usnctam perspectives on mechanics in medicine · body. although they obviously obey the general...

, 20140301, published 28 May 201411 2014 J. R. Soc. Interface Marsden and Bernhard SchreflerHuajian Gao, Shaolie S. Hossain, Thomas J. R. Hughes, Roger D. Kamm, Wing Kam Liu, Alison Gang Bao, Yuri Bazilevs, Jae-Hyun Chung, Paolo Decuzzi, Horacio D. Espinosa, Mauro Ferrari, USNCTAM perspectives on mechanics in medicine

Referenceshttp://rsif.royalsocietypublishing.org/content/11/97/20140301.full.html#ref-list-1

This article cites 186 articles, 22 of which can be accessed free

Subject collections (100 articles)nanotechnology

Articles on similar topics can be found in the following collections

Email alerting service hereright-hand corner of the article or click Receive free email alerts when new articles cite this article - sign up in the box at the top

http://rsif.royalsocietypublishing.org/subscriptions go to: J. R. Soc. InterfaceTo subscribe to

on May 29, 2014rsif.royalsocietypublishing.orgDownloaded from on May 29, 2014rsif.royalsocietypublishing.orgDownloaded from

http://rsif.royalsocietypublishing.org/content/11/97/20140301.full.html#ref-list-1http://rsif.royalsocietypublishing.org/cgi/collection/nanotechnologyhttp://rsif.royalsocietypublishing.org/cgi/alerts/ctalert?alertType=citedby&addAlert=cited_by&saveAlert=no&cited_by_criteria_resid=royinterface;11/97/20140301&return_type=article&return_url=http://rsif.royalsocietypublishing.org/content/11/97/20140301.full.pdf?keytype=ref&ijkey=UhCBonBahCMFmGdhttp://rsif.royalsocietypublishing.org/subscriptionshttp://rsif.royalsocietypublishing.org/http://rsif.royalsocietypublishing.org/

on May 29, 2014rsif.royalsocietypublishing.orgDownloaded from

rsif.royalsocietypublishing.org

PerspectiveCite this article: Bao G et al. 2014 USNCTAMperspectives on mechanics in medicine.

J. R. Soc. Interface 11: 20140301.http://dx.doi.org/10.1098/rsif.2014.0301

Received: 25 March 2014

Accepted: 7 May 2014

Subject Areas:biomechanics, nanotechnology

Keywords:nanoparticle-mediated drug delivery,

biomedical device design, cell mechanics

Authors for correspondence:Roger D. Kamm

e-mail: [email protected]

Wing Kam Liu

e-mail: [email protected]

†US National Committee on Theoretical and

Applied Mechanics (USNCTAM) Coordinator.

& 2014 The Author(s) Published by the Royal Society. All rights reserved.

USNCTAM perspectives on mechanicsin medicine

Gang Bao1, Yuri Bazilevs2, Jae-Hyun Chung3, Paolo Decuzzi4,Horacio D. Espinosa5, Mauro Ferrari4, Huajian Gao6, Shaolie S. Hossain7,Thomas J. R. Hughes8, Roger D. Kamm9, Wing Kam Liu5,†, Alison Marsden10

and Bernhard Schrefler11

1Department of Biomedical Engineering, Georgia Institute of Technology and Emory University, Atlanta, GA, USA2Department of Structural Engineering, University of California, San Diego, CA, USA3Mechanical Engineering, University of Washington, Seattle, WA 98195, USA4Department of Translational Imaging, The Methodist Hospital Research Institute in Houston, Houston,TX 77030, USA5Department of Mechanical Engineering, Northwestern University, Evanston, IL 60208, USA6School of Engineering, Brown University, Providence, RI 02912, USA7Molecular Cardiology, Texas Heart Institute, 6770 Bertner Avenue, MC 2-255, Houston, TX 77030, USA8Institute for Computational Engineering and Sciences, The University of Texas at Austin, Austin, TX78712-1229, USA9Mechanical Engineering, Biological Engineering, Massachusetts Institute of Technology, 77 Mass Avenue,Cambridge, MA, USA10Mechanical and Aerospace Engineering, University of California San Diego, La Jolla, CA, USA11Centre for Mechanics of Biological Materials, University of Padova, Padova, Italy

Over decades, the theoretical and applied mechanics community hasdeveloped sophisticated approaches for analysing the behaviour of complexengineering systems. Most of these approaches have targeted systems in thetransportation, materials, defence and energy industries. Applying andfurther developing engineering approaches for understanding, predictingand modulating the response of complicated biomedical processes not onlyholds great promise in meeting societal needs, but also poses serious chal-lenges. This report, prepared for the US National Committee on Theoreticaland Applied Mechanics, aims to identify the most pressing challenges in bio-logical sciences and medicine that can be tackled within the broad field ofmechanics. This echoes and complements a number of national and inter-national initiatives aiming at fostering interdisciplinary biomedical research.This report also comments on cultural/educational challenges. Specifically,this report focuses on three major thrusts in which we believe mechanics hasand will continue to have a substantial impact. (i) Rationally engineeringinjectable nano/microdevices for imaging and therapy of disease. Withinthis context, we discuss nanoparticle carrier design, vascular transport andadhesion, endocytosis and tumour growth in response to therapy, as well asuncertainty quantification techniques to better connect models and exper-iments. (ii) Design of biomedical devices, including point-of-care diagnosticsystems, model organ and multi-organ microdevices, and pulsatile ventricularassistant devices. (iii) Mechanics of cellular processes, including mechano-sensing and mechanotransduction, improved characterization of cellularconstitutive behaviour, and microfluidic systems for single-cell studies.

