7.8 Case Study: Changing Fiber Orientation During Cyclic Stretch
387
7.8 Case Study: Changing Fiber Orientation During Cyclic
Stretch
In the problems considered thus far in this chapter, newly synthesized constituents
are deposited with the same orientation as those they replace. This is not always
the case, however, as experiments have shown that cells and fibers can change their
orientation in response to mechanical cues. In the early embryo, for example, heart
muscle cells initially contain relatively few sarcomeres with no preferred alignment.
As the tubular heart begins to beat and pump blood, these cells begin to fill with
sarcomeres and become circumferentially oriented on the way to creating the highly
organized fiber architecture in the mature heart (see Sect. 5.5.4). Mathematical
models have supported the notion that wall stress or strain regulates this remodeling
(Bovendeerd 2012).
In arteries, endothelial cells respond to fluid shear stress by aligning in the
direction of blood flow. In contrast, endothelial and other types of cells attached
to a flexible membrane undergoing cyclic uniaxial stretch (actually strip biaxial, see
below) tend to align perpendicular to the direction of stretch (Taber 1995; Chen
et al. 2018). Since the arterial wall expands circumferentially with each heartbeat,
both effects cause endothelial cells to align in the longitudinal direction, reducing
resistance to flow.
This section considers reorientation of cells undergoing cyclic stretch in 2D.
When cells attach to a surface, stress fibers (SFs) form in the cytoskeleton and
generally align with the long axes of elongated cells. As cell orientation changes,
the SFs disassemble and gradually reassemble in the new direction. Here, adapting
the model proposed by Kaunas and Hsu (2009), we use Humphrey-Rajagopal
remodeling theory to simulate this turnover of SFs in response to stretch.
Before presenting this 2D model, we note that the behavior is different in 3D.
When cells embedded in a 3D gel undergo cyclic uniaxial stretch, they align parallel
to, rather than away from, the stretch direction. To be consistent with these results,
the present model would need to be modified (Chen et al. 2018), but this is not
considered here.
7.8.1 Model
According to Humphrey–Rajagopal theory, new fibers are created with a certain
deposition stretch ratio λ 0 corresponding to homeostasis. In SFs, stretch relative to
the zero-stress state may not occur until the SF contracts and stabilizes, and then
λ 0 = 1/K 0 with K 0 being the homeostatic contraction ratio. The present model
does not include possible delays in establishing λ 0 .
Assuming that the cells and SFs experience the same deformation as the
substrate, we treat a cell layer as an incompressible rectangular membrane. For
convenience, the reference configuration is taken as the homeostatic state with the
387
7.8 Case Study: Changing Fiber Orientation During Cyclic
Stretch
In the problems considered thus far in this chapter, newly synthesized constituents
are deposited with the same orientation as those they replace. This is not always
the case, however, as experiments have shown that cells and fibers can change their
orientation in response to mechanical cues. In the early embryo, for example, heart
muscle cells initially contain relatively few sarcomeres with no preferred alignment.
As the tubular heart begins to beat and pump blood, these cells begin to fill with
sarcomeres and become circumferentially oriented on the way to creating the highly
organized fiber architecture in the mature heart (see Sect. 5.5.4). Mathematical
models have supported the notion that wall stress or strain regulates this remodeling
(Bovendeerd 2012).
In arteries, endothelial cells respond to fluid shear stress by aligning in the
direction of blood flow. In contrast, endothelial and other types of cells attached
to a flexible membrane undergoing cyclic uniaxial stretch (actually strip biaxial, see
below) tend to align perpendicular to the direction of stretch (Taber 1995; Chen
et al. 2018). Since the arterial wall expands circumferentially with each heartbeat,
both effects cause endothelial cells to align in the longitudinal direction, reducing
resistance to flow.
This section considers reorientation of cells undergoing cyclic stretch in 2D.
When cells attach to a surface, stress fibers (SFs) form in the cytoskeleton and
generally align with the long axes of elongated cells. As cell orientation changes,
the SFs disassemble and gradually reassemble in the new direction. Here, adapting
the model proposed by Kaunas and Hsu (2009), we use Humphrey-Rajagopal
remodeling theory to simulate this turnover of SFs in response to stretch.
Before presenting this 2D model, we note that the behavior is different in 3D.
When cells embedded in a 3D gel undergo cyclic uniaxial stretch, they align parallel
to, rather than away from, the stretch direction. To be consistent with these results,
the present model would need to be modified (Chen et al. 2018), but this is not
considered here.
7.8.1 Model
According to Humphrey–Rajagopal theory, new fibers are created with a certain
deposition stretch ratio λ 0 corresponding to homeostasis. In SFs, stretch relative to
the zero-stress state may not occur until the SF contracts and stabilizes, and then
λ 0 = 1/K 0 with K 0 being the homeostatic contraction ratio. The present model
does not include possible delays in establishing λ 0 .
Assuming that the cells and SFs experience the same deformation as the
substrate, we treat a cell layer as an incompressible rectangular membrane. For
convenience, the reference configuration is taken as the homeostatic state with the