Modeling the dynamics of platelet-like particles under ultrasound stimulation forwound healing applications

Modeling the dynamics of platelet-like particles under ultrasound stimulation for would healing applications

Lead: Mansoor Haider (Mathematics, NCSU)
Collaborators: Marie Muller (Mechanical & Aerospace Engineering, NCSU)  and Ashley Brown (Biomedical Engineering, NCSU & UNC-CH)

Intellectual merit and significance: 
During wound healing, successful clot formation and clot retraction depend on interactions among fibrinogen, thrombin, fibrin matrix and platelets. Biomimetic systems aim to enhance wound healing using platelet-like particles (PLPs) made from soft biomaterials. PLPs are highly
deformable particles with tunable properties, such as concentration and cross-link density, that are engineered to imitate the behavior of natural platelets. The combination of ultrasound with PLPs has potential therapeutic benefit in wound healing; ultrasonic waves can be targeted to
selectively induce dynamic motion of these particles, increasing their mechanical interactions with fibrin matrix [1]. Yet, the optimal combination of PLP design and ultrasound stimulation to achieve such benefits is unknown.

This study will develop mathematical and computational models for dynamic mechanical stimulation of microgel particles immersed in the pores of hydrogels or soft tissues. Existing differential equation models for ultrasound stimulation of (gas) microbubbles [2] (e.g. Rayleigh- Plesset equation) will be extended to consider spherical particles comprised of biomaterials used in the manufacture and design of PLPs. Models will be developed, calibrated, compared and refined in consultation with collaborators having expertise in biomaterial design of PLPs and in acoustic force ultrasound.

Analytical and computational models comparing different dynamic soft tissue and soft matter [3] continuum descriptions of microgels particles; application of models for identifying regimes where ultrasonic waves selectively stimulate microgel particles and enhance interactions with fibrin matrix; development and comparison of dynamic elastic, viscoelastic, shell and soft matter models of PLPs; optimal design of biomaterial properties and ultrasound protocols to enhance would healing outcomes; parameter estimation, local sensitivity analysis and local identifiability analysis for data-driven models [4].


  1. Joshi A, Nandi S, Chester D, Brown AC, Muller M, Study of poly(N-isopropylacrylamide-co- acrylic acid) (pNIPAM) microgel particle induced deformations of tissue-mimicking phantom by ultrasound stimulation. Langmuir 2018; 34:1457-1465.
  2. Doinikov AA, Bouakaz A. Review of shell models for contrast agent microbubbles. IEEE Trans Ultrason Ferroelectr Freq Control. 2011; 58:981-93.
  3. Bachman HN, Brown AC et. al. Ultrasoft, highly deformable microgels Soft Matter 2015; 2018-28.
  4. Pearce KJ, Nellenbach K, Smith RC, Brown AC, Haider MA, Modeling and parameter subset selection for fibrin polymerization kinetics with applications to wound healing. Bulletin of Mathematical Biology 2021; 83:1-22.