Lorenzo Tiacci
email: lorenzo.tiacci@unipg.itchiara.paltriccia@studenti.unipg.it

Chiara

Chiara Paltriccia

Collaborative Supplying Networks: Reducing Materials Management Costs in Healthcare

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

Introduction

Providing health services with high quality standards and containing public expenditure are increasingly important objectives to be achieved in the context of public healthcare. Among the solutions adopted to contain healthcare spending, one of the most important trend in the public healthcare sector is to entrust some outsourced services, optimizing performance through a contract. In this way, healthcare managers tried to reduce spending without affecting the quality of service offered [START_REF] Roberts | Managing strategic outsourcing in the healthcare industry[END_REF]. The spread of non-core processes outsourcing in healthcare has become very fast because, being the hospital a set of many departments handling a large number of activities, there is the need to entrust outside the no core ones [START_REF] Baffo | A Cooperative Model to Improve Hospital Equipments and Drugs Management[END_REF]. Cost effectiveness is important even for activities that have greater impact on the hospital core business; among those, there is the surgical instruments reprocessing process, which is considered to be a potential area for important cost savings [START_REF] Reymondon | Optimization of hospital sterilization costs proposing new grouping choices of medical devices into packages[END_REF]. van de Klundert, Muls and Schadd [START_REF] Van De Klundert | Optimizing sterilization logistics in hospitals[END_REF] studied the logistic activities between the central sterilization service department and the operating theater. These activities affect total costs faced by the operating block. Hospitals that outsource these types of activities are still very few.

Inventory management of drugs and medical devices is also become a very important argument for hospital management. Many medical organizations reorganized their logistics in order to contain costs and ensure quality in services provided [START_REF] De Vries | The shaping of inventory systems in health services: A stakeholder analysis[END_REF].

This paper investigates a new outsourcing model for the management of the operating room materials, inspired by a real case study of a network of enterprises born in Central Italy, in the Umbria Region. The network is based on the VDO network model [START_REF] Saetta | The innovative model of the Virtual Development Office for collaborative networked enterprises: the GPT network case study[END_REF] and provides the supplying of all the consumables for the operating room and the reprocessing service of surgical instruments. The network business model provides the implementation of the RFId technology for the automatic and continuous monitoring of hospital's inventories, and for the total traceability of all the materials utilized during surgeries. Through reading tags, stickers on which one can transcribe information on circuits, it is possible to have remote tracking. Inventory tracking becomes easier than ever and many other probable applications of RFId technologies have been proposed [START_REF] Choi | Pre-season stocking and pricing decisions for fashion retailers with multiple information updating[END_REF]. As evidenced by Sarac, Absi and Dauzere-Peres [START_REF] Sarac | A literature review on the impact of RFID technologies on supply chain management[END_REF] this technology may improve the potential benefits along the supply chain reducing inventory losses, increasing efficiency and speed of the processes involved and improving information accuracy.

The integrated service, provided by the network as a single entity, includes: 1) surgical instruments sterilization service; 2) provision of sets of surgical instruments for surgical procedures; 3) provision of disposable non-woven materials, such as surgical drapes, masks, gloves, caps, gowns; 4) provision of disposable surgical devices, such as suture threads, syringes, video-laparoscopic devices; 5) provision, control and maintenance of medical equipment.

The specific characteristic of the case study, with respect to traditional models of materials management, consists in the implementation of the RFId technology, and in the long-term strategic cooperation between the supplying companies. Aim of the work is to provide a model to evaluate the effect of these two key factors on total operational costs.

2

The model

This case study refers to a stable network of companies located in central Italy, in the region of Umbria. The network provides an integrated set of services for the operating room. The network, named Sanitanet, is composed of five companies: four of them are companies already operating as single suppliers in the healthcare sector, while the fifth one is a University Spinoff in the field of collaborative networks management. For the purpose of the present work, we consider in the model just two of the five companies (Company A and Company B).

Company A provides a 'pay per use' service of sterile surgical instruments kits. These single-use kits are specifically designed for each surgery. This company owns all the surgical instruments composing the kits and reprocesses them in its own plant outside the hospital. At the beginning of each day, the company brings all the surgical kits needed for the daily planned surgery to the hospital. At that time, it withdraws the kits utilized the day before to reprocess them at its plant.

Company B provides non-woven surgical protective drapes for patients, operators and furniture (beds, trolleys, etc.). The supplied materials include masks, gloves, caps, gowns and drapes. All these items are packaged as single-use 'custom pack', specifically designed for each surgery type. Thus, each custom pack provides all the necessary materials for a single surgery. The company periodically delivers its supplies, based on orders placed by the hospital staff every month.

As already mentioned, the specific characteristic of the case study consists in: 1) the implementation of the RFId technology; 2) the long-term strategic cooperation between the supplying companies. We will refer to these two key factors with the terms 'RFId effect' and 'Network effect' respectively. The impact of these two factors on the Expected Total Relevant Costs (ETRC) will be evaluated through an analysis of scenarios. In the next sections we will formalize the 'Network effect' and the 'RFId effect'.

Notation

i: different products line Q i : order quantity of item i [units] D i : mean annual demand of item i [units/year] A: cost per shipment for Company B without the network effect [€/roundtrip] A': cost per shipment for Company B with the network effect [€/roundtrip] r: inventory carrying charge [€/€/year] v i : unit variable cost of item i [€/unit] k i : safety factor for item i

Network effect

The Network effect allows companies to share setup costs, which substantially correspond to transportation costs. We assume that cost per shipment is proportional to the Euclidean distance covered for the shipment. Companies A and B may share some part of the way to the hospital. In particular, Company B can take advantage of the daily frequency of the shipment of Company A. In this case, the lower distance that can be covered in a roundtrip is equal to the perimeter of the triangle (see Fig. 1) formed by the Hospital (point H), Company A (point A), and Company B (point B). Thus, when the two companies cooperate as a network, the shipment trip will always start from, and finish at, Company A plant, due to the necessity to bring back the utilized kits from the hospital. The round trip will consist of:  load of sterile kits at Company A plants  trip from Company A to Company B  load of packs from company B  trip from Company B to the Hospital for the delivery of kits and packs  trip from the Hospital to Company A to bring back utilized kits

Fig. 1. Schematic position of companies and hospital

To estimate the savings achievable through the network effect, the cost per shipment related to the network configuration have to be compared with cost per shipment when companies act individually. The condition for evaluating the convenience of the network collaboration is that (

22 AB AH BH BH AH    
). In this relation, the first term represents the total length of the round trip in a network collaboration. The second term describes the total distance travelled by the two companies, if they work individually. The relation can be simplified in the following way: AB BH AH . As the sum of two sides of a triangle is always greater than only one side, the last relation is always verified. This implies that working as a network always allows reducing cost per shipment.

The total savings SV achievable under the 'network effect' will be proportional to 2 2 ( )

SV BH AH AB AH BH     
. From a Network perspective, this reduction of shipment cost can be entirely assigned to Company B. Indeed, it is noteworthy that shipment cost does not affect the replenishment policy of Company A, which is obliged to ship the required quantities on a daily basis. On the contrary, a reduction of shipment cost could determine a variation of the optimal quantity shipped by Company B. In fact, the optimal reorder quantity for each item i is equal to the Economic Order Quantity 2/

EOQ

A D v r    . So if the shipment cost A drops to A' when the network effect is present, the optimal order quantities of each item also decrease. In this view, as the Company B shipment cost without the network is equal to A = 2BH, A' can be estimated as:

A' = A -SV =2BH -[2BH +2AH -(AB + AH + BH)]=BH + AB -AH.
Thus, it is possible to define the 'Network coefficient' λ as the ratio between A' and A, with 0 ≤ λ ≤ 1:

1 2 - 2 AH AH BA A B      (1)
λ depends from the mutual positions of Company A, Company B and the Hospital. In summary, when the scenario provides the network effect, the cost per shipment will be equal to λA, and consequently, if a continuous review policy is adopted, reorder quantity Q i will be calculated as:

2/ i i i Q A D v r     (2)

2.2

RFId effect

Among the advantages related to the implementation of RFID technology, we consider: 1) to avoid incomplete shipments, misplacements and theft; 2) to possibly implement a continuous review policy. The first benefit has been modelled using the study by Ustundag and Tanyas [START_REF] Ustundag | The impacts of Radio Frequency Identification (RFID) technology on supply chain costs[END_REF]. They considered that RFID technology implementation eliminates item losses caused by theft, incorrect positioning and incomplete shipments. Only damages that can occur during transportation cannot be avoided. This effect can be considered using the following four coefficients: α (incorrect positioning), β (damage), γ (theft) and δ (incomplete shipment). They represent the error rates related to the corresponding causes. Table 1 shows the values, derived from the experimental study of Ustundag and Tanyas [START_REF] Ustundag | The impacts of Radio Frequency Identification (RFID) technology on supply chain costs[END_REF], that has been assumed in our study.

