Presentation Chondrocytes

Presentation Chondrocytes - linical arti reations orp...

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Unformatted text preview: linical arti reations orp Cartilage Tissue Engineering Emily Burdett Victoria Froude May 2, 2006 Overview C C Cartilage damage in the knee is a major problem We present a novel tissue engineering technique for repairing cartilage damage with autologous chondrocyte cells Mathematical modeling can be useful to help predict implant behavior The FDA approval process and product pricing were modeled in order to evaluate risk Cartilage C C Connective tissue found in all joints Functions as cushioning and support Cartilage is composed of chondrocytes, collagen, and proteoglycans. Articular cartilage is found in the knee joint. Strongest type of cartilage Ref: football.calsci.com/ images/knee_cartilage.jpg Cartilage Damage Tears and holes develop in cartilage due to injury and stress. No vascular system is present throughout the cartilage to initiate repair after damage. Damage develops in cartilage and extends into the underlying bone. C C http://www.orthogastonia.com/index.php/fuseaction/patient_ed.top icdetail/TopicID/a93dd54cd3d79c0d8bedae1537bc7659/area/17 Reparative Surgeries C C Inflict further damage to initiate the healing response. New tissue does not have the required mechanical strength. Results are temporary. http://www.orthogastonia.com/index.php/fuseaction/patient_ed.topicdetail/TopicID/a93dd54cd3d79c0d8bedae153 7bc7659/area/17 Restorative Surgeries C C Replace cartilage with cells or donor tissue. Invasive Lack reliability High risk of initiating an immune response Cells migrate from damage site http://www.orthogastonia.com/index.php/fuseaction/patient_ed.to picdetail/TopicID/a93dd54cd3d79c0d8bedae1537bc7659/area/17 Our Solution 1) Harvest and proliferate cells from patient 3) Suspend capsules in crosslinkable polymer C C 2) Embed cells in gelatin microcapsules 4) Inject polymer into defect and crosslink in situ After crosslinking, microcapsules will release cells. Over time, polymer will degrade and cells will produce new tissue Cartilage Repair C C 1. Bone replacement: Made of poly(propylene fumarate) (PPF) combined with β-TCP particles Seeded with mesenchymal stem cells taken from the patient’s bone marrow. N-vinylpyrrolidinone serves as a crosslink and benzoyl peroxide initiates crosslinking upon injection 1 C C Cartilage Repair 2. Cartilage Replacement: Made of a copolymer containing PPF and poly(ethylene glycol) (PPFco-EG) Seeded with chondrocytes taken from a non-load bearing joint Undergoes the same crosslinking reaction as the bone replacement 2 Cartilage Repair C C 3. Cell Microcapsules Microcapsules will contain porcine gelatin and DMEM cell culture media Surface will be crosslinked using DSP to prevent reverse gelation of microparticles during PPF crosslinking 3 Cartilage Repair C C 4. Growth Factors PLGA microparticles containing growth factors will also be suspended in the polymer These will release growth factors slowly throughout tissue regeneration to promote cell growth and activity 4 Technical Models C C Mathematical modeling of aspects of this procedure will decrease the amount of experimentation needed and decrease the risk associated with lack of knowledge. Aspects that can be modeled: Heat Transfer Mechanical Strength / Porosity Polymer Degradation Heat Transfer When cell suspension polymerizes in vivo, heat is produced. This causes the temperature of the polymer construct to increase. Excessive temperatures can kill the cells before they can begin to proliferate and create tissue. Will increased polymer temperatures allow enough cell survival for tissue growth? C C C C Heat Transfer Air Fluid Inside Implant ∂T & α1 = ∇ 2T + q(t ) ∂t Cartilage Implant Q Cartilage Bone Outside Implant ∂T α2 = ∇ 2T ∂t C C Heat Transfer First attempt: 1-D Analytical Solution Solution of inner equation is not consistent with boundary conditions. 