BME6101/BME8103
Manufacturing of Biomedical Engineering
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Problem Set 3
(Textbook Problem 12.9, due on Nov 28, 2022)
Imagine that you are responsible for manufacturing an artificial ear for replacement of an ear cartilage of a
patient who has a chronic inflammatory disease (left photograph of Fig. 1). Generally, cartilage is composed
of specialized cells called chondrocytes that produce a large amount of collagenous extracellular matrix, an
abundant ground substance that is rich in proteoglycan and elastin fibers.
Throughout the process, your role as a biomedical engineer in the hospital is to design the rapid
prototyping manufacturing process for the scaffold and facilitate the subsequent chondrocyte seeding and
culture to develop the in vitro artificial ear. The scaffold fabrication is based on the 3D printing like the
fused deposition modeling (FDM) of a biomaterial with the ‘designed’ architecture (right photograph of Fig.
a) Before the manufacturing, imaging of the ear cartilage should be performed to obtain the 3D geometry
of the missing part of the bone. Can you suggest a bio-imaging method? Please briefly describe the
working principle with 30 words or less.
b) The scaffold was then fabricated by a rapid prototyping machine. The substrate material you could use
is the composite of biodegradable poly-caprolactone (PCL) and lignin. The chemical synthesis of the
poly-PCL-lignin is shown in Fig. 2. What kind of polymerization is involved in this process? Please
c) The composite should include mostly volumetric ratios of 80% PCL, 2% lignin, and 18% acetone,
whose viscosity (µ) is ~180 × 10-3 kg/m·s and density (ρ) is 1.145 g/cm3. During the rapid prototyping
process, the composite should be applied onto the sample for deposition using a syringe. The injection
operation was driven by a computer-controlled pressure supply. The composite solution should flow
through a syringe needle with a length of 0.1 mm (Lneedle) and an inner radius (Rneedle) of 50 μm. The
inner radius of the syringe body (Rsyringe) is 10 mm, and the length of the syringe body (Lsyringe) is 10 cm.
Assume that the solution flow rate is 0.5 nL/hr. Should the flow be laminar or turbulent? Please explain.
What is the minimum required applied pressure to support the required rate of the liquid injection?
d) Let’s assume that the soft-bone of the ear has the shape as a half circular disc (i.e. a half circle with a
certain thickness) with radius Rscaffold and thickness Hscaffold. Taking into account that a bone cell in
suspension should have a diameter ~10 µm, the scaffold should have a large enough separating
hole/gap widths Dgap such that the cells can deposit and migrate inside the scaffold. We set Dgap ≥ 30
µm. Considering that the cured scaffold material has a Young’s modulus close to cured PCL (EPCL = 1
GPa), please express the equivalent compressive stiffness of the scaffold Escaffold as a function of the
printed fiber diameter Dfiber and Dgap. Please assume that Dfiber contains mainly the poly-PCL-lignin
without acetone, and therefore, the cross-sectional area of the fiber is ~82 % of the inner cross-section
area of the syringe needle, given that the moving speed of the syringe is fast enough. (Note: Use
symbols only, but not the given values, for this part.)
e) The scaffold with a ‘designed’ architecture may be printed as a multilayer mesh. However, the printed
poly-PCL-lignin fibers have a diameter smaller than the cell, the gap with one layer of the fibers, i.e.
Dfiber. In order to fulfill the required Dgap as mentioned in (d), please design an IMPROVED printing
strategy, and explain it using drawings and descriptions. Please consider that the proposed strategy can
still adopt the estimation of Escaffold as described in (d). Please also specify the values of (1) Dfiber, (2) Dgap,
and (3) number of each key-feature layers for your design.
f) Based on the design and fabrication strategy you provided in part (e) and further considering the
injection pressure P of the composite (in other words, the flow rate is no longer fixed as 0.5 nL/hr),
please estimate the manufacturing time. (Note: Use symbols only, but not the given values, for this part.)
g) We wish to select the optimum material for a sufficiently light and stiff fiber/beam supported by the
two previously printed fibers as shown in Fig. 3. It is required that the beam has a fixed length of Lfiber
where its fiber diameter on the side Dfiber is adjustable to fit the design requirement. The mass of the
beam is M = πDfiber2Lfiber ρPCL /4 where ρPCL is the density of the polymerized PCL material (1.145
g/cm3). For a simply supported beam with a pressure per length Pfiber along the beam length caused by
the fiber weight Pfiber = πDfiber2ρPCLg/4 where g is the gravitational acceleration, the central deflection δ
fiber fiber
where the moment of inertia Ifiber = MDfiber2/16.
Determine the appropriate material performance index.
For your final design configuration (after you finish Part (i) later), please find the central deflection δ,
and check if it is within 0.1 µm.
h) Please propose an optimization statement (including both the objective function and the constraints)
for the shortest manufacturing time by considering the following additional information:
The disposition is achieved by injection of the PCL-lignin dissolved in a solvent (acetone) with a
volumetric ratio Ω, which can be set between 0.6 (60 %) and 0.8 (80 %) for different fiber diameters
Dfiber, under a fast enough syringe movement as mentioned previously in Part (d). A maximum flow rate
of 3 nL/hr and a maximum pressure of 100 kPa can be offered by the injection system. The allowable
separating distance of the designed architecture Dgap should be ≥30 µm in all x, y, and z directions such
that cells can migrate freely into the inner scaffold body. The equivalent compressive stiffness Escaffold of
the ‘designed’ scaffold should be larger than the level of the cartilage (≥2 MPa) to maintain the
structural shape after implantation. (Note: Use symbols only, but not the given values, for this part.)
i) Given Dscaffold should be ~2 cm and Hscaffold should be between 2.95 mm and 3.05 mm, can you find out
the minimum manufacturing time based on your optimization statement above? Should the result
correspond to the maximum injection flowrate, the minimum equivalent stiffness, and/or the
maximum porosity?
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