As far as the second benefit is concerned, the conceptual model assumes that without the implementation of the RFId technology a periodic review policy is adopted, while the RFId effect allow implementing a continuous review policy. In the following subsections, the description of both policies is carried out.

Technology α (%) β (%) γ (%) δ (%) non RFID 2 0.2 0.5 0.3 RFID 0 0.2 0 0 Table 1.
Error rates of non-RFId and RFId integrated systems Periodic reviewno RFId effect. Without the RFID effect, Company B actually adopts a periodic review policy (R, S), with a review period R equal to 2 weeks, which is common for all the four items. This type of policy is very common in healthcare [START_REF] Nicholson | Outsourcing inventory management decisions in healthcare: Models and application[END_REF], and it is often adopted when it is not possible to have an automatic monitoring of the warehouse. Indeed, if the inventory has to be checked manually, it is usually preferred to limit the number of times the checking activities have to be performed. Furthermore, if the orders are placed on a periodic basis, different items can be incorporated in the same shipment in order to save on transportation costs. For each item i, the order-up to level S i and the safety stocks SS i are calculated respectively as: S i =SS i + D i (R+L); SS i = k i σ (R+L)I , where σ (R+L)i is the standard deviation of demand during R+L, and k i is the safety factor. The safety factor k i is determined by imposing a specified service level required by the customer. Given the critical function of the supplied items, the required service level is high. We assumed a value of P = 99.9% of demand satisfied immediately from the shelf ('fill rate'). From this condition, the value of k i can be calculated in the considering the following function [START_REF] Silver | Inventory Management and Production Planning and Scheduling[END_REF]:

  () 1 () ii ui R L i P D R Gk     (3)
where G u ( . ) is the loss probability function, equal to:

( ) ( ) ( ) d ( ) (1 ( )) u k G k u k u u k k k          (4)
() k  being the unit normal density function, and Φ(k) the corresponding distribution function. From the value of G u (k i ), calculated from (3), it is possible to determine the value of k i using the tabular form of eq. ( 4).

Continuous review -RFId effect.

When RFID technology is implemented, Company B can apply a continuous review policy (s, Q). In this case the optimal order quantity Q i , for each item i, is calculated through the Economic Order Quantity (EOQ):

2/ i i i i Q EOQ AD v r  (5)
Note that, if the network effect is simultaneously present, the network coefficient λ has to be considered to calculate order quantities using eq. ( 2), because A decrease to A'=λA. The reorder-point s i and safety stocks SS i are calculated in this case through:

s i =SS i + D i L; SS i = k i σ (L)I
, where σ (L)i is the demand standard deviation during the lead time L. To find the values of the safety factors k i that allows us to reach the fill rate P = 99.9%, it is necessary to calculate the loss function as (see [START_REF] Silver | Inventory Management and Production Planning and Scheduling[END_REF]):

  () 1- () i i ui L PQ Gk   (6)
Then the value of k i can be determined using the tabular form of eq(4).

Scenario Analysis

Four different scenarios will be compared on the basis of the annual Expected Total Relevant Costs (ETRC), which is considered composed by four components: replenishment costs, holding costs, RFId implementation costs, and costs related to thefts and misplacements. The total annual costs related to RFId implementation has been estimated by summing the periodic amortization payment, related to hardware and software investments, and the annual costs of the 'one use' UHF tags, and it is equal to 4434 [€/year] (the detailed costs are omitted due to space limitation). The impact of thefts on the ETRC is calculated considering a cost equal to the value of each item stolen. The cost of items misplaced is considered equal to item value only when item are expired and cannot be used if they are found. In the model it is assumed that the 50% of misplaced items expires before the finding, and a cost equal to the value of the item is considered; the other 50% is considered utilizable and for this reason it does not represent a cost. The four scenarios considered are described in the following.

Scenario 'AS IS'. In the 'as is' scenario neither the 'Network effect' nor the 'RFId effect' are present. Thus, the companies operate individually, Company B utilizes a periodic review policy, with a cost per shipment equal to A, where the products line share the same shipment. ETRC can be estimated through:

() 22 i i R L i i i i i i DR A ETRC k v r D v R                      (7)
In [START_REF] Choi | Pre-season stocking and pricing decisions for fashion retailers with multiple information updating[END_REF], the first term corresponds to replenishment costs, the second one to carrying costs, and the last one approximate costs associated to thefts and misplacements.

Scenario 1 -Network effect. Company A and B belong to the same network. Company B still adopts a Periodic Review policy, but it is possible to share the cost per shipment with Company A. Thus, ETRC can be estimated through [START_REF] Choi | Pre-season stocking and pricing decisions for fashion retailers with multiple information updating[END_REF] by substituting the shipment cost A with A'=λA.

Scenario 2 -RFID effect. In this scenario, the companies still operates individually, but Company B implements a continuous review policy, which is enabled by the RFId implementation. The cost per shipment between Company B and the Hospital is still equal to A, because it is not shared. Each shipment contains only one product line, due to the different times each product line reaches the respective reorder point. In this case, there are no costs related to thefts and misplacements, while the annual cost related to RFId implementation is considered:

() 2 ii i L i i RFId ii i D EOQ ETRC A k v r C EOQ             (8)
Scenario 3 -Network + RFId effects. The Network effect and the RFId effect are simultaneously present. Thanks to RFId technology Company B can implement a continuous review policy. At the same time, each time a product line reaches the reorder point, the corresponding shipment can be shared with Company A, thanks to the network effect. Thus, ETRC can be estimated through eq.( 8) by considering a shipment cost equal to A'=λA, instead of A. Note that even the optimal quantities EOQ i are affected by the decrease of the shipment cost (see eq. ( 5)).

Numerical experiment and discussion

The values utilized in the experiments are related to a hospital placed in a city in the south of the Umbria region, in Italy: cost per roundtrip between Company B and the Hospital A = 50 [€], network coefficient λ = 0.1158, inventory carrying charge r = 0.25 [€/€/year], lead time L = 2 days, required service level (demand satisfied directly from the shelf) P = 99.9%. The annual demand data of the four item lines considered are related to the surgeries done in the hospital during the year 2012. Each product line represents a specific surgical discipline custom pack of non-woven drapes. Demand is assumed to be exponentially distributed, and the annual average values Di and the value vi of each item are reported in Table 2.

The value of k i for both the periodic and the continuous review policies have been derived using the procedures described in Section 5. Table 3 to the numerical experiment. In scenario 1, by virtue of the option of cooperating as a network, there is the possibility for Company B to share shipment costs with Company A, which supplies the hospital on a daily basis. This is of course preferable with respect to the AS IS scenario, because holding costs remain unchanged, and transportation costs are reduced by a factor equal to λ. Results related to scenario 2 show that, even in absence of the network effect, the implementation of the RFId technology makes the adoption of a continuous review policy more convenient. This is due to two reasons: firstly, the RFId annual investment is lower than the annual costs related to thefts and misplacements. Secondly, the parameters of the continuous review policy (s and Q) are optimized for each product line, while in the periodic review policy the review period R is the same for all product lines and it is imposed by the hospital organization (R = 1 month). In scenario 3, the effect obtainable combining the RFId technology with networked cooperation among enterprises is evaluated. The reduction achievable in terms of ETRC is notable, reaching almost the 48% with respect to the AS IS scenario. It is noteworthy that the interaction of the two effects brings to a cost reduction higher than the sum of the savings obtainable when the two effects are applied separately. This is due to the fact that the Network Effect, by allowing decreasing the cost per shipment, has a much more great impact on policies with frequent of shipments (s, Q) then on policies with low number of shipments (R, S). Thus, only the simultaneous adoption of the RFId technology and the collaborative network model allows maximizing the expected savings.

Conclusions

In the paper a methodology to evaluate possible savings of a new business model of collaborative supply network in the healthcare sector is described. The case study show that an integrated supplying service for the operating room can be less expen-sive than traditional models, while maintaining an adequate service level to the patient. In fact, the presence of RFId technology allows the implementation of a continuous review policy, which is known to reduce the uncertainty period with respect to periodic review policies. Consequently, relevant savings related to holding costs are achievable. At the same time, the collaborative network of suppliers allows sharing transportation costs. In this way, the costs connected to shipments, which are typically higher in continuous review policy, are limited.

It is reasonable to assume that the economic benefits achievable in reality may increase as the number of different products handled and the number of companies involved increase. In fact, when there are more than four products considered in this work, it is correct to assume that, even by adopting a continuous review policy, the replenishment instant may be the same for more products simultaneously. In the same way, shipment costs can be lowered even in the case where more than two companies are considered, by optimizing the routing from Company A to the Hospital.