45 44 Temperature (C) 43 42 41 0 0 hr min 40 39 2 2 hr min 4 4 hr min 8 8 hr min 38 37 36 35 -0.03 -0.02 -0.01 0 0.01 Distance from center (m) 0.02 0.03 Heat Transfer C C Temperature (C) Second Attempt: find 1-D solution numerically using finite differences 49 Temperature 47 raises to 45 almost 47ºC x=0 and stays 43 x=L/2 above 40ºC for 41 x=L several hours 39 This would 37 cause 35 significant cell 0 20 40 60 Time (min) death C C Heat Transfer Temperature (C) . Third Attempt: Find 3-D solution in cylindrical coordinates using finite differences Temperature 40.5 only increases to 40 40 C at the 39.5 39 Center of the 38.5 Implant 38 This temperature 37.5 37 increase will 36.5 cause minimal 0 10 20 cell death Time (min) r =0 r = R/2 r =R C C Heat Transfer Comparison between methods 1-D Models do not consider heat lost through the top and bottom of the implant 47 Temperature (C) 45 43 1-D Numerical 1-D Analytical 41 3-D Numerical 39 37 35 0 10 Time (min) 20 Heat Transfer C C Model shows that temperature increase will not cause significant cell death. This prediction gives a starting point for experiments in cell seeding. The model saves us money and time that would otherwise be used to find these results experimentally Mechanical Strength C C Proper mechanical strength will allow for better recovery for the patient Natural compressive strength Bone ~ 5 MPa Cartilage ~ 0.4 – 1.4 MPa Variables affecting construct strength throughout device life: Cross-linking density Porosity Degradation and cell growth C C Porosity Void space is necessary to create pathways for nutrient and waste movement. Porosity affects compressive strength of the material Percent porosity of material Size and morphology of pores Atzeni equation developed for hardened pastes with spherical pores. Empirical constant is necessary σ =K σ 0 (1 − p ) rm C C PPF/β-TCP Porosity Strength (MPa) 14 12 10 8 6 σ = 4.3 4 2 σ 0 (1 − p ) rm 0 0.7 0.8 0.9 1 Porosity 150 um 300 um 500 um 600 um Natural bone has a compressive strength of 5 MPa. Bone substitute could have a porosity over 75% based on this model. PPF-co-EG Porosity C C Polymer matrix forms a hydrogel, which has natural void space. Dependent on cross-linking density Shown to have adequate diffusion of nutrients, waste, and large proteins. Diffusion of nutrients and mechanical strength are affected by the cross-linking density of the polymer. Construct degradation C C Time after implantation Degradation occurs by hydrolysis of PPF bonds. Pseudo-first order kinetics because water concentration is relatively constant. Degradation decreases cross-linking density Decreases compressive strength Increases swelling ratio C C Degradation Effects Compressive Modulus K = K 0e −t τ K Q = Q0e Sw elling Ratio t τQ Degradation Time As degradation increases, polymer loses strength Degradation rate is dependent on initial cross-linking density Cell growth must replace degraded polymer to maintain strength. Modeling C C We now have a better idea of which experiments must be done in order to make this process work. Overall, numerical models like this help to reduce cost and more accurately quantify risk… Risk Analysis C C Need for Risk Analysis C C New technologies include an incredible amount of risk 5 of every 5,000 medical technologies that enters the FDA approval process enters human clinical testing. Only 1 of those 5 technologies will eventually be approved for the medical market. On average, it takes 15 years for the approval process. It takes approximately $360 million for a new technology to reach the public. FDA Approval C C Necessary before the use of any medical device. Experiments determine the positive and negative affects of the treatment. Lab scale testing Animal testing Human clinical trials Application can be filed in a traditional or modular form. Modular FDA Approval Modules are determined based on assessment of needed experiments. Request approval at the end of each module Failure within a module does not indicate total product failure Data appendices can be sent in after approval was requested. Project can be abandoned after failure at any module. C C FDA Approval Module 1 – Laboratory testing Bench scale testing Basic material properties Initial optimization of construct Module 2 – Non-clinical animal studies Defining surgical procedure Biocompatibility and toxicity studies Further optimization of construct Module 3 – Human clinical trials Mechanical strength and integrity Long-term in vivo results C C Assessing Pathways C C Each step has an associated time, cost, and probability. To assess the FDA process, estimations