolic function
		Normal	Fair	Moderate/
				poor
	Men	n = 938 n = 699 n = 67
	Age (years)	69.7	72.0 à	73.1 à
	Body mass index (kg/m 2 )	26.9	27.5 à	26.9
	Systolic blood pressure (mmHg) 149	147*	146
	Diastolic blood pressure (mmHg) 81	82	82
	Total cholesterol (mmol/l)	5.4	5.4	5.4
	HDL-cholesterol (mmol/l)	1.33	1.31	1.32
	Diabetes mellitus (%)	13.0	12.3	21.2
	Current smoking (%)	16.6	21.1*	15.5
	Women	n = 1,725 n = 879 n = 54
	Age (years)	70.8	73.5 à	75.5 à
	Body mass index (kg/m 2 )	27.5	28.1 à	27.7
	Systolic blood pressure (mmHg)	152	150	143 à
	Diastolic blood pressure (mmHg) 79	80 à	81*
	Total cholesterol (mmol/l)	5.9	5.9	5.6
	HDL-cholesterol (mmol/l)	1.58	1.57	1.51
	Diabetes mellitus (%)	11.9	14.0	7.4
	Current smoking (%)	13.8	14.8	20.1

All models are adjusted (where appropriate) for ultrasonography system, age, BMI, systolic and diastolic blood pressure, total and HDL cholesterol, diabetes mellitus, smoking, use of diuretics, betablockers, ACE inhibitors, lipid lowering drugs and heart rat * 0.01 \ P \ 0.05, 0.001 \ P \ 0.01, à P \ 0.001, compared to normal left ventricular systolic function

Table 5

 5 Structural echocardiographic parameters and fractional shortening according to left ventricular systolic function, multivariable adjusted

	Variable

Table 6

 6 Population characteristics according to E/A ratio, multivariable adjusted

	Variable	E/A ratio
		E/A \ 0.75	0.75 B E/A B 1.50	E/A [ 1.50
	Men	n = 457 (27.4%)	n = 1,183 (70.9%)	n = 29 (1.7%)
	Age (years)	73.5 à	69.7	69.2
	Body mass index (kg/m 2 )	27.2	27.2	27.2
	Systolic blood pressure (mmHg)	147	148	149
	Diastolic blood pressure (mmHg)	82	81	80
	Total cholesterol (mmol/l)	5.4	5.4	5.2
	HDL-cholesterol (mmol/l)	1.31	1.32	1.33
	Diabetes mellitus (%)	14.7	12.1	16.0
	Current smoking (%)	29.9	18.0	11.3
	Women	n = 824 (31.8%)	n = 1,730 (70.9%)	n = 36 (1.4%)
	Age (years)	74.6 à	70.4	69.7
	Body mass index (kg/m 2 )	27.9	27.6	26.9
	Systolic blood pressure (mmHg)	149	151	152
	Diastolic blood pressure (mmHg)	81 à	79	77
	Total cholesterol (mmol/l)	6.0	5.9	5.7
	HDL-cholesterol (mmol/l)	1.55*	1.59	1.59
	Diabetes mellitus (%)	11.6	12.6	21.9
	Current smoking (%)	14.6	14.4	13.0

All models are adjusted (where appropriate) for ultrasonography system, age, BMI, systolic and diastolic blood pressure, total and HDL cholesterol, diabetes mellitus, smoking, use of diuretics, beta-blockers, ACE inhibitors, lipid lowering drugs and heart rate * 0.01 \ P \ 0.05, 0.001 \ P \ 0.01, à P \ 0.001, compared to 0.75 B E/A B 1.50

Table 7

 7 Systolic and diastolic left ventricular function examined in several large studies

	Diastolic function;	associations				Age, sex, height,	weight, blood	pressure, heart rate	and hematocrit	Age, cardiovascular	disease, diabetes,	systolic dysfunction.	No association with	sex.				Age, and to a lesser	extent sex, heart rate,	PR interval, LV	systolic function, and	systolic blood	pressure	Age, sex, BMI, blood	pressure, heart rate,	diabetes, coronary	heart disease,	smoking			Age, sex, blood	pressure
	Prevalence of	decreased	diastolic	function		Women: lower	E/A ratio	than men		Mild	dysfunction:	20.8%,	moderate:	6.6%,	severe: 0.7%									E/A	ratio \ 0.6:	16%,	E/A	ratio [ 1.5:	3%	Men: 27%	E/A \ 0.75,	1.7% E/	A [ 1.5;	Women:	32% E/	A \ 0.75,	1.4%	E/A [ 1.5
	Diastolic function;	assessment				Transmitral early and late	diastolic peak filling	velocities		Pulsed wave Doppler	examination of mitral	inflow, pulmonary venous	inflow and Doppler tissue	imaging of the mitral	annulus			127 randomly selected,	''normal''male and female	subjects; E/A ratio by	Doppler echocardiogrphy			3,008 subjects; E/A ratio	assessed by Doppler	echocardiography						E/A ratio assessed	by Doppler	echocardiography
	Systolic function;	associations				Age, sex, clinical coronary	heart disease,	hypertension		Age and sex								Age, sex, myocardial	infarction, diabetes	mellitus, blood pressure	(P-values not mentioned)			Age, sex, BMI, congestive	heart failure, coronary	heart disease,	hypertension, creatinine	level, arterial stiffness,	LV mass	Age, sex, BMI, blood	pressure
	N Systolic function; assessment Prevalence	of	decreased	systolic	function	5,201 Qualitatively assessed left Women	ventricular ejection fraction 1.8%,	men	6.3%	2,042 Ejection fraction measured by Women	M-mode echocardiography 3.8%,	(modified Quinones men	formula), by the quantitative 10.2%	2-D (biplane Simpson)	method, and by	semiquantitative	2-D visual estimate method	4,257 Visual assessment of left Women	ventricular contractile 0.8%,	performance in multipe men	2-D views 6.0%			3,184 Calculation of ejection Women:	fraction by using end-9.0%,	diastolic and and-systolic men:	left ventricular volumes 22.1%	calculated by the Teichholz	method	4,425 Qualitative assessment from Women:	2-D views 2.1%,	men	3.9%
	Design					Cohort study; men	and women	aged 65-100	years	Cohort study; men	and women	aged 45 years or	older					Cohort study; men	and women	aged 40-95	years			Cohort study;	male and female	American	Indians aged 45	to 74 years			Cohort study; men	and women	aged C 55 years
	Study					Cardiovascular	health study	[8, 34]		Olmsted	County [3]							Framingham	heart study	[5, 13]				Strong Heart	Study [6, 11]							Rotterdam	Study	(current	paper)

Echocardiographic in the Rotterdam Study

Acknowledgments This study was supported by grant 2002B190 from the Netherlands Heart Foundation. The authors would like to thank Inge Haumersen, Saskia Hoornweg, Annemarieke Knetsch and Toos Stehmann for performing echocardiograms.

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