In order to generalize the results obtainable by the proposed approach, future improvements consists in performing a sensitivity analysis on the parameters that can have a direct influence on total costs, starting from the network coefficient λ. Finally, a discrete event simulation model could be designed to accurately evaluate the impact of thefts and misplacement on real costs and service level, in order to better quantify the benefits connected to RFId implementation.

Table 2 .

 2 Data related to the 4 product lines

	shows the results related

Table 3 .

 3 Results of the numerical experiment


Suthep Butdee1

Uten Khanawapee2

Collaborative Knowledge for Analysis Material Flow of a Complex Long Stud using Multiple Stoke Cold Heading

Keywords: Collaborative Knowledge, DEFORM, Complex Long Stud Head Forging, Analysis Material Flow

Productivity Improvement is one of the most important strategies for every enterprise. Head cold forging is a widely common production process which can achieve economical processes and less energy consumption. Die is the major key of the forging process but how to perform an effective design, needs several years of experiences or using engineering tools for assistance. This paper proposes the collaborative die design and analysis by combining engineering methods and industrial experts to correct problems and to validate a new and complex design. DEFORM is used to investigate suitable parameters by guidance from the expert. One of the classical problem in the head cold forging is to make a small long complex stud. It is found from simulation that a five step of punch with suitable taper angle is the most effectiveness.

Introduction

Cold forging aims for producing net and near-net-shape parts, such as shafts, axles, bolts, gears and so on, using room temperature. Products in different shapes and sizes are formed by high speed and high pressure processes with tool steel or carbide dies which are able to increase the hardness, yield, and tensile strengths. Cold heading is used for making screw production. It transforms wire into the designed shapes by die and punch cavities. Die is one of critical components of such processes. The force of the blow creates enough pressure to cause the metal to flow outward into a die cavity. The head or upset portion of the part is larger in diameter than the original billet. It commonly deforms aluminum, carbon and alloy steels. Presently, cold forging can produce ± 0.025 mm. of tolerance. The process is applied for producing nuts, bolts, screws, rivets, and other fasteners. Complex shapes of products require multi-step of cold heading or combine with other processes. Consequently, the blows may be struck, with the billet moving through a sequence of dies. Extrusion is one of the effective process applied to assist the cold forging for creating the ratio of head to shank size beyond the normal cold heading capability. Cold heading shape design can be single blow headers or double blow headers. The single blow headers are the simplest and fastest process.

They can produce hundreds of pieces per minute but are limited to minor shank extrusion and simple head shapes using a single stroke machines which a wire roll is sheared in a die, struck one blow, and ejected. The process type is suitable for the material lends itself easily to upsetting. Hard materials are deformed by double blows. The first punch delivers the metal flow. The shape is completed with the second blow. Double stoke headers are necessary when the diameter of the head is more than two sizes. The large heads of a nut needs multi-die machines and multiple step cold heading process. Multistation or progressive headers are used, when many strokes are required for more complicated contours dies [1]. In our work recently, university-industrial collaboration is preferable to Thai-government policy. In production engineering department and department of tool and die are concentrated on material flow analysis using DEFORM, a commercial software. Different types of products, processes and material flow of cold and hot forging are captured for knowledge. It is rarely used and validated even on the real-time problem solving. In this case of research study, collaborative works of specialist CAE lab engineer and industrial die design expert team are on-line discussing via a suitable social media platform that will be explained in a next section. Industry has received more and more complex and hard shapes of products. The paper proposes and discusses an analysis of material flow for a long stud via a line environment. Such product needs a multi-stoke machine together with progressive die and punch. DEFORM, is applied to solve problem of material flow in a particular shape, size, and its tolerances. The knowledge of die and punch design has been built in the library before being used and routinely updated by both sides. A collaborative design process is created via a common social network on their own smart mobile phones. Therefore, A LINE network is created in group in order to share knowledge and ideas. Including some parts of solving solutions before they have been stored in the database library.

Related Works and Problems

This section presents previous works which relate to our paper and defines scope of study. Im et al. [START_REF] Im | Computer aided process design in cold-former forging using a forging simulator and a commercial CAD software[END_REF] presented computer aided process design in cold-former forging of ball joint using a forging simulator and a commercial CAD software. The forging sequence design and its detail design are generated interactively from a design database, knowledge-based rules and basic laws. The simulation technique is used for verification. Die set design and die manufacturing information are generated automatically. Such techniques can improve productivity. Kim and Im [START_REF] Kim | An expert system for cold forging process design based on a depth-first search[END_REF] proposed an expert system for multi-stage cold-forging process design with a re-designing algorithm. The system consists of a user interface, a system shell, a material data-base, and a design rule-base. The system developed is able to reduce trial-and-error by design engineers in determining forging parameters. Stephen and Vollertsen [START_REF] Stephen | Upset Ratio in Laser-based Free Form Heading[END_REF] presented a laser-based micro upsetting process which takes advantage of scaling effects to optimize the conventional multi-stage upsetting. In conventional process, it is risk of bulking and cracks, whereas the laser-based process separate treatment process between the upsetting steps omitted. MaCormack and Monaghan [START_REF] Conor | A finite element analysis of cold forging dies using two and three dimension models[END_REF] proposed the FEA of clod forging die using two and three dimensional models using DEFORM. The result showed contact and friction.

Finding that the highest stress concentration occurred within the body of the tool and not along the contact surface. Weroński et. al. [START_REF] Weronski | Research of upsetting ratio in forming processes on a threeslides forging press[END_REF] explained research of upsetting ratio in forming processes on a three slides forging press. Hussain et. al [START_REF] Hussain | A Study on Cold Forging Die Design Using Different Techniques[END_REF] proposed a study on cold forging die design using different techniques. Danno et.al. [START_REF] Danno | Multistage cold forging of thin-walled components[END_REF] proposed multistage cold forging of thin-walled components. The case studies were conducted through FE simulation and experiments. The result showed that the process was effective to reduce the forming load and improve flow in the forming of two kinds of thin aluminum alloy components with multi thickness. Tae-Wan Ku et. al. [START_REF] Ku | Multi-stage cold forging and experimental investigation for the outer race of constant velocity joints[END_REF] proposed multi-stage cold forging and experimental investigation for the outer race of constant velocity joints. Joun et.al [START_REF] Joun | Finite element analysis of presented die set in cold forging[END_REF] presented an application-oriented finite element approach to forging die structural analysis. Stress on tools and work pieces are the critical problems in cold forging processes which may cause fatigue cracks. Several experimental and numerical have been studied on the fracture and estimations of service life of forging tools. However, little research is on the complex stud analysis using tool steel and hard steel. It rarely presented collaborative sharing knowledge between university and industry in aspect of real time and on-line. The next section explains the collaborative model. Industrial knowledge is indispensable context for improving productive and competitive enterprises. Particularly in the area of tools and die design because it needs many years of learning by their own experiences. In addition, different areas requires alter knowledge and know-how. In the aluminum extrusion die design requires a specific knowledge together with global collaborative working group [START_REF] Tichkiewitch | Knowledge Management for the design of dies in aluminum extrusion process[END_REF][START_REF] Butdee | Methodology of Knowledge Library Management for Concurrent Cooperative Design[END_REF][START_REF] Pimapunsri | Industrial Knowledge Management using Collaborative Knowledge Acquisition in a Consultancy Project[END_REF][START_REF] Pimapunsri | Collaborative Negotiation between Designers and Manufacturers in the Wood Furniture Industry using Particleboard or Fiberboard[END_REF]. Knowledge is able to manage in different types. Case-based reasoning is well known and suitable for industrial knowledge because it can learn knowledge more from the previous experience comparing theory general basic knowledge and adapt to fit to solve new problems quickly [15, [START_REF] Janthong | Combining Axiomatic Design and Case-Based Reasoning in a Design Methodology of Mechatronics[END_REF][START_REF] Butdee | Collaborative Aluminum Profile Design to Adaptable Die Process Planning Using Neural Networks[END_REF]. Knowledge management plays an important role of an advanced enterprise. Basically, knowledge can be explicit and implicit but need to capture and store in a well-structure system. Capitalization knowledge is a critical part of knowledge management [18, 19, 20, and 21].

Collaborative University and Industry system

In some areas of cold forging design needs a lot of experience in order to improve productivity, quality and efficiency. Presently, customers can easily link to global sourcing and need a manufacturer to response satisfactory and competitively in aspects of cost and time. This paper proposes a creative model which collaborate among involving workforces. They are design knowledge engineer, advisor and industrial knowledge designer via a common social media, LINE tool. Problems comes to industrial design department all the time of working day, and it is time consuming to solve such problems. It routinely uses narrow scope of experience. The company's need is to improve productivity and increase more competitiveness by sharing problems and solutions. Fig. 1 shows the collaborative design system which composes of three main players; the industry design engineer, the university advisor and the lab knowledge engineer. They are all participants via LINE environment. The problem-solving procedures and solutions are stored in the knowledge base which can be useful as a reference and future use on both sides. The lab knowledge engineer can perform a new experiment shortly, whereas the industry design engineer can trial a new process whenever the production line is available.