1. IntroductionFor many years, the theoretical and applied mechanics community has addressedcomplex engineering problems, primarily in the fields of energy, materials, trans-portation and defence. In addressing these problems, a broad array of tools, bothexperimental and theoretical, have been developed, tested and honed. Thesetechniques allow for detailed characterization and behavioural prediction of thehighly complex systems encountered in engineering applications. The traditionalapplications for which these tools were developed have large numbers of degrees

http://crossmark.crossref.org/dialog/?doi=10.1098/rsif.2014.0301&domain=pdf&date_stamp=2014-05-28mailto:[email protected]:[email protected]://rsif.royalsocietypublishing.org/

rsif.royalsocietypublishing.orgJ.R.Soc.Interface

11:20140301

2


of freedom and operate under unpredictable conditions. How-ever, by using the framework of engineering and science,engineers and scientists can design these systems with a highdegree of fidelity.

For most of its history, medical practice has been basedon qualitative approaches often guided solely by externalinspections and the analysis of the patients’ vital signs,such as the body temperature, blood pressure, pulse, respir-ation rate and weight. The interconnection of medicine andtechnology has led to the development of a series of instru-ments and equipment that are used daily in clinical practiceto assist medical intervention and planning of treatment.This includes the development of the imaging technologies,such as X-ray, ultrasound, magnetic resonance and nuclearimaging, and any combination thereof, for the non-invasive,internal inspection of a patient’s body; external machinesfor assisting the natural function of the kidneys, heart andlungs; artificial implants for cardiovascular and orthopaedicapplications. The recent strides in computational engineeringand sciences and nano/microtechnologies present the fieldof medicine with new opportunities for developing personal-ized interventions and predictive tools and, possibly, forradically changing clinical practice. Mechanics, intended asthe science concerned with the behaviour of bodies and theirinteraction with the environment, can contribute significantlyto this development.

In this report, prepared for the US National Committeeon Theoretical and Applied Mechanics (USNCTAM), we ident-ify and discuss what we consider to be the most pressingchallenges in biological sciences and medicine for which mech-anics can have a substantial impact. These challenges are (i) therational engineering of injectable nano/microdevices forimaging and therapy of disease, with discussions on nanopar-ticle (NP) carrier design, vascular transport and adhesion,endocytosis, tumour growth in response to therapy, and uncer-tainty quantification techniques to better guide models andexperiments, (ii) design of biomedical devices, includingpoint-of-care (POC) diagnostic systems, model organ andmulti-organ microdevices and pulsatile ventricular assistantdevices, and (iii) mechanics of cellular processes, includingmechanosensing and mechanotransduction, improved charac-terization of cellular constitutive behaviour and microfluidicsystems for single-cell studies. In addition to these specific,scientific problems, we highlight the educational/cultural chal-lenges and opportunities stemming from the interdisciplinarynature of mechanics in medicine.

2. Nanoparticle-mediated drug delivery2.1. OverviewThe history of applications of mechanics to medicine andbiology is extraordinarily rich and diverse; suffice it to recognizeits fundamental role in orthopaedics, or the absolute reliance ofpharmacokinetics and pharmacodynamics on the equationsof mass transport, or the centrality of fluid dynamics in theunderstanding of cardiovascular physiology and pathology.Beyond these traditional, yet still very productive and importantareas, it is now possible to envision novel connections betweenmechanics and medicine in ways that were unimaginable untilrecent times, because they are made possible by the emergenceof novel disciplines.

A first paradigm for this convergence is embodied by thetriangulation of biology and medicine with mechanics bymeans of nanotechnology; a second, corollary example is theframework of transport oncophysics; yet another is the newfield of predictive anatomy. By way of illustration, one mayconsider the problem of transport of nanoscale objects (biologi-cal such as protein, or synthetic such as a chemotherapeuticmolecule, a radiological contrast agent or an NP) inside thebody. Although they obviously obey the general mechanicallaws of transport, their distribution in the body is largelyimpossible to predict a priori, in view of the impossibility toestablish general governing equations, which will take intoaccount the various biological barriers of the body, which inturn ultimately determine the transport profiles. However,this is as central a problem as there can be in the field of bio-mechanics—life is predicated upon the ability of the bodyto succeed in transporting nanoscale objects in a very accu-rately controlled manner. Although there is no current hopefor a master equation of transport of an arbitrary biologicalnanoscale object, great simplifications can be attained by con-sidering the body transport of synthetic NPs with preciseengineering properties, so that the number of independentvariables may be reduced to reason. Thus, nanotechnologyenables the understanding of some fundamental aspects ofbiomechanics of mass transport in a manner that was unat-tainable before the development of precise methods forthe manufacturing of NPs and their characterization. Theadditional beauty of this is that the very NPs that are developedfor the study of the mechanics of body transport can then beused as agents of therapy once the ability to distribute prefer-entially in target organs of the body is understood—this isthe basis for new perspectives of cancer therapy and the perso-nalization of treatment, based on mechanics and the rationaldesign of vectors for the targeted delivery of drugs. A secondexample of nanotechnologies as models for otherwise intract-able biomechanical transport problems is the use of syntheticnanochannels to replicate and study transport through nano-scale environments such as ionic and molecular channels onthe surfaces of biological cells.