of where failures will occur must be made. Number of failures allowable within a pathway will greatly affect the risk assessment. Probabilities of success would increase if Pre-FDA testing is completed More experiments are performed Advance and accurate modeling is available Pre-FDA Trials C C Reduces the chance of early failure Abandon or change project based on results Predict necessity of more expensive experiments and optimizations Increases accuracy of risk analysis Business Decisions C C First Stage Decisions: Second Stage Decisions: Number of experiments Product price Number of workers Advertising Costs Number of Allowable Failures Production facility location and size We will find risk associated with several first stage scenarios – it is assumed that second stage decisions can be made later for optimum performance Module 1 Testing $500,000 3 years Approval Granted 70%, 60%, 35% Module 2 Failure due to polymer problems Failure due to gelatin microparticles Failure due to growth factor microspheres Failure due to poor cell adhesion 5%, 7%, 10% 7%, 9%, 15% 5%, 7%, 15% 7%, 9%, 13% Change polymer synthesis procedure $40,000 2 months Change gelatin formulation/ seeding density $20,000 1 month Change microsphere fabrication procedure $60,000 3 months Attach RGD peptides to polymer surface $20,000 2 months Reapply for Module 1 Module 1 testing $500,000 3 years Approval Granted 90%, 85%, 75% Module 2 Failure due to polymer synthesis 4%, 7%, 10% Abandon Project Failure due to microparticle synthesis 3%, 5%, 9% Abandon Project Failure due to growth factor microspheres 3%, 3%, 6% Abandon Project Failure due to poor cell survival in encapsulated microparticles 6%, 8%, 12% Abandon Project Module 1 Testing $500,000 3 years Approval Granted 70%, 60%, 35% Module 2 Failure due to polymer problems Failure due to gelatin microparticles Failure due to growth factor microspheres Failure due to poor cell adhesion 5%, 7%, 10% 7%, 9%, 15% 5%, 7%, 15% 7%, 9%, 13% Change polymer synthesis procedure $40,000 2 months Change gelatin formulation/ seeding density $20,000 1 month Change microsphere fabrication procedure $60,000 3 months Attach RGD peptides to polymer surface $20,000 2 months Reapply for Module 1 Module 1 testing $500,000 3 years Approval Granted 90%, 85%, 75% Module 2 Failure due to polymer synthesis 4%, 7%, 10% Abandon Project Failure due to microparticle synthesis 3%, 5%, 9% Abandon Project Failure due to growth factor microspheres 3%, 3%, 6% Abandon Project Failure due to poor cell survival in encapsulated microparticles 6%, 8%, 12% Abandon Project Module 1 Testing $500,000 3 years Approval Granted 70%, 60%, 35% Module 2 Failure due to polymer problems Failure due to gelatin microparticles Failure due to growth factor microspheres Failure due to poor cell adhesion 5%, 7%, 10% 7%, 9%, 15% 5%, 7%, 15% 7%, 9%, 13% Change polymer synthesis procedure $40,000 2 months Change gelatin formulation/ seeding density $20,000 1 month Change microsphere fabrication procedure $60,000 3 months Attach RGD peptides to polymer surface $20,000 2 months Reapply for Module 1 Cost Module 1 testing $500,000 3 years = $500,000 + $60,000 + $500,000 Approval Granted 90%, 85%, 75% Failure due to polymer synthesis 4%, 7%, 10% $1,060,000 Module 2 Abandon Project Failure due to microparticle synthesis 3%, 5%, 9% Abandon Project Failure due to growth factor microspheres 3%, 3%, 6% Abandon Project Failure due to poor cell survival in encapsulated microparticles 6%, 8%, 12% Abandon Project Module 1 Testing $500,000 3 years Approval Granted 70%, 60%, 35% Module 2 Failure due to polymer problems Failure due to gelatin microparticles Failure due to growth factor microspheres Failure due to poor cell adhesion 5%, 7%, 10% 7%, 9%, 15% 5%, 7%, 15% 7%, 9%, 13% Change polymer synthesis procedure $40,000 2 months Change gelatin formulation/ seeding density $20,000 1 month Change microsphere fabrication procedure $60,000 3 months Attach RGD peptides to polymer surface $20,000 2 months Reapply for Module 1 Time = Module 1 testing $500,000 3 years 3 Years + 0.25 Years + 3 Years Approval Granted 90%, 85%, 75% Failure due to polymer synthesis 4%, 7%, 10% 6.25 Years Module 2 Abandon Project Failure due to microparticle synthesis 3%, 5%, 9% Abandon Project Failure due