Fig.1. Collaborative knowledge design system

Figure 1 shows the collaborative knowledge design system. It is the simplest communication media system using LINE which popular in Thailand. New specific problems (products) coming from customer which are different from the previous parts are posted in the LINE group linked to every member on their smart phones. The LINE is interfaced to the knowledge base library which attracts the useful knowledge in a certain format. The solution is divided into two categories; real-time and storage. Some experience problems can be provided directly by specialists whereas the other some need time to analysis. Storage knowledge is retrieved from library. Some new solution which is invested from diary performance will be recorded in the new solution part of the memory. On the other hand, the new experiment which existed from the lab will store the new experiment part. Both parts of memory are linked to the knowledge base library (KBL). However, the KBL requires an effective management to share and not share information. It is defined as public and private sections.

Experimental Study

The case study selected to show how problems can be solved by collaborative model. A long small complex stud using 1035 (S35C) as shown in the Fig. 1. The present facing problem is that the material has blended because of the length of work-piece. The collaborative team is discussed and agreed that the process should be increased one more step of deforming. Process change causes risk of failure and take more time to solve problems. Fortunately, the collaborative method can reduce the risk and time saving. The session presents the new process of the developed model. The team members agree to start with the three punch and three die process. It consists of a body and steps on the head and tail. The difficulty areas are the chafer and fillet. They are very small and have close tolerances.

. Fig. 2. Example of a long small complex stud heading part DEFORM of CAE is taken into account for the three punch and three die process analysis. The parameter assigned for heading speed is 300 m/s and fiction coefficient is 0.08. The first experiment on the 150 th step. The heading process is stopped. It is because a shock size reduction. The design expert suggests that heading step should be increased. The knowledge engineer takes the five punch and five die process with the concave size reduction. 4 shows the third experiment of using five punch and 5 die process the first modification. It is found that the billet could not go through. It occurs a flashing problem in the third die. The collaborative team is then agrees to modify as an opening die. The billet is formed to become tapers on both sides. The second die is modified by increasing on the straight flow line to support the billet. Fig. 5. The five punch and die process with the second modification Fig. 5 shows the result of the forth experiment. It is still having flashing problem on the fifth die. The expert suggests that the punch 2 and punch 4 should be modified. The angle must be reduced smaller than the former in order to improve a better flow inside the third die. In addition, the straight line area must be extended to protect distortion. Fig. 6. The final modification and its result Fig. 6 shows the final modification which the second and third die are modified. The second die should be a very small angle of orifice whereas the fourth die must have very long straight line area in order to support the billet while is flowing through the whole die.

Concluding Remarks

The new concept of collaborative knowledge for analyzing material flow of a long complex stud using multi stoke cold heading has been presented. The cold heading die process design is discussed followed by the related works and problems statement. The collaborative industrial design is also expressed. The proposed development system is shown. A selected case experiment study is presented. A small long complex stud is experimented and investigated the best result from the collaborative team. It is only the fifth time of trial on the DEFORM software and can achieve a well-result to guide the industrial design engineer. This method impacts productivity and is less time consuming to reach an effective design and manufacturing.

Fig. 3 .

 3 Fig. 3. The second experiment of using the five punch and five die process The Fig. 3 illustrates the result of the second experiment. The flashing problem still occurs in the third die of the 301 st step. The expert further suggests that the second die

Fig. 4 .

 4 Fig.4. The five punch and five die with the first modification Fig.4shows the third experiment of using five punch and 5 die process the first modification. It is found that the billet could not go through. It occurs a flashing problem in the third die. The collaborative team is then agrees to modify as an opening die. The billet is formed to become tapers on both sides. The second die is modified by increasing on the straight flow line to support the billet.


Florent Moissenet
email: florent.moissenet@mailoo.org

Laurence Chèze

Raphaël Dumas

Moissenet Florent

Cnrfr -Rehazenter

joint contact, ligament and bone forces during gait

Keywords: Musculoskeletal modeling, musculo-tendon force, joint contact force, ligament force, bone force, musculoskeletal structures interaction, static optimization, model validation Musculoskeletal modeling, musculo-tendon force, joint contact force, ligament force, bone force, musculoskeletal structures interaction, static optimization, model validation

Musculo-tendon forces and joint reaction forces are typically estimated using a two-step method, computing first the musculo-tendon forces by a static optimization procedure and then deducing the joint reaction forces from the force equilibrium. However, this method does not allow studying the interactions between musculo-tendon forces and joint reaction forces in establishing this equilibrium and the joint reaction forces are usually overestimated. This study introduces a new 3D lower limb musculoskeletal model based on a one-step static optimization procedure allowing simultaneous musculo-tendon, joint contact, ligament and bone forces estimation during gait. It is postulated that this approach, by giving access to the forces transmitted by these musculoskeletal structures at hip, tibiofemoral, patellofemoral and ankle joints, modeled using anatomically consistent kinematic models, should ease the validation of the model using joint contact forces measured with instrumented prostheses. A blinded validation based on four datasets was made under two different minimization conditions (i.e., C1 -only musculo-tendon forces are minimized, C2musculo-tendon, joint contact, ligament and bone forces are minimized while focusing more specifically on tibiofemoral joint contacts). The results show that the model is able to estimate in most cases the correct timing of musculo-tendon forces during normal gait (i.e., the mean coefficient of active/inactive state concordance between estimated musculo-tendon force and measured EMG envelopes was C1: 65.87%, C2: 60.46%). The results also showed that the model is potentially able to well estimate joint contact, ligament and bone forces and more specifically medial (i.e., the mean RMSE between estimated joint contact force and in vivo measurement was C1: 1.14BW, C2: 0.39BW) and lateral (i.e., C1: 0.65BW, C2: 0.28BW) tibiofemoral contact forces during normal gait. However, the results remain highly influenced by the optimization weights that can bring to somewhat aphysiological musculo-tendon forces.

Introduction

Many musculoskeletal structures (e.g., bones, ligaments, muscles, tendons) are solicited to perform a movement [START_REF] Pandy | Muscle and joint function in human locomotion[END_REF]. The understanding of these structures function and the interaction between them [START_REF] Cleather | An optimization-based simultaneous approach to the determination of muscular, ligamentous, and joint contact forces provides insight into musculoligamentous interaction[END_REF][START_REF] Collins | Muscle-ligament interactions at the knee during walking[END_REF][START_REF] Pandy | Muscle and joint function in human locomotion[END_REF] remains a challenge that could allow in the future assisting clinicians in term of diagnosis and treatments in case of orthopaedic or neurologic disorders. In vivo measurements of musculo-tendon, joint contact, ligament and bone forces exist [START_REF] Behrmann | Fiber optic micro sensor for the measurement of tendon forces[END_REF][START_REF] Bergmann | Hip contact forces and gait patterns from routine activities[END_REF][START_REF] Bey | Measurement of in vivo tendon function[END_REF][START_REF] Beynnon | Anterior cruciate ligament strain in-vivo: a review of previous work[END_REF][START_REF] D'lima | In vivo contact stresses during activities of daily living after knee arthroplasty[END_REF][START_REF] Lu | Validation of a lower limb model with in vivo femoral forces telemetered from two subjects[END_REF], but the protocols are invasive and inappropriate for a daily clinical use [START_REF] Fleming | In vivo measurement of ligament/tendon strains and forces: a review[END_REF]. Consequently, 3D musculoskeletal modeling of the lower limb has been proposed [START_REF] Al Nazer | Flexible multibody simulation approach in the analysis of tibial strain during walking[END_REF][START_REF] Anderson | Dynamic optimization of human walking[END_REF][START_REF] Cleather | An optimization-based simultaneous approach to the determination of muscular, ligamentous, and joint contact forces provides insight into musculoligamentous interaction[END_REF][START_REF] Crowninshield | A physiologically based criterion of muscle force prediction in locomotion[END_REF][START_REF] Fraysse | Comparison of global and joint-to-joint methods for estimating the hip joint load and the muscle forces during walking[END_REF][START_REF] Glitsch | The three-dimensional determination of internal loads in the lower extremity[END_REF][START_REF] Hu | Influence of model complexity and problem formulation on the forces in the knee calculated using optimization methods[END_REF][START_REF] Lenaerts | Subject-specific hip geometry affects predicted hip joint contact forces during gait[END_REF]Moissenet et al., 2012a;[START_REF] Pierrynowski | A physiological model for the evaluation of muscular forces in human locomotion: theoretical aspects[END_REF][START_REF] Seireg | The prediction of muscular lad sharing and joint forces in the lower extremities during walking[END_REF][START_REF] Stansfield | Direct comparison of calculated hip joint contact forces with those measured using instrumented implants. An evaluation of a three-dimensional mathematical model of the lower limb[END_REF][START_REF] Wehner | Internal loads in the human tibia during gait[END_REF] as an interesting alternative and several models have been developed [START_REF] Arnold | A model of the lower limb for analysis of human movement[END_REF][START_REF] Delp | An interactive graphics-based model of the lower extremity to study orthopaedic surgical procedures[END_REF][START_REF] Klein Horsman | Morphological muscle and joint parameters for musculoskeletal modelling of the lower extremity[END_REF].