It is insightful to observe that the study of the body trans-port and selective accumulation of chemotherapeutic agentsand nanomedicines has revealed that cancer is in reality aproliferative disease of mass transport disregulation, at mul-tiple scales, from the local (tissue invasion by cells) to thesystemic (distant metastases) and the molecular level (subcel-lular signalling pathologies). In this case, mechanics by wayof nanotechnology yielded transport oncophysics, i.e. the rec-ognition of entirely novel perspectives on the nature of amajor class of diseases such as cancer. Based on this para-digm, it may well be expected that further advances inmechanics could offer transformational insights into manyother domains of medicine and biology.

Predictive anatomy uses the mechanical tools of mathe-matical, multi-scale homogenization theory to predict thecharacteristics of body parts, as they are most likely to emergein the course of evolutionary selection. The engineering counter-part of this novel discipline is the methodology of optimaldesign, which involves the statement of an objective functionto be optimized, a space of design variables and a set of con-straints. Exactly the same approach can be applied to yield‘best designs’ of body parts that serve mechanical functionssuch as the ability to bear loads, or transport mass andheat. Thus, recent methodologies such as the emergence of

http://rsif.royalsocietypublishing.org/

endocytosis

adsorption

red blood cell (RBC)

7.82 mm

(b)

(c)

(d)

(a)10 – 1000 nm

PEI800 siRNA

zx

y

endosomalrupture

Figure 1. A schematic of the nanoparticle-mediated drug delivery process [10]. (a) A solution containing nanoparticle delivery platforms is injected into a patient’scirculatory system [11]. (b) In the microvasculature, nanoparticles are segregated from red blood cells, increasing their interaction with the endothelium, eventuallyleading to their removal from circulation [12]. (c) Nanoparticles diffuse through the extracellular matrix, eventually adsorbing onto the surface of a target cell. Thenanoparticles are then endocytosed from the lipid membrane. (d ) The endosome containing the drug delivery complex ruptures, releasing the therapeutic agentsinto the cytoplasm. When released from the endosome, the nanoparticle cargo may be dissociated due to the local pH environment change.


11:20140301

3


nanotechnology and advances in the mathematical theory ofmulti-scale homogenization can serve to join mechanics withmedicine and biology in very innovative manners that providenew horizons for scientific advances, and opportunities formedical breakthroughs.

The expansion of nanotechnology over the past twodecades has led to a paradigm shift in drug delivery. Formost of the history of chemical therapeutics, delivery wasnon-specific and the single controllable parameter was con-centration. Although targeting of specific pathways throughdrug design was first introduced in the 1950s [1], the controlover molecular properties afforded by advances in nanotech-nology has ushered in a new era in drug delivery. Whereasearly targeting strategies relied on chemical changes to indi-vidual molecules, it is now possible to synthesize NPs withprecisely controlled size, shape, stiffness and surface chem-istry to efficiently deliver drug molecules into diseasedcells/tissues [2,3]. Although researchers now have a greatlyexpanded set of knobs to turn when designing NPs, it is gen-erally not clear how a change to a specific vehicle feature willalter the effectiveness of a drug, and hence design of noveldrug carriers requires extensive and costly parametric studiesthat are generally specific to the system upon which theexperiments were performed. Theoretical and computationalmodelling of the delivery process can greatly reduce theneed for physical experiments and provide general designprinciples to expedite the design process [4–9].

Any modelling strategy that aims to predict a drug’seffectiveness based on the nanoscopic features of the deliveryplatform must account for processes across the disparatespatial and temporal scales travelled by an NP during deliv-ery. Initially, a solution of drug carriers is introduced tothe circulatory system, either through absorption or direct

injection (figure 1a). The circulation of the particles in the vas-culature network can greatly affect the concentration of drugdelivered to the area of diseased cells and depends on thegeometry and chemistry of the particles. Modelling transportthrough the vasculature has presented significant challengesowing to the vastly different length scales of the vascularnetwork, which can range from centimetres for the diameterof the ascending aorta to micrometres in the case of capillaries[11–15]. In the macrovasculature, particle transport can bemodelled as an advection–diffusion process through complexnetworks. State-of-the-art techniques involve simulationsthrough patient-specific vascular networks [13]. However,near the endothelium and in the microvasculature, complexinteractions between blood plasma, red blood cells (RBCs)and NPs require more detailed approaches that explici-tly account for the interactions between RBCs and NPs(figure 1b). These complex interactions can be studied by theimmersed finite-element technique [12,15–33], accounting forthe microcirculation behaviour of NPs, under the influence ofRBCs and fluid flow. These models are proved to be capableof capturing the segregation of NPs and RBCs as well asparticle adhesion to the vascular walls [12,14].