to growth factor microspheres 3%, 3%, 6% Abandon Project Failure due to poor cell survival in encapsulated microparticles 6%, 8%, 12% Abandon Project Module 1 Testing $500,000 3 years Approval Granted 70%, 60%, 35% Module 2 Failure due to polymer problems Failure due to gelatin microparticles Failure due to growth factor microspheres Failure due to poor cell adhesion 5%, 7%, 10% 7%, 9%, 15% 5%, 7%, 15% 7%, 9%, 13% Change polymer synthesis procedure $40,000 2 months Change gelatin formulation/ seeding density $20,000 1 month Change microsphere fabrication procedure $60,000 3 months Attach RGD peptides to polymer surface $20,000 2 months Reapply for Module 1 Probability = 0.05 x Module 1 testing $500,000 3 years 0.90 0.045 Approval Granted 90%, 85%, 75% Module 2 Failure due to polymer synthesis 4%, 7%, 10% Abandon Project Failure due to microparticle synthesis 3%, 5%, 9% Abandon Project Failure due to growth factor microspheres 3%, 3%, 6% Abandon Project Failure due to poor cell survival in encapsulated microparticles 6%, 8%, 12% Abandon Project Cost $1,060,000 Time 6.25 Years Probability 0.0015 Module 2 Testing $500,000 3 years Approval Granted 60%, 50%, 35% Module 3 Failure due to donor site morbidity Failure due to biocompatibility issues Failure due to injection complications Failure due to construct integrity in vivo Failure due to in vivo toxicity 7%, 8%, 10% 12%, 15%, 20% 7%, 9%, 12% 6%, 8%, 10% 8%, 10%, 13% Improve cell harvesting techniques $20,000 1 month Purify materials, improve procedures $50,000 3 months Redefine surgical procedures $30,000 2 months Alter polymer formulation or M.W. to find optimal $30,000 2 months Abandon Project Reapply for Module 2 Module 2 testing $500,000 2 years Approval Granted 70%, 60%, 50% Module 3 Failure due to biocompatibility Failure due to surgical procedure 10%, 13%, 18% Failure due to toxicity 10%, 15%, 18% 5%, 6%, 7% Abandon Project Hire new surgeons $200,000 1 month Abandon Project Reapply for Module 2 Failure due to polymer formulation 5%, 6%, 7% Abandon Project Module 2 testing $500,000 1 year Approval Granted 90%, 75%, 65% Failure due to surgical procedure 10%, 25%, 35% Abandon Project Module 3 Module 2 Testing $500,000 3 years Approval Granted 60%, 50%, 35% Module 3 Failure due to donor site morbidity Failure due to biocompatibility issues Failure due to injection complications Failure due to construct integrity in vivo Failure due to in vivo toxicity 7%, 8%, 10% 12%, 15%, 20% 7%, 9%, 12% 6%, 8%, 10% 8%, 10%, 13% Improve cell harvesting techniques $20,000 1 month Purify materials, improve procedures $50,000 3 months Redefine surgical procedures $30,000 2 months Alter polymer formulation or M.W. to find optimal $30,000 2 months Abandon Project Reapply for Module 2 Module 2 testing $500,000 2 years Approval Granted 70%, 60%, 50% Module 3 Failure due to biocompatibility Failure due to surgical procedure 10%, 13%, 18% Failure due to toxicity 10%, 15%, 18% 5%, 6%, 7% Abandon Project Hire new surgeons $200,000 1 month Abandon Project Reapply for Module 2 Failure due to polymer formulation 5%, 6%, 7% Abandon Project Module 2 testing $500,000 1 year Approval Granted 90%, 75%, 65% Failure due to surgical procedure 10%, 25%, 35% Abandon Project Module 3 Module 2 Testing $500,000 3 years Approval Granted 60%, 50%, 35% Module 3 Failure due to donor site morbidity Failure due to biocompatibility issues Failure due to injection complications Failure due to construct integrity in vivo Failure due to in vivo toxicity 7%, 8%, 10% 12%, 15%, 20% 7%, 9%, 12% 6%, 8%, 10% 8%, 10%, 13% Improve cell harvesting techniques $20,000 1 month Purify materials, improve procedures $50,000 3 months Redefine surgical procedures $30,000 2 months Alter polymer formulation or M.W. to find optimal $30,000 2 months Abandon Project Reapply for Module 2 Module 2 testing $500,000 2 years Approval Granted Cost $2,660,000 70%, 60%, 50% Module 3 Failure due to biocompatibility Failure due to surgical procedure 10%, 13%, 18% Failure due to toxicity 10%, 15%, 18% 5%, 6%, 7% Abandon Project Hire new surgeons $200,000 1 month Abandon Project Failure due to polymer formulation 5%, 6%, 7% Abandon Project Time 12.5 Years Reapply for Module 2 Module 2 testing $500,000 1 year Probability 0.00028 Approval Granted 90%, 75%, 