These models allow solving the muscular redundancy problem and estimating the forces transmitted by these musculoskeletal structures during a movement [START_REF] Chèze | State of the art and current limits of musculoskeletal models for clinical applications[END_REF][START_REF] Erdemir | Model-based estimation of muscle forces exerted during movements[END_REF]. However, the validation of these models is arduous [START_REF] Lund | On validation of multibody musculoskeletal models[END_REF]. Electromyographic (EMG) signals are often used to evaluate the estimated musculo-tendon forces but only provide a qualitative [START_REF] Dumas | Influence of joint models on lower-limb musculo-tendon forces and three-dimensional joint reaction forces during gait[END_REF][START_REF] Modenese | An open source lower limb model: Hip joint validation[END_REF][START_REF] Neptune | Contributions of the individual ankle plantar flexors to support, forward progression and swing initiation during walking[END_REF][START_REF] Selk Ghafari | Muscle-driven forward dynamics simulation for the study of differences in muscle function during stair ascent and descent[END_REF][START_REF] Stansfield | Direct comparison of calculated hip joint contact forces with those measured using instrumented implants. An evaluation of a three-dimensional mathematical model of the lower limb[END_REF][START_REF] Thelen | Using computed muscle control to generate forward dynamic simulations of human walking from experimental data[END_REF] or semi-quantitative validation [START_REF] Giroux | EMG-based validation of musculo-skeletal models for gait analysis[END_REF][START_REF] Kaufman | Physiological prediction of muscle forces--II. Application to isokinetic exercise[END_REF][START_REF] Prilutsky | Optimization-based models of muscle coordination[END_REF]). An alternative is to collect joint contact forces using instrumented prostheses [START_REF] Bergmann | Hip contact forces and gait patterns from routine activities[END_REF][START_REF] Brand | Comparison of hip force calculations and measurements in the same patient[END_REF][START_REF] D'lima | In vivo contact stresses during activities of daily living after knee arthroplasty[END_REF][START_REF] Lin | Simultaneous prediction of muscle and contact forces in the knee during gait[END_REF][START_REF] Stansfield | Direct comparison of calculated hip joint contact forces with those measured using instrumented implants. An evaluation of a three-dimensional mathematical model of the lower limb[END_REF]. Indeed, since musculo-tendon forces have a primary role in the joint contact force generation [START_REF] Herzog | The role of muscles in joint adaptation and degeneration[END_REF], a pertinent estimation of joint contact forces should be a reflection of the quality of the estimated musculo-tendon forces and consequently it should provide a quantitative validation metric for the validation of musculoskeletal models [START_REF] Lund | On validation of multibody musculoskeletal models[END_REF].

In such a context, it is necessary to ensure a good interaction between musculoskeletal structures in the model in order to assess the quality of the estimated musculo-tendon forces from the joint contact forces data. However, studies are often based on a traditional two-step method [START_REF] Chèze | State of the art and current limits of musculoskeletal models for clinical applications[END_REF][START_REF] Erdemir | Model-based estimation of muscle forces exerted during movements[END_REF]. First, the musculo-tendon forces are computed using a static optimization procedure and, second, the joint reaction forces (i.e., joint contact and ligament forces) are deduced from the dynamics equation using the optimal muscular solution. Even if this method complies with the forces equilibrium, it does not allow studying the musculoskeletal structures interaction in establishing this equilibrium [START_REF] Cleather | An optimization-based simultaneous approach to the determination of muscular, ligamentous, and joint contact forces provides insight into musculoligamentous interaction[END_REF]. Based on this observation, Lin et al. [START_REF] Lin | Simultaneous prediction of muscle and contact forces in the knee during gait[END_REF] proposed an optimization procedure estimating simultaneously musculo-tendon and joint contact forces using a deformable model of the knee. However, ligaments were omitted and the study was limited to the knee joint that may bring a negative impact on the bi-articular musculo-tendon forces estimation [START_REF] Fraysse | Comparison of global and joint-to-joint methods for estimating the hip joint load and the muscle forces during walking[END_REF]. Optimization based methods computing simultaneously musculo-tendon, joint contact and knee ligaments forces have also been proposed recently [START_REF] Cleather | An optimization-based simultaneous approach to the determination of muscular, ligamentous, and joint contact forces provides insight into musculoligamentous interaction[END_REF][START_REF] Hu | Influence of model complexity and problem formulation on the forces in the knee calculated using optimization methods[END_REF]. However, the estimated forces were not validated.

The first aim of this study is to propose a 3D lower limb musculoskeletal model based on a one-step static optimization procedure allowing simultaneous musculo-tendon, joint contact, ligament and bone forces estimation during normal gait. It is postulated that this approach, by giving access to the forces transmitted by these musculoskeletal structures at both hip, tibiofemoral, patellofemoral and ankle joints, modeled using anatomically consistent kinematic models [START_REF] Gregorio | Mathematical models of passive motion at the human ankle joint by equivalent spatial parallel mechanisms[END_REF][START_REF] Feikes | A constraint-based approach to modelling the mobility of the human knee joint[END_REF]Sancisi and Parenti-Castelli, 2011a), should ease the validation of the model using joint contact forces measured with instrumented prostheses. The second aim is to perform a blinded model validation based on the datasets provided for the "Grand Challenge Competition to Predict in Vivo Knee Loads" organized by Fregly et al. [START_REF] Fregly | Grand challenge competition to predict in vivo knee loads[END_REF].

Material and methods

3D lower limb musculoskeletal model

A previously described [START_REF] Dumas | Influence of joint models on lower-limb musculo-tendon forces and three-dimensional joint reaction forces during gait[END_REF]Moissenet et al., 2012a) 3D lower limb musculoskeletal model, consisting of pelvis, thigh, shank and foot segments and 43 muscular lines of action, was extended by adding the patella to perform this study (Fig. 1). Hip, tibiofemoral, patellofemoral and ankle joint kinematic models are all based on anatomical considerations (Fig. 1). Hip joint is modeled by a spherical joint. Tibiofemoral joint is modeled by a parallel mechanism made of 2 sphere-on-plane contacts (i.e., medial and lateral) and 3 isometric ligaments (i.e., anterior cruciate ligament -ACL, posterior cruciate ligament -PCL and medial collateral ligament -MCL) [START_REF] Feikes | A constraint-based approach to modelling the mobility of the human knee joint[END_REF]. The choice of these ligament combination was made for kinematic reasons in order to ensure a 1-DOF model [START_REF] Ottoboni | Articular surface approximation in equivalent spatial parallel mechanism models of the human knee joint: an experiment-based assessment[END_REF]Sancisi and Parenti-Castelli, 2011b). Patellofemoral joint is modeled by a hinge joint between the patella and the femur and an isometric ligament (i.e., the patellar ligament -PT) between the patella and the tibia (Sancisi and Parenti-Castelli, 2011a). Ankle joint is modeled by a parallel mechanism made of a spherical joint and 2 isometric ligaments (between tibia and calcaneus -TiCaL and between fibula and calcaneus -CaFiL) (Di [START_REF] Gregorio | Mathematical models of passive motion at the human ankle joint by equivalent spatial parallel mechanisms[END_REF]. In the same way as for the tibiofemoral joint, this ligament combination is the one that most fittingly models the joint movement. Then, in order to compute muscular lever arms, a widely-used generic musculoskeletal geometric model [START_REF] Delp | An interactive graphics-based model of the lower extremity to study orthopaedic surgical procedures[END_REF] was adapted to our model (Fig. 1).