Upon adhesion, particles diffuse through the extracellularmatrix (ECM), eventually reaching a cell possessing the tar-geted marker (figure 1c). The adsorption of NPs onto thecell membrane is heavily influenced by the functionalizationof the carrier surface, the local molecular composition of themembrane and extracellular environmental variables such aspH and salt concentration [34]. Adsorbed particles are thenwrapped by the cell membrane and endocytosed. The endo-somes containing the NP–drug complexes can then eitherfuse into lysosomes, which can degrade the drug moleculesin the process, or they can rupture, releasing their contents


rsif.royalsocietypublishing.org

4


into the cytoplasm (figure 1d ). To understand the interactionsbetween particles and cell membranes, it is necessary tomodel the systems at the molecular scale. Techniques suchas molecular dynamics and molecular mean-field theorycalculations are capable of illuminating the effect of particlesize, shape and chemistry on cellular uptake rates [35,36].Although molecular calculations provide far more detailfor specific systems, continuum theories can also provideuseful guiding principles for NP design, even at lengthscales of the order of a single NP [37–41].

J.R.Soc.Interface11:20140301

2.2. Nanoparticle-based drug carrier designNanoscale technologies can improve the bioavailability andbiodistribution of systemically injected therapeutic and ima-ging agents [42,43]. Nanoconstructs can navigate throughthe circulatory system and preferentially recognize thetumour neovasculature [5,44] and encapsulate large amountsof different agents, for both therapy and imaging [45]. It isknown that the blood vessel network in primary and metastatictumours is different from the healthy vasculature [46,47].Endothelial cells form an imperfect lining with wide junctions(fenestrations), ranging in size from 100 to 1000 nm. This leadsto vascular hyper-permeability, lower mean blood velocity(1–10 versus approx. 100 mm s21 in normal microvessels)and higher interstitial fluid (IF) pressure (up to 5–7 kPa).Furthermore, the surface density of inflammatory vascularmolecules, such as intercellular cell adhesion molecules(ICAM-1) and E-selectin, is one to two orders of magnitudehigher on the tumour endothelium. In addition, tumour-specific vascular receptors, such as the avb3 integrins, areexpressed at levels of 100–1000 molecules mm22 [48]. Takingadvantage of all of these differences between healthy and dis-eased vessels, a plethora of nanoconstructs with different sizes,surface properties and, more recently, shapes have been devel-oped over the past 20 years for delivering imaging andtherapeutic agents preferentially to the malignant tissue.Indeed, the encapsulation of different, and multiple, agentsinto nanoconstructs has provided significant improvementsin pharmacokinetics, toxicity and biodistribution. Despite allof this, the effective detection and treatment of malignantmasses via the systemic injection of nanoconstructs is still lim-ited by insufficient accumulation at the biological target(� 10% injected dose per gram tumour—%ID g21) and non-specific sequestration by organs of the reticulo-endothelialsystem (RES; tumour-to-liver , 0.1). Even the notion of target-ing nanoconstructs to specific receptors, expressed on thetumour neovasculature or cells, has often led to contradictoryresults. The development of novel, clinically relevant deliverysystems with high tumouritropic accumulation is critical forfurther improvement of therapeutic outcomes and the earlydetection of solid tumours.

The size, surface properties, stiffness and shape of the nano-constructs affect their in vivo behaviour and therapeuticefficacy. The importance of tuning the nanoconstruct sizeand surface properties has been recognized since the late1990s. In a series of seminal papers, Jain and co-workers [49]showed that liposomes and latex beads smaller than300–400 nm in diameter would accumulate more efficientlyin tumours than larger beads, via passive extravasation at thetumour fenestrations. This is the ‘dogma’ that has guided thefield of nanomedicine since then and is known as the enhancedpermeability and retention (EPR) effect. In addition, further

studies [50,51] showed that the surface charge of lipid-basednanoconstructs can control accumulation in tumours as wellas in the liver and lungs. These were followed by many studiesfurther elaborating on the role of nanoconstruct size and sur-face charge, for different material formulations and surfacechemistry [52–54]. Molecular-specific nanoconstructs havealso been developed, where the particle surface is coatedwith ligand molecules capable of recognizing and binding tocounter molecules (receptors) expressed on the target cells[55]. Despite its high in vitro efficiency, this approach suffersin vivo owing to reduced binding affinity, lack of ligand immu-nogenicity and the limited number of ligand moleculesavailable, especially for the smaller particles. Because of this,data in the literature on specific tumour targeting of nanocon-structs are still highly controversial [56,57]. Following the EPRdogma, a myriad of nanoconstructs have been developed withdifferent surface properties and sizes, often presenting onlyminimal improvements in terms of tumour accumulationand liver escape. More recently, novel nanofabrication strat-egies have been presented for the synthesis of non-sphericalnanoconstructs [58–61]. This fostered new theoretical [5,38,39,62–64], in vitro [65–69] and in vivo [44,70–74] studiesdemonstrating the importance of shape in controlling thevascular behaviour, cellular uptake and differential organaccumulation of the systemically injected nanoconstructs.Size, shape and surface properties can be envisioned as threeindependent variables in an optimization problem where theobjectives are to maximize tumour accumulation and minimizethe non-specific sequestration of nanoconstructs.