65% Failure due to surgical procedure 10%, 25%, 35% Abandon Project Module 3 Module 2 Testing $500,000 3 years Approval Granted 60%, 50%, 35% Module 3 Failure due to donor site morbidity Failure due to biocompatibility issues Failure due to injection complications Failure due to construct integrity in vivo Failure due to in vivo toxicity 7%, 8%, 10% 12%, 15%, 20% 7%, 9%, 12% 6%, 8%, 10% 8%, 10%, 13% Improve cell harvesting techniques $20,000 1 month Purify materials, improve procedures $50,000 3 months Redefine surgical procedures $30,000 2 months Alter polymer formulation or M.W. to find optimal $30,000 2 months Abandon Project Reapply for Module 2 Module 2 testing $500,000 2 years Approval Granted 70%, 60%, 50% Module 3 Failure due to biocompatibility Failure due to surgical procedure 10%, 13%, 18% Failure due to toxicity 10%, 15%, 18% 5%, 6%, 7% Abandon Project Hire new surgeons $200,000 1 month Abandon Project Reapply for Module 2 Failure due to polymer formulation 5%, 6%, 7% Abandon Project Module 2 testing $500,000 1 year Approval Granted 90%, 75%, 65% Failure due to surgical procedure 10%, 25%, 35% Abandon Project Module 3 Module 3 Testing $85,000,000 5 years Module 1 Module 2 Medical Market Failure due to poor integration with surrounding tissue 20%, 25%, 25% Failure due to unviable construct post-injection 20%, 25%, 30% Failure due to infection 10%, 10%, 15% Improve polymer properties $300,000 6 months Approval Granted 50%, 40%, 30% Purify materials, improve procedures $500,000 8 months Add antibiotics, further purify materials $300,000 6 months Module 3 Module 3 testing $4,000,000 4 years Reapply for Module 3 Market Introduction Approval Granted 60%, 50%, 35% Medical Market Module 3 testing $4,000,000 3 years Approval Granted 80%, 70%, 55% Medical Market Failure due to poor mechanical integrity 10%, 10%, 15% Failure due to poor long-term patient results 10%, 20%, 30% Change polymer constiuent concentrations $750,000 6 months Improve degradative properties of polymer $500,000 1 year Approval Granted 90%, 80%, 70% Failure due to slow tissue ingrowth 10%, 10%, 15% Improve polymer properties $500,000 1 year Increase scaffold pore size $50,000 1 month Reapply for Module 3 Reapply Module 3 and Testing $4,000,000 2 years Medical Market Failure due to poor integration with surrounding tissue 10%, 15%, 15% Failure 10%, 20%, 30% Abandon Project Failure due to unviable construct post-injection 20%, 25%, 35% Abandon Project Module 1 Module 2 Module 3 Market Introduction Module 1 Module 2 Module 3 Market Introduction Cost $100,510,000 Time 28 Years Probability 0.000000504 Modeling Pathways C C Models can quickly become complicated 5,291 total pathways through FDA 2,970 pathways lead to success 2,321 pathways lead to failure First stage decisions shape FDA model Probabilities, time, and cost are estimated based on all available knowledge. Modeling technical details increases accuracy of the FDA model. Risk Assessment C C The probability, time until completion, and net present cost for each pathway was calculated Scenarios varying by the number of workers and the number of experiments were created 2, 5, or 10 workers 45, 60, or 70 experiments Net present worth of the product was calculated to evaluate the possible profit Price and demand must be considered C C Pricing To know the expected value of each pathway, the profit for each operating year must be estimated. Profit n = pd n − ICn d n − FCn IC = Surgery and material cost per implant, FC = Fixed annual operating costs The price and demand are classically related by a simple expression pd = Constant C C Pricing How do we choose a price? Less than competitor: More than competitor: Get the majority of the market Get the smaller market share Price: $15,000 Price: $35,000 Demand: ~15,000 Demand: ~7,000 Profit: ~$70,000,000 Profit: ~$170,000,000 We will need a more detailed model to find the optimum price C C Pricing A more detailed pricing model involves maximizing consumer utility (happiness) With only one competitor, the utility (U) is: α U = d1 + d 2 β α = f (knowledge) β = f (happiness) This is maximized subject to two constraints: p1d1 + p2 d 2 ≤ Y d1 + d 2 ≤ D Y = Total Consumer Budget D = Total Demand C C Pricing This gives two possible equations relating demand and price: Budget Controlled Solution Demand Controlled Solution 1− β α p2 Y − p1d1 d1 = p β p1 2 α d1 α α 1− β d1 = (D − d1 ) d1 β These are both solved for d1; the lower solution satisfies both constraints. C C Pricing Estimating α and β: Knowledge increases gradually until it becomes perfect (α = 1) alpha 1.5 β is estimated by assuming happiness values and weights for various attributes β= 1 H2 = H1 ∑w y ∑w y i 2 ,i = 0.8 i 1,i 0.5 Description 0 0 1 2 3 Year 4 5 Weight y1 y2 Long-term outcome 0.70 1 0.8 Invasiveness 0.15 0.8 0.4 Recovery Time 0.15 0.75 0.65 Pricing C C Estimating Y and D Values are assumed from knowledge of the competitor’s current market and statistics on the number of people with this kind of knee problem. Y = $250,000,000 / year D = 15,000 Implants / year C C Pricing The demand and the profitability were evaluated for a range of prices. When α = 1, the maximum profitability was found at: p1 = $95,000 d1 = 2573 Implants / year Profit = $217,000,000 / year This price was used to find profitability during the first five years Year 1 Year 2 Year 3 Year 4 Year 5 $0 -$500,000 $600,000 $217,000,000 $217,000,000 C C Risk Curve These profits during operation give these risk curves for the NPW forty years from now 1.2 1 Probability 0.8 0.6 45 Experiments 60 Experiments 70 Experiments 0.4 0.2 0 -200 0 200 400 600 NPW ($ million) 800 1000 1200 1400 Pricing Model Deviations C C The values used for α, β, Y, and D are variable. To make this evaluation more rigorous, several values of each are used with their associated probabilities. α (years to reach 1) 5 (50%) 4 (33%) 3 (17%) β 0.5 (25%) 0.8 (50%) 0.999 (25%) Y $150,000,000 (33%) $250,000,000 (33%) $400,000,000 (33%) D 10,000 (33%) 15,000 (33%) 20,000 (33%) Profitability The most profitable price for each scenario, is most strongly dependent on β. Changing D values have no effect on profitability; Budget constraint dominates at high prices. C C When products are almost equal (β = 1), most profitable price is competitor’s price. For low values of β, the most profitable price is surprisingly large - as much as $590,000! We may want to charge lower prices to capture a larger segment of the market. C C 2 Workers 1.2 1 Probability . 0.8 0.6 45 Experiments 60 Experiments 0.4 70 Experiments 0.2 0 -500 0 500 1000 1500 2000 NPW ($ million) 2500 3000 3500 4000 C C 2 Workers 45 Experiments 60 Experiments 70 Experiments 45 Experiments 60 Experiments 70 Experiments C C 2 Workers 45 Experiments 60 Experiments 70 Experiments C C 2 Workers 45 Experiments 60 Experiments 70 Experiments C C 5 Workers 1.2 1 Probability . 0.8 0.6 45 Experiments 60 Experiments 0.4 70 Experiments 0.2 0 -500 0 500 1000 1500 NPW ($ million) 2000 2500 3000 3500 C C 10 Workers 1.2 1 Probability . 0.8 0.6 45 Experiments 60 Experiments 0.4 70 Experiments 0.2 0 -500 0 500 1000 1500 2000 NPW ($ million) 2500 3000 3500 4000 C C 45 Experiments 1.2 1 Probability 0.8 0.6 10 Workers 5 Workers 0.4 2 Workers 0.2 0 -500 0 500 1000 1500 2000 NPW ($ Millions) 2500 3000 3500 4000 C C 45 Experiments 10 Workers 5 Workers 2 Workers C C 45 Experiments 10 Workers 5 Workers 2 Workers C C 45 Experiments 10 Workers 5 Workers 2 Workers C C 60 Experiments 1.2 1 Probability 0.8 0.6 10 Workers 5 Workers 0.4 2 Workers 0.2 0 -500 0 500 1000 1500 2000 NPW ($ million) 2500 3000 3500 4000 C C 70 Experiments 1.2 1 Probability 0.8 0.6 10 Workers 5 Workers 0.4 2 Workers 0.2 0 -500 0 500 1000 1500 2000 NPW ($ million) 2500 3000 3500 4000 Profitability Conclusions C C This process has the possibility of being remarkably profitable. The expected NPW can increase by: Increasing the number of experiments Increasing the number of workers The costs associated with these first stage decisions is minimal when compared to the possible gains. There are inherent limitations to how much the NPW would be expected to increase. Conclusions C C Cartilage damage is a problem that may be solved with a tissue engineered solution Mathematical modeling can help to guide experimentation and give insight into a process. The FDA process can be modeled, with first stage decisions taken into consideration. Risk analysis does have some limitations, but is useful in deciding if this procedure is a worthwhile investment. ...
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