Computation framework

First, each segment position is defined using generalized coordinates [START_REF] Dumas | 3D inverse dynamics in non-orthonormal segment coordinate system[END_REF] that consist, for each segment i , in two position vectors (i.e., the proximal i P and distal i D joint centers) and two unitary direction vectors (i.e., i u and i w ) (Fig. 1):

i i T i i P D i ⎡ ⎤ = ⎣ ⎦ Q u r r w (1)
These parameters correspond to a classic set of natural coordinates (Garcia de [START_REF] Garcia De Jalon | Kinematic and dynamic simulation of multibody systems[END_REF]. Details of the segment parameters can be found in [START_REF] Dumas | 3D inverse dynamics in non-orthonormal segment coordinate system[END_REF].

Second, the kinematic constraints k Φ and the associated Jacobian matrix k K are defined for each joint. Since 12 parameters represent the 6 degrees-of-freedom of each segment, rigid body constraints r Φ have to be considered in addition to the kinematic constraints with the associated Jacobian matrix r K [START_REF] Duprey | Influence of joint constraints on lower limb kinematics estimation from skin markers using global optimization[END_REF].

Third, a constrained multi-body optimization [START_REF] Duprey | Influence of joint constraints on lower limb kinematics estimation from skin markers using global optimization[END_REF]Moissenet et al., 2012a) is performed in order to obtain consistent segments positions Q , velocities Q and accelerations Q .

Fourth, the full dynamics equation of the lower limb is written. In contrast with the classical approach, the dynamics equation of the whole kinematic chain is used here [START_REF] Pennestrì | Virtual musculo-skeletal model for the biomechanical analysis of the upper limb[END_REF], introducing the musculo-tendon forces and the Lagrange multipliers instead of motor joint moments [START_REF] Dumas | Influence of joint models on lower-limb musculo-tendon forces and three-dimensional joint reaction forces during gait[END_REF]Moissenet et al., 2012a):

T GQ + K λ = E + Lf (2)
where G is the generalized mass matrix, Q the consistent generalized accelerations,

k r ⎡ ⎤ = ⎣ ⎦ K K K
the Jacobian matrix of both joint kinematic and rigid body constraints, λ the Lagrange multipliers, E the external forces, including both weight and ground reaction forces and moments, L the generalized muscular lever arms and f the musculo-tendon forces.

Fifth, equation 2 gives a direct access to the unknowns only composed of the musculotendon forces and the Lagrange multipliers corresponding straightforwardly to the joint contact, ligament and bone forces (Moissenet et al., 2012a). At this level, the traditional twostep method can be used (Moissenet et al., 2012a) when a parameter reduction (Garcia de [START_REF] Garcia De Jalon | Kinematic and dynamic simulation of multibody systems[END_REF] is introduced. This parameter reduction means that all the Lagrange multipliers can be removed from equation 2. However, a selection of Lagrange multipliers can also be introduced in the objective function with the partial parameter reduction described below.

Partial parameter reduction and one-step optimization

The following linear system can be obtained from the dynamics equation 2:

1 2 1 2 T T ⎡ ⎤ ⎢ ⎥ ⎡ ⎤ - - = - ⎣ ⎦ ⎢ ⎥ ⎢ ⎥ ⎣ ⎦ f L K K λ GQ E λ (3)
where 1 λ are the Lagrange multipliers that we want to introduce in the objective function, 2 λ all the other ones, 1 K and 2 K the associated Jacobian matrices. The second group of Lagrange multipliers 2 λ can be cancelled from equation 3 by projecting the system on the kernel of 2 K , using the projection matrix The unknowns [ ] 1 T f λ , corresponding respectively to the musculo-tendon forces and the selected joint contact, ligament and bone forces, are then introduced in a one-step optimization procedure in order to solve the muscular redundancy problem. A typical static optimization procedure is used and defined as follow [START_REF] Dumas | Influence of joint models on lower-limb musculo-tendon forces and three-dimensional joint reaction forces during gait[END_REF]Moissenet et al., 2012aMoissenet et al., , 2012b):

2 K Z : ( ) ( ) ( ) 2 2 2 2 2 2 2 2 2 1 1 2 2 1 1 1 1 T T T T T T T T T T T T T - - - ⇔ - - ⎡ ⎤ ⎡ ⎤ ⇔ - = - ⎢ ⎥ ⎣ ⎦ ⎣ ⎦ K K K K K K K K K Z Lf Z K λ Z K λ = Z GQ E Z Lf Z K λ = Z GQ E f Z L K Z GQ E λ (4)
( )

1 2 2 1 1 1 1 1 1 min 2 constraint to : T T T T J ⎡ ⎤ ⎢ ⎥ ⎣ ⎦ ⎡ ⎤ ⎡ ⎤ = ⎢ ⎥ ⎢ ⎥ ⎣ ⎦ ⎣ ⎦ ⎧ ⎡ ⎤ ⎡ ⎤ - = - ⎪ ⎢ ⎥ ⎣ ⎦ ⎪ ⎣ ⎦ ⎨ ⎡ ⎤ ⎪ ≥ ⎢ ⎥ ⎪ ⎣ ⎦ ⎩ f λ K K f f W λ λ f Z L K Z GQ E λ f 0 λ (5)
where J is the objective function and W a diagonal matrix composed of the optimization weights associated to the unknowns [ ] 1 T f λ . When an optimization weight is not null, the associated force is minimized and constrained to be positive. Otherwise, when the optimization weight is null, the associated force is only constrained to be positive. The optimization weights used for this study are described below.

Experimental dataset and estimations

In order to perform the blinded validation of this model, a set of estimations was performed based on the datasets provided for the "Grand Challenge Competition to Predict in Vivo Knee Loads" [START_REF] Fregly | Grand challenge competition to predict in vivo knee loads[END_REF]. We present here the mean results for 5 normal gait cycles for each of the four last competitions (subject1: male/166cm/64.6kg, subject2: male/172cm/67kg, subject3: female/167cm/78.4kg, subject4: male/168cm/66.7kg). All subjects have the particularity to have an instrumented knee prosthesis that allows comparing the estimated and the measured medial and lateral knee contact forces during the gait cycle. A full description of the datasets is provided by Fregly et al. [START_REF] Fregly | Grand challenge competition to predict in vivo knee loads[END_REF].

The RMS values of the recorded EMG signals were processed within a window of 25ms (De Luca, 1997) to obtain the EMG envelopes.

Regarding the number of parameters to be minimized (i.e., musculo-tendon, joint contact, ligament and bone forces), many combinations of optimization weights are possible. In order to illustrate the impact of the optimization weights, two minimization conditions were performed for each gait cycle of each subject. Condition 1 (i.e., C1) stands for the traditional optimization strategy where only musculo-tendon forces are minimized. Under condition 2 (i.e., C2), all the musculo-tendon forces and Lagrange multipliers 1 λ are minimized while focusing more specifically on tibiofemoral joint contact forces since these forces are usually overestimated [START_REF] Fregly | Grand challenge competition to predict in vivo knee loads[END_REF][START_REF] Gerus | Subject-specific knee joint geometry improves predictions of medial tibiofemoral contact forces[END_REF]. The optimization weights chosen for each condition are given in Table 1.

Blinded model validation

A blinded validation was performed in order to evaluate the model's ability to estimate musculo-tendon, joint contact and bone forces during normal gait.

First, the estimated musculo-tendon forces were compared to the subject's EMG envelopes using the coefficient of concordance proposed by Dickerson et al. [START_REF] Dickerson | Experimental evaluation of a computational shoulder musculoskeletal model[END_REF] and recently extended to the gait analysis by Giroux et al. (Giroux et al., n.d.).

Briefly, this method uses active/inactive state concordance between the estimated musculotendon forces and the EMG envelopes to compute a coefficient of concordance defined as the percentage of concordance elements. For this study, muscles were defined active when the mean value was above 20 percent of the maximum of the estimated musculo-tendon force and of the EMG envelope, respectively [START_REF] Pedersen | Direct comparison of muscle force predictions using linear and nonlinear programming[END_REF] during each of the 7 gait phases [START_REF] Perry | Gait Analysis: Normal and Pathological Function[END_REF]) (Fig. 2 &5). A set of published EMG envelopes [START_REF] Perry | Gait Analysis: Normal and Pathological Function[END_REF] was processed similarly (Fig. 2 & 5) and stands for an asymptomatic active/inactive state reference. This method allows a semi-quantitative validation regarding the model's ability to estimate musculo-tendon forces in concordance with the subject's EMG envelopes and with asymptomatic reference as in previous studies [START_REF] Modenese | An open source lower limb model: Hip joint validation[END_REF][START_REF] Stansfield | Direct comparison of calculated hip joint contact forces with those measured using instrumented implants. An evaluation of a three-dimensional mathematical model of the lower limb[END_REF].

Second, the estimated tibiofemoral contact forces (i.e., medial and lateral contact forces)

were compared to the measured tibiofemoral contact forces. For this, first and second force peaks root mean square error (i.e., RMSE) and correlation coefficient (i.e., R 2 ) were computed. This method allows a quantitative validation regarding the model's ability to estimate tibiofemoral joint contacts forces.