The physico-chemical properties of NPs, such as size,shape, surface charge and stiffness, can affect their biologicalclearance. Therefore, NPs can be modified in various ways toextend their circulation time. In recent decades, the designof NPs for biomedical applications has been advanced bystudying their biological responses. The evolution of the NPcarriers has followed advances in understanding of howsize, shape, surface and stiffness affect efficacy. As shownin figure 2, there are three generations of NPs developedfor biomedical applications [75]. In the first generation ofNPs, the NPs are functionalized with basic surface chemistry(charges/ligands) and are evaluated through their bio-compatibility and toxicity [76,77]. However, these NPs areunstable and usually internalized by the immune cellsduring circulation. To overcome these problems in thesecond generation, the surfaces of NPs are grafted with poly-mer chains, improving their water solubility and allowingthem to avoid aggregation and opsonization. Comparedwith the first generation, the second-generation NPs demon-strate improved stability and targeting in biological systems.However, the active targeting of these NPs to the tumourcells (TCs) or other diseased cells is still disappointing.Thus, the third-generation NPs shift the design paradigmfrom stable materials to ‘intelligent’ and environmentallyresponsive materials with improved targeting capabilities.Local environmental (i.e. pH value) changes cause the prop-erties of these NPs to change in a prescribed way. Here, weshould emphasize that although the design of NPs shiftsfrom the first generation to the third generation, the first-and second-generation NPs still have many applications indifferent areas, and their behaviours are still poorly under-stood. Moreover, a comprehensive understanding of thefirst- and second-generation NPs will help us to efficientlydesign the third-generation NPs.


first generation

material designwater solubilitybiocompatibility

unstableremoval by mononuclear phagocytic systempoor tumour targeting

nano-materials

biologicalchallenges

maximize delivery

active targeting isdisappointing

active targeting

overreliance on EPReffectno ‘universal’ antigen

no ‘universal’ designprinciple

(a)

(c) (d)

(b)randomlydistributedNPs

(i)

(iv) (v) (vi)

(ii) (iii)10

NP diameter: 10 nm

boundary NP

randomly distributed NP

thickness of cell free layer

8

radi

al d

ista

nce

(μm

)

6

4

2

00.2 0.4 0.6

time (s)0.8 1.0

10 –0.020

disc g = 0.20disc g = 0.33

disc g = 0.50disc g = 0.67disc g = 0.80

ellipsoid g = 0.5hemisphere

sphere

–0.015

–0.010

–0.005

6.05.0

4.0

3.0

2.0

1.5

100.0

70.060.050.040.0

30.0

20.0

15.0

5.0 6.0 7.0 10.0

shear rate [s–1]

15.0 20.0 30.0 40.0 50.0

0.0000.01

y

u = Sy h

x

q

0.1 1

St

vSa

10 100

NP diameter: 50 nm

boundary NP



8

radi

al d

ista

nce

(μm

)

6

4

2

000 0.2 0.4 0.6

time (s)0.8 1.0

10NP diameter: 500 nm

boundary NP



8

radi

al d

ista

nce

(μm

)6

4

2

00 0.2 0.4 0.6

time (s)0.8 1.0


boundary NP



8

radi

al d

ista

nce

(μm

)

6

4

2

00 0.2 0.4 0.6

time (s)0.8 1.0


boundary NP



8

radi

al d

ista

nce

(μm

)

6

4

2

00 0.2 0.4 0.6

time (s)

C

2b 2H

2a 2c 2d 2e

2005.83

S0.852

0.8 1.0

boundaryNPs

n

discoidal (r = 2200 kg m–3, d = 1.5 mm)

spherical (r = 2200 kg m–3, d = 1.0 mm)

quasi–hemispherical (r = 1840 kg m–3, d = 1.6 mm)

1262.96

S1.021

225.228

S0.630

Figure 3. Vascular dynamics of non-spherical nanoconstructs. (a) Fast moving RBCs confine submicrometre-sized nanoconstructs in proximity of the vessel walls,which favours the recognition of the diseased endothelium [12]. (b) Thin discoidal nanoconstructs drift laterally, across the stream lines, with a higher velocity ascompared to spherical, quasi-hemispherical or thick discoidal nanoconstructs [78]. (c) In vitro parallel plate flow chamber experiments confirm that thin discoidalnanoconstructs would deposit and adhere more efficiently than spherical and quasi-hemispherical nanoconstructs, over a wide range of wall shear rates S [79].

