0
TECHNICAL PAPERS: Soft Tissue

A Theoretical Model of Enlarging Intracranial Fusiform Aneurysms

[+] Author and Article Information
S. Baek

Department of Biomedical Engineering, Texas A&M University, College Station, TX 77843-3120

K. R. Rajagopal

Department of Mechanical Engineering, Texas A&M University, College Station, TX 77843-3120

J. D. Humphrey1

Department of Biomedical Engineering, Texas A&M University, College Station, TX 77843-3120jhumphrey@tamu.edu

1

To whom correspondence should be addressed.

J Biomech Eng 128(1), 142-149 (Sep 27, 2005) (8 pages) doi:10.1115/1.2132374 History: Received April 08, 2005; Revised September 27, 2005

The mechanisms by which intracranial aneurysms develop, enlarge, and rupture are unknown, and it remains difficult to collect the longitudinal patient-based information needed to improve our understanding. We submit, therefore, that mathematical models hold promise by allowing us to propose and test competing hypotheses on potential mechanisms of aneurysmal enlargement and to compare predicted outcomes with limited clinical information—in this way, we may begin to narrow the possible mechanisms and thereby focus experimental studies. In this paper, we present a constrained mixture model of evolving thin-walled, fusiform aneurysms and compare multiple competing hypotheses with regard to the production, removal, and alignment of the collagen that provides the structural integrity of the wall. The results show that this type of approach has the capability to infer potential means by which lesions enlarge and whether such changes are likely to produce a stable or unstable process. Such information can better direct the requisite histopathological examinations, particularly on the need to quantify collagen orientations as a function of lesion geometry.

FIGURES IN THIS ARTICLE
<>
Copyright © 2006 by American Society of Mechanical Engineers
Topics: Stress , Aneurysms , Fibers
Your Session has timed out. Please sign back in to continue.

References

Figures

Grahic Jump Location
Figure 3

Simulation of the enlargement of an axisymmetric lesion, as a function of nondimensional time s=t∕t2, for the case 3 preferred deposition (i.e., preferred direction of new collagen dictated by larger principal stretch) and K̂g=0

Grahic Jump Location
Figure 1

Schema of important configurations. The common traction-free (but not necessarily stress-free) reference configuration κ0, at time 0 and P=0, need not be occupied by the lesion or constituents, but it is useful nonetheless for computation. The current mixture configurations κ(τ) with τ∊[0,t] track the evolution of the lesion; they are experimentally observable and, via the assumption of a constrained mixture, provide the current configuration of individual constituents. Finally, although the newly produced collagen is incorporated into the wall under stress, we imagine the existence of individual natural (stress-free) configurations κnk(τ) associated with each instant of production; hence, the natural configurations also evolve.

Grahic Jump Location
Figure 2

Experimentally observable axisymmetric geometries of a lesion in current (i.e., pressurized) configurations at time τ=0 and t as well as a convenient unpressurized reference configuration (which need not be stress-free if different families of collagen-proteoglycans are in tension/compression and self equilibrate). Compare to Fig. 1.

Grahic Jump Location
Figure 4

Effect of the stress mediation parameter K̂g on the enlargement of a lesion due to a 20% initial mass reduction within the central region of the wall given by Eq. 39 and growth and remodeling for different hypotheses on the alignment of newly deposited collagen fibers: (a) case 1, (b) case 2, (c) case 3. Recall that radius and time are nondimensionalized via r∕rh and t∕t2.

Grahic Jump Location
Figure 5

Evolution of a lesion (K̂g=0.48) with a 20% initial mass reduction within the central region of the wall given by Eq. 39 and case 1 preferred deposition: (a) radius, (b) thickness, (c) fiber orientation of new collagen, and (d) principal stresses. The simulation shows that fiber reorientation by case 1 causes an unstable enlargement. Results are similar for K̂g=0 and 0.24. Recall that radius, thickness, and stress are nondimensionalized via r∕rh, h∕rh, and σii∕σh(i=θ,z).

Grahic Jump Location
Figure 6

Evolution of a lesion (K̂g=0.24) with a 20% initial mass reduction given by 39 for case 2 preferred deposition, i.e., the preferred direction tends toward the smaller principal stress direction. Shown are (a) radius, (b) thickness, (c) fiber orientation of new collagen, and (d) principal stresses. Recall from Fig. 4 that this is a stable enlargement.

Grahic Jump Location
Figure 7

Evolution of a lesion (K̂g=0.24) with a 20% initial mass reduction given by Eq. 39 and case 3 preferred deposition: (a) radius, (b) thickness, (c) fiber orientation of new collagen, and (d) principal stresses. Recall from Fig. 4 that this is a stable enlargement.

Grahic Jump Location
Figure 8

Comparison of the enlargement of a lesion between a 20% (fMR=0.2) or 50% (fMR=0.5) initial mass reduction within the central region of the vessel given by Eq. 39 for case 3 preferred deposition

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In