Third, the estimated hip contact and femur axial forces were compared qualitatively to measured data of the literature.

Only a selection of musculo-tendon, joint contact, ligament and bone forces are reported in the results. The most important muscles during gait were kept and the muscles having similar activities (e.g., vastus medialis and vastus lateralis) were removed. Moreover, only the joint contact and bone forces for which in vivo measurements are available are presented. For illustrative purpose, ACL and PCL forces are also reported. Additional results are available in the Supplementary material.

Results

Under the condition C1, the estimated musculo-tendon forces patterns are in a good agreement with most of the subject's or the asymptomatic active/inactive states (Fig. 2). This observation is confirmed by substantial coefficients of concordance (Table 2). However, abnormal forces appear on gastrocnemius medialis during phase 1 (i.e., loading response) and on gluteus maximus during phase 4 and 5 (i.e., pre-swing and initial swing). Vastus medialis shows an abnormal force during all the stance phase. It also shows abnormal peaks of force during phases 4 and 5 unlike the asymptomatic inactive state, but like the active state of subjects 1, 3 and 4. Rectus femoris shows a force during almost the whole stance phase. The estimated tibiofemoral forces present a good correlation with implant measurements (Table 2 ). On the whole, the estimated medial and lateral tibiofemoral contact forces have a similar pattern and amplitude with a second peak of force higher than the first one (Fig. 3). The estimated hip contact and femur axial forces present similarities with literature measurements [START_REF] Lu | Validation of a lower limb model with in vivo femoral forces telemetered from two subjects[END_REF][START_REF] Stansfield | Direct comparison of calculated hip joint contact forces with those measured using instrumented implants. An evaluation of a three-dimensional mathematical model of the lower limb[END_REF]. But again, these forces are overestimated. Roughly, ACL and PCL forces produce one or two peaks of force under 2 BW (Fig. 4).

Under the condition C2, the tibiofemoral contact forces are strongly improved ( ). The amplitudes of the hip contact force and femur axial forces are reduced and in better agreement with the literature values. However, the coefficients of concordance of estimated musculo-tendon forces are decreased (Table 2). This is illustrated, in most of the cases, by the aphysiological extinction of the semimembranosus and gastrocnemius medialis during stance phase, and by a decreased force of the tibialis anterior during swing phase. It is interesting to observe that the decrease of the gastrocnemii force is compensated by a force increase of the soleus. Nevertheless, the vastus medialis force is decreased during stance phase since it only remains force peaks at phases 1 and 4. Roughly, ACL and PCL forces patterns still present one or two peaks of force but their amplitude is decreased and is now under 1 BW (Fig. 7).

Discussion

3D musculoskeletal modeling is opening new possibilities in terms of movement simulation and understanding of the interaction between the underlying structures (e.g., bones, ligaments, muscles, tendons). Moreover, the use of instrumented prostheses now offers a unique chance to validate the models in terms of forces estimation during a movement. For example, some datasets have been recently made available [START_REF] Fregly | Grand challenge competition to predict in vivo knee loads[END_REF] to evaluate models during gait [START_REF] Hast | Dual-joint modeling for estimation of total knee replacement contact forces during locomotion[END_REF][START_REF] Lundberg | Fine tuning total knee replacement contact force prediction algorithms using blinded model validation[END_REF][START_REF] Manal | An electromyogram-driven musculoskeletal model of the knee to predict in vivo joint contact forces during normal and novel gait patterns[END_REF]. This has motivated us to validate our model using these datasets.

Our first goal was to present our 3D lower limb musculoskeletal model. This model, previously described by [START_REF] Dumas | Influence of joint models on lower-limb musculo-tendon forces and three-dimensional joint reaction forces during gait[END_REF] and Moissenet et al. (Moissenet et al., 2012a, 2012b), was updated by introducing the patella segment. A description of this model was given to allow a good understanding of its composition. More details and discussions can be found in the previous publications [START_REF] Dumas | Influence of joint models on lower-limb musculo-tendon forces and three-dimensional joint reaction forces during gait[END_REF][START_REF] Duprey | Influence of joint constraints on lower limb kinematics estimation from skin markers using global optimization[END_REF]Moissenet et al., 2012aMoissenet et al., , 2012b)). This model enables studying musculo-tendon, detailed joint contact, ligament and bone forces at hip, tibiofemoral, patellofemoral and ankle joints during gait thanks to an underlying computation framework based on the partial parameter reduction method, introducing a selection of Lagrange multipliers (i.e., joint contact, ligament and bone forces) in the optimization procedure. This method enables defining a large range of optimization criteria for potential future clinical applications. The second optimization condition presented here shows that the estimation is closer to the implant measurements when joint contact forces, and more specifically tibiofemoral contact forces, are minimized. However, when these forces are introduced in the optimization procedure, some aphysiological results can arise, such as the extinction of the gastrocnemius medialis and semimembranosus during the stance phase. Such result was also reported on the gastrocnemii when simulating gait [START_REF] Lin | Simultaneous prediction of muscle and contact forces in the knee during gait[END_REF] and when testing different objective functions during a vertical jumping simulation [START_REF] Cleather | An optimization-based simultaneous approach to the determination of muscular, ligamentous, and joint contact forces provides insight into musculoligamentous interaction[END_REF].

Similarly, Modenese et al. [START_REF] Modenese | An open source lower limb model: Hip joint validation[END_REF] have compared, for gait and stair climbing, the minimization of the musculo-tendon forces using different powers in the objective function. They show that the use of a unitary power provided aphysiological musculo-tendon forces compared to EMG envelopes, but hip contact force was in better agreement with in vivo measurements. All these results highlight an important limit of the current musculoskeletal models and methods since it remains difficult to define an objective function (e.g., minimization of the musculo-tendon forces appended with joint reactions forces or not, with a power one or more), that provides simultaneously physiological musculo-tendon forces and valid joint contact forces.

The second goal of this study was to perform a blinded model validation. A semiquantitative validation of the estimated musculo-tendon forces and a quantitative validation of the estimated tibiofemoral joint contacts forces were completed by a qualitative evaluation of hip contact force and femur axial force. On the one hand, the results show that the model is able to estimate in most cases the correct pattern and timing of these forces, but the force amplitude is highly influenced by the optimization weights. On the whole, the coefficients of active/inactive state concordance obtained when comparing to the subject's EMG envelopes or the asymptomatic EMG envelopes [START_REF] Perry | Gait Analysis: Normal and Pathological Function[END_REF] were similar in terms of value. Specifically, the estimated rectus femoris forces, under condition C1, show a peak of force during terminal stance and preswing. These results, already reported by Modenese et al. [START_REF] Modenese | An open source lower limb model: Hip joint validation[END_REF], are in contrast with the subject's EMG envelopes, but in accordance with those reported by [START_REF] Perry | Gait Analysis: Normal and Pathological Function[END_REF]. It shows that, since our model, in its current state, should only be used for asymptomatic subjects, the timing of onset of estimated musculo-tendon forces can differ to the onset of EMG of a subject presenting a gait disorder. In other words, when the subject's EMG envelopes highly differ from the asymptomatic ones, the quality of musculo-tendon forces estimation seems degrade. With that respect, only methods that quantitatively include EMG data in the optimization process [START_REF] Gerus | Subject-specific knee joint geometry improves predictions of medial tibiofemoral contact forces[END_REF][START_REF] Manal | An electromyogram-driven musculoskeletal model of the knee to predict in vivo joint contact forces during normal and novel gait patterns[END_REF] seem able to deal with such issue. On the other hand, the second optimization condition shows that the model is potentially able to well estimate medial and lateral tibiofemoral joint contacts forces during normal gait. Moreover, the lateral tibiofemoral compartment remains loaded during most of the stance phase, as recorded by the implant, instead of previously reported results (Moissenet et al., 2012a;[START_REF] Shelburne | Contributions of muscles, ligaments, and the ground-reaction force to tibiofemoral joint loading during normal gait[END_REF]. Finally, the results suggest that the musculoskeletal system, in order to minimize tibiofemoral joint contacts forces, tries first to reduce the vastii, gastrocnemii and hamstrings forces during stance. This observation is consistent with the repartition of the musculo-tendon forces contribution to the tibiofemoral joint contacts forces previously described [START_REF] Pandy | Muscle and joint function in human locomotion[END_REF][START_REF] Sritharan | Muscles that do not cross the knee contribute to the knee adduction moment and tibiofemoral compartment loading during gait[END_REF]. Indeed, it has been reported that these muscles have the highest contribution to the resultant tibiofemoral contacts forces. However, it results in aphysiological musculo-tendon forces.