(a)

0

ICP-AESuntargeted

% in

ject

ed d

ose/

gram

org

an

600 × 200 nm disc1000 × 400 nm disc1800 × 600 nm disc

RGD-targeted

2

4

6

8

10(c)

0600 × 200 1000 × 400

particle size d × h (nm)

norm

aliz

ed n

o. o

f ad

here

nt P

s

1800 × 600

5

10

15

20

25

30

35 S = 10 s–1

S = 50 s–1

S = 100 s–1

S = 200 s–1

(b)

(d)

0.001

g = 9

g = 3

g = 1linear shear flow U = sh

Tligand

endothelial substrate

F

Ae

h oδ oqreceptor

g = 7

g = 5

0.001prob

abili

ty o

f ad

hesi

on

0.01

0.1

1

0.01 0.1volume

1 10

Figure 4. Vascular adhesion of non-spherical nanoconstructs. (a) The probability of vascular adhesion grows as the shape deviates from spherical (g ¼ 1, sphere;g� 1, quasi-discoidal particles) [2]. (b) Parallel plate flow chamber experiments showing a maximum vascular adhesion occurring for 1000 � 400 nm discoidalnanoconstructs [82]. (c) Tumour accumulation of untargeted and RGD-4C targeted discoidal nanoconstructs, demonstrating again a maximum accumulation for the1000 � 400 nm discoidal nanoconstructs [44]. (d ) Fluorescent images and scanning electron micrographs showing discoidal nanoconstructs (see yellow arrows)laying on the tumour neovasculature. 10% of the RBCs were stained in blue [44].


11:20140301

6



0

0

10

20

30

40

(a) (d)

(b)

(c)

no inhibitor

% o

f ce

lls w

ith C

NT

s%

of

cells

with

CN

Ts

**p < 0.005inhibitor

37°C***p < 0.0005

***

**

4°C

5

10

15

15

25

30

Figure 5. Experimental observations of energy-dependent tip entry of one-dimensional nanomaterials into cells. (a) Carbon nanotubes entering murine liver cells.Arrow in middle panel shows carbon shell at the tube tip that distinguishes the nanotubes from surface microvilli. Arrows in right panels show close views ofmembrane invaginations surrounding the tubes at the point of entry. (b) Examples of nanotube tip entry in human mesothelial cells. Both an isolated tube(single arrow) and a tube bundle (double arrow) are seen in the process of high-angle entry. (c) Examples of active tip entry for other one-dimensional materials:30 nm gold nanowires (left) and a 500 nm crocidolite asbestos fibre (right). (d ) Effects of temperature and metabolic inhibitors on multi-walled CNT uptake as testsfor active endocytic uptake. All images are obtained by field emission scanning electron microscopy following fixation and contrast enhancement with osmiumtetroxide. All scale bars are 300 nm. Figure from [35].


11:20140301

7


multiple disciplines and expertise pertaining to the field of com-putational mechanics, chemistry, physics as well as biology,immunology and biomedical sciences. This will eventuallylead to the development of a new class of truly interdisciplinaryscientists that would grasp the details of each individual field,facilitate constructive synergies, and be capable of synthesistowards the achievement of the common goal.

2.4. Endocytosis2.4.1. Cell uptake of one-dimensional nanomaterialsVarious types of NPs, nanowires, nanofibres, nanotubes andatomically thin plates and sheets have emerged as promisingcandidates for potential applications in next-generationbiosensors, drug delivery and medical imaging. There is anurgent societal need for better understanding of both ben-eficial and hazardous effects of these nanotechnologies.Below is a summary of some recent work on the mechanicsof cell uptake of one-dimensional nanomaterials such asnanotubes and nanowires. A combined study based on elec-tron microscopy, theoretical modelling and moleculardynamics simulations shows that carbon nanotubes (CNTs)enter cells via a tip recognition pathway that involves recep-tor binding, tube rotation driven by elastic energy at thetube–bilayer interface and near-vertical entry.

Research on the mechanics of cell–nanomaterials inter-action is of significance not only to the understanding ofhazardous effects of viruses and nanomaterials in general,but also to biomedical applications such as gene/drug deliv-ery and medical imaging [84–86]. A current problem ofimmediate concern to society is that nanomaterials, whichinclude various types of NPs, nanowires, nanofibres,

nanotubes and atomically thin plates and sheets, could pene-trate the membrane of human and animal cells. It is knownthat geometrical properties of NPs such as size [37,40],shape [5,38,39,87–90], elastic modulus [41] and surfacemicrostructure [91,92] can substantially influence endocyto-sis, phagocytosis, circulation [85] and targeting [86]. Belowis a summary of some recent work at Brown University onthe mechanics of cell uptake of one-dimensional nanomater-ials [35]. Compared with other non-spherical NPs, thecellular interactions of one-dimensional nanomaterials suchas CNTs are particularly important for biomedical diagnos-tics and therapies [93,94], and for managing health impactsof nanomaterials following occupational or environmentalexposure [95–97].

Recently, we carried out a combined study by electronmicroscopy, theoretical modelling and molecular dynamicsto elucidate the fundamental interactions of cylindrical one-dimensional nanomaterials with eukaryotic cell membranes[35]. Figure 5 shows electron micrographs of common mor-phologies in the near-membrane region following in vitroexposure of murine liver cells or human mesothelial cells todifferent types of one-dimensional nanomaterials, includingCNTs, crocidolite asbestos nanofibres and amine-terminatedgold nanowires [35]. It can be seen that near-vertical tipentry is a common uptake pathway for geometrically similar,but chemically very different nanomaterials. To determinewhether the uptake of CNTs is mediated by energy-dependentendocytosis, murine liver cells were incubated either at 4 or378C. Internalization of CNTs was significantly decreased at48C (figure 5d). In the presence of metabolic inhibitors, theuptake of CNTs was also significantly decreased (figure 5d )confirming that this uptake requires adenosine triphosphate.