Even if our model provides new opportunities for musculoskeletal estimations, this study still possesses a number of limitations. First, the model is based on different scaled generic models and so do not represent the real geometry of the subjects. It is well known that musculoskeletal geometry affects the forces computation [START_REF] Bonnefoy | Influence of the moment arms on the quadriceps muscular force of the knee during the stance phase of the gait[END_REF][START_REF] Carbone | Sensitivity of subject-specific models to errors in musculo-skeletal geometry[END_REF][START_REF] Cleather | An optimization-based simultaneous approach to the determination of muscular, ligamentous, and joint contact forces provides insight into musculoligamentous interaction[END_REF] and that a solution is to combine medical imaging techniques with musculoskeletal modeling to improve accuracy of the models [START_REF] Arnold | Accuracy of muscle moment arms estimated from MRI-based musculoskeletal models of the lower extremity[END_REF][START_REF] Scheys | Image based methods to generate subject-specific musculoskeletal models for gait analysis[END_REF]. Even if the present study uses basically generic models, it should be noted that the joint kinematic models used for tibiofemoral, patellofemoral and ankle joints may be easily adjusted to the patient's geometry using medical imaging. Second, the use of an inverse dynamics based optimization procedure can bring perturbation as input of the model with the well-known soft tissue artifacts. The results show that artifacts can appear on musculo-tendon, joint contact and bone forces (Figs. 234567) at heel strike and toe off events.

Third, the use of parallel mechanisms models for gait simulations can be discussed. Indeed, these models have been developed based on in vitro unloaded knee movements and consider ligaments as isometric structures. However, it has been shown that the kinematics of tibiofemoral and patellofemoral joints are similar between loaded and unloaded conditions during knee extension [START_REF] Lu | In vivo three-dimensional kinematics of the normal knee during active extension under unloaded and loaded conditions using single-plane fluoroscopy[END_REF] and that the ligament lengthening is limited during gait [START_REF] Liu | In vivo length patterns of the medial collateral ligament during the stance phase of gait. Knee surgery, sports[END_REF][START_REF] Wu | Kinematics of the anterior cruciate ligament during gait[END_REF]. Nevertheless, the isometric condition would have brought to pushing ligaments (i.e., negative force) if the associated Lagrange multiplier have not been introduced in the optimization procedure. This issue has been previously reported for the MCL force (Moissenet et al., 2012a) and can be avoided by introducing deformable ligaments in our model [START_REF] Gasparutto | Multi-body optimisation with deformable ligament constraints: influence of ligament geometry[END_REF]. Fourth, the choice of the musculoskeletal geometric model may have a significant impact on the results. Indeed, the current model is only composed of 43 muscular lines of action [START_REF] Delp | An interactive graphics-based model of the lower extremity to study orthopaedic surgical procedures[END_REF]) that may not be enough to describe accurately the mechanical effect of the muscles [START_REF] Valente | Muscle discretization affects the loading transferred to bones in lower-limb musculoskeletal models[END_REF][START_REF] Van Der Helm | Modelling the mechanical effect of muscles with large attachment sites: application to the shoulder mechanism[END_REF]. Models with additional muscular lines of action exist [START_REF] Klein Horsman | Morphological muscle and joint parameters for musculoskeletal modelling of the lower extremity[END_REF] and may enlarge the optimization solution space. Last but not least, the optimization weights were chosen in order to illustrate two specific strategies. As discussed previously, they can have positive and negative impacts on the results. In the literature, the inverse of squared average cross-sectional area of the muscles is classically used, but other coefficients should also be introduced in order to modulate the minimization of each group of force (i.e., musculo-tendon, joint contact, ligament and bone forces). Up to now, such weighting has been arbitrary assigned [START_REF] Cleather | An optimization-based simultaneous approach to the determination of muscular, ligamentous, and joint contact forces provides insight into musculoligamentous interaction[END_REF][START_REF] Hu | Influence of model complexity and problem formulation on the forces in the knee calculated using optimization methods[END_REF][START_REF] Lin | Simultaneous prediction of muscle and contact forces in the knee during gait[END_REF][START_REF] Raikova | Investigation of the influence of the elbow joint reaction on the predicted muscle forces using different optimization functions[END_REF]. However, because it could be an image of the motor control strategy, the question of relative weights in the objective function should be investigated in the future.

For example, it should be possible to determine some optimal weights by using a two-level optimization [START_REF] Mombaur | From human to humanoid locomotion-an inverse optimal control approach[END_REF].

To conclude, our 3D lower limb musculoskeletal model is versatile, in the sense that generic models implemented can be personalized and that it allows infinite optimization criteria to model motor control strategies and interactions between underlying structures (e.g., bones, ligaments, muscles, tendons). Moreover, the blinded model validation shows the potential of this model to estimate both and simultaneously musculo-tendon, joint contact and bone forces during normal gait. This demonstrates the value of the modeling and computation framework proposed in this study. However some limitations remain and the selection of optimization weights will be a huge challenge for the further development of our model. patellofemoral and ankle joints) and musculo-tendon geometry [START_REF] Delp | An interactive graphics-based model of the lower extremity to study orthopaedic surgical procedures[END_REF].

Tables and figures captions:

  null eigenvalues. If necessary, Lagrange multipliers 2 λ can be computed a posteriori using the optimal solution [ ] 1 T f λ (Moissenet et al., 2012a).

Figure 1 :

 1 Figure 1: Musculoskeletal model: segment parameters (Dumas and Chèze, 2007) (i.e.,

Figure 2 :

 2 Figure 2: Comparison between a set of mean estimated musculo-tendon forces (i.e., gluteus maximus -Gmax, gluteus medius -Gmed, adductor magnus -Addmagnus, vastus medialis -Vasmed, vastus lateralis -Vaslat, rectus femoris -RF, semimembranosus -Semimem, biceps femoris long head -Bifem, tensor fascia lata -TFL, gastrocnemius medialis -Gasmed, gastrocnemius lateralis -Gaslat, soleus -Soleus, tibialis anterior -Tibant and peroneus longus -Peronl) and the corresponding active/inactive state (i.e., from the subject and asymptomatic measured EMG envelopes) under condition C1 (i.e., only musculo-tendon forces are minimized). The results are given in bodyweights over the gait cycle for each of the subjects. Standard deviations (i.e., std) are given for the estimated

Figure 7 :

 7 Figure 7: Mean estimated ligament forces under condition C2 (i.e., musculo-tendon, joint contact, ligament and bone forces are minimized while focusing more specifically on tibiofemoral joint contacts). The results are given in bodyweights over the gait cycle for each of the subjects. Standard deviations (i.e., std) are given for the estimated forces. The toe off is indicated by a vertical dotted line. For additional results, please see the Supplementary material.

  :

	2 0.6588 R 0.9040 ≤ ≤	) but are overestimated (Table 2:
	0.4356 BW RMSE 1.3931 BW ≤ ≤	) with high errors at the second peak of force (Table 2:
	1.1052 BW Peak2 3.6722 BW ≤ ≤

Table 2

 2

	:

Table 1 :

 1 Lagrange multipliers introduced in the objective function (i.e., 1

	λ ) and

Table 2 :

 2 Descriptive statistics under condition C1 (i.e., only musculo-tendon forces are minimized) and condition C2 (i.e., musculo-tendon, joint contact, ligament and bone forces are minimized while focusing more specifically on tibiofemoral joint contacts) model estimations. The coefficient of concordance is defined as the percentage of active/inactive state concordance elements between the estimated musculo-tendon forces (i.e., m-t f.) and the measured EMG envelopes (subject and asymptomatic). Peak1 and Peak2 are the differences at first and second peak forces between the estimated tibiofemoral joint contact forces and the in vivo measurements in bodyweights. RMSE is the root mean square error over the gait cycle in bodyweights. R 2 is correlation coefficient over the gait cycle.

Table 1 :

 1

		Selected Lagrange	Associated optimization
		multipliers 1 λ		weight
		C1 & C2	C1	C2
	Musculo-tendon forces	/	1	1
		Hip	0	1e0
	Joint contact forces	Medial tibiofemoral Lateral tibiofemoral	0 0	2e0 4e0
		Patellofemoral	0	1e-6
		Ankle	0	1e0
		ACL	0	1e-6
		PCL	0	1e-6
	Ligament forces	PT	0	1e-6
		TiCaL	0	1e-6
		CaFiL	0	1e-6
	Bone forces	Femur Tibia	0 0	1e-6 1e-6

Acknowledgements

The authors gratefully acknowledge Edouard Jouan and Matthieu Giroux (MSc) for their involvement and their work in this project during their master thesis.

Conflict of interest

The authors do not have any financial or personal relationship with other people or organization that could inappropriately influence their work.

forces. The toe off is indicated by a vertical dotted line. For additional results, please see the Supplementary material.