(a) (b) (c)side view

308 ms 210 ms 30 ns

side view side viewtop view

leftside right

side

top viewt = 0 t = 0 t = 0

top view

Figure 6. Time sequence of coarse-grained molecular dynamics simulation results showing a multi-walled carbon nanotube penetrating a cell membrane at an initialentry angle of u0¼ 458 as a function of receptor density. The receptor (green) densities are (a) f ¼ 0.25, (b) f ¼ 0.33 and (c) f ¼ 1. Figure from [35].


11:20140301

8


Why is tip entry the preferred mode of cellular uptakeof one-dimensional nanomaterials? This fundamental ques-tion has been investigated using coarse-grained moleculardynamics simulations under the basic hypothesis that nano-tubes with closed, rounded caps can mimic particles andinitiate endocytosis, and that elastic energy in the plasmamembrane provides a driving force to rotate one-dimensionalnanostructures from their initial angle of contact to highangles. In the simulations, a capped multi-walled CNT isinitially positioned in close proximity above the surface of apatch of bilayer. The initial angle between the axis of thenanotube and the bilayer is pre-selected and a range of recep-tor densities, f, are considered. The receptors diffuse alongthe bilayer and aggregate around the nanotube owing tobinding affinity. As receptors cluster and adhere to the nano-tube surface, the tube is pulled into the bilayer and wrapped.In this process, the tube is observed to spontaneously rotateto achieve an entry angle close to 908, driven by membraneelastic energy minimization during wrapping (figure 6).Figure 6b shows that, at a higher receptor density of f ¼ 0.33,the nanotube can become fully wrapped before it reaches the908 entry angle. Generally, increasing receptor density tendsto hinder the rotation towards 908 entry. In the extreme caseof f ¼ 1, in which the adhesion loses specificity, the membraneon the right side of the nanotube adheres to the tube muchfaster than that on the left side (figure 6c), and the nanotubeadopts a very small entry angle. This can be understood fromthe fact that, for non-specific adhesion, the right side mem-brane has the distinct advantage of being initially closerto the tube surface and dominates the early-stage receptorbinding before rotation can occur. These simulations revealtwo competing kinetic processes: rotation of the tube towardsa 908 entry angle to relax elastic energy in the membraneand wrapping speeds on different sides of the tube governedby receptor diffusion. If the former prevails, as would beexpected at relatively low receptor densities, then the finalentry angle will be close to 908. Note that the extreme case ofnon-specific interactions shown in figure 6c is an interestingtheoretical limit which is not expected to be important for areal cellular system.

Similar observations of tip entry and rotation towards 908entry have been noted in simulations for different CNTdiameters and lengths, receptor densities, receptor bindingstrengths and initial entry angles, and the results show thatthe tube still adopts a 908 entry pathway [35]. Further

simulations show that the tip-entry mechanism is essentiallyunchanged if the hemispherical caps are replaced by enlargedshells typical of catalytically produced CNTs, or if the nano-tubes exist in suspension as small bundles. Interestingly, it isfound that open-ended nanotubes do not undergo tip entrybecause they lack carbon atom sites for receptor binding onthe cap in the early stages of wrapping. This suggests that oxi-dative cutting or other intelligent tip modification may be usedto control the membrane interaction and cell entry of a subclassof hollow one-dimensional nanomaterials. Moreover, simpleanalytical models and coarse-grained molecular dynamicssimulations show that the time scale for tip rotation is one ortwo orders of magnitude smaller than that for the overall wrap-ping of the NPs, and tip entry is expected to be a favourablepathway for cellular uptake of capped nanotubes and otherone-dimensional nanomaterials [35]. This tip-entry mechanismis proposed as a key initiator of frustrated uptake and toxicity,because a vertical alignment provides no opportunity for thecell membrane to sense or anticipate the ultimate length ofthe fibrous target material.

The latest theoretical studies in molecular dynamicssimulations show that the cell uptake of one-dimensional nano-materials via receptor-mediated endocytosis is governed by asingle dimensionless parameter, the normalized membrane ten-sion �s ; 2sa2/k, where a denotes the nanomaterial radius, s isthe membrane tension and k is the bending stiffness of cellmembrane. As cell membrane internalizes one-dimensionalnanomaterials, the uptake follows a near-perpendicular entrymode at small membrane tension but it switches to a near-parallel interaction mode at large membrane tension. This�s-dependent uptake behaviour is also found to be ubiquitousin the interplay between cell membranes and one-dimensionalnanostructures, and has broad implications for the differentinteraction modes exhibited by single nanotubes and nanotubebundles, tubulation of NPs and bacterial toxins on cell mem-branes, control of the size of filopodia and measurement ofcell membrane tension [98].

In physiological situations such as endocytosis, adhesionbonds between biomolecules on NPs and cell surfaces usuallyoperate cooperatively, and an initial phase of particle attach-ment or docking should, in fact, play a very important role inthe overall process of endocytosis. The large surface areaenables CNTs to achieve sidewall functionalization, to actas a template for cargo molecules such as proteins [99],small molecules [100] and nucleic acids [101]. It will be


0

1

2

3

4

5

6

7

0.4no wrapping

no wrapping

part

ial w

rapp

ing

partial wrapping

partial wrapping

complete wrapping

complete wrapping

0.8grafting density (chains nm–2)

bind

ing

stre

ngth

eb

(kB

T)

1.2 1.6

Figure 7. Phase diagram of receptor-mediated endocytosis of the second-generation NPs. The figure is taken and modified from [114].


11:20140301

9


interesting to consider different functional groups on CNTwalls, the kinetic process of receptor diffusion [102–105],interaction and docking of particles of different sizes,shapes and elastic modulus near a cell, extending a recentstudy by Shi et al. [89]. It can be imagined that CNTs withdifferent sizes, tip shapes and patterns of functional groupscan form a tunable platform for designing controlled cellularuptake. Substantial challenges exist when considering elasticnanofibres instead of stiff CNTs. This extension will requiresolving diffusion equations on curved deforming surfaces,and can therefore be extremely difficult especially in three-dimensional modelling. Simulation studies will also playcritical roles in the interaction mechanism between cell mem-branes and nanomaterials, especially in the case where NPscan penetrate into or destructively extract phospholipids[90,106]. Overall, the cellular uptake of NPs is a multi-scaleprocess both in spatial and temporal scales, which requiresa coordinated study between experimental, theoretical oratomic/molecular simulation approaches.

2.4.2. Cell uptake of polymer-coated nanomaterialsIn the first-generation NPs, only ligands are attached to theirsurfaces. To improve the water solubility and avoid aggregationof NPs, the surfaces of the second-generation NPs are usuallygrafted with polymer chains, i.e. PEG, which is a hydrophilicand biocompatible polymer. After PEGylation, the propertiesof the NPs are dramatically changed. For example, the surfacecharge of the NPs will be shielded by tethered chains, andNPs with grafted chains can be well dispersed in the solution.More importantly, a ‘stealth’ shell will be formed by the graftedchains which can prevent clearance by the immune system(opsonization) [52,107]. Therefore, PEGylated NPs display pro-longed blood circulation time. To improve the endoctyosis ofNPs, the free ends of grafted chains are conjugated with target-ing moieties, e.g. cell-penetrating peptides [108–110], RGDpeptides [111,112] and anti-HER2 antibodies [113]. With thehelp of these specific ligand–receptor interactions, the cellularuptake of PEGylated NPs is tremendously enhanced. However,the interplay between NP core diameter, grafting density andpolymer chain length makes cellular uptake of the second-generation NPs distinct from the first-generation NPs [114].To understand these effects, we study the receptor-mediatedendocytosis of polymer-coated NPs through large-scalecoarse-grained molecular dynamics simulations and self-consistent field theory [114]. A realistic coarse-grained modelhas also been developed to correctly reproduce the confor-mation of PEG polymers in water [114,115], based on the

inverse Boltzmann method [116–118]. The following resultsare obtained through our simulations. First, the non-specificsteric (repulsive) interaction between grafted chains and thecell membrane is found to have an effect which is comparableto, or even larger than, the bending energy of the membraneduring endocytosis. By incorporating this non-specific stericinteraction, the critical ligand–receptor binding strength forNPs to be internalized can be correctly predicted by a simpleanalytical equation. Second, an optimal grafting density ofapproximately 0.80 chain nm22, which can enhance the specificligand–receptor interactions and reduce both non-specificsteric repulsions and opsonization during blood circulation, isalso identified through our simulations. Third, a phase diagramhas been constructed according to the polymer grafting densityand ligand–receptor binding strength, as described in figure 7.Three different phases, including no wrapping, partial wrap-ping and complete wrapping, have been identified throughour simulations. These findings pave the way for designingnew-generation, NP-based therapeutic carriers with improvedcellular targeting and uptake.

2.5. Uncertainty quantification of drug delivery processThe NP-mediated drug delivery process involves many differ-ent spatial and temporal scales. These different scales interplaywith each other with many uncertainties. To design efficientdelivery platforms, these uncertainties cannot be ignored. Forexample, individual patients have different health histories,which may affect their immune systems. The heart pumpingrate, vasculature network and circulatory network may alsovary from one person to another. The circulation of NPs inthe body can be greatly affected by these factors. The local-specific vessel characteristics, i.e. vessel diameter, flow rateand haematocrit, can change the near-wall concentration ofNPs tremendously during microcirculation. As we have seen,the endocytosis of NPs depends on cell types, ligand–receptorinteractions and particle sizes and shapes [5,38]. Uncertaintiesin a model at one scale can propagate to the others when theinputs to simulations are informed by results of another, asdescribed in figure 8. The transport of NPs in the circulatorynetwork can change their concentrations in microvasculaturenetwork. The near-wall concentration of NPs can influencethe endocytosis process. Therefore, it is crucial to considerthese uncertainties in the modelling and design of NPplatforms, especially connecting models across scales [15].

However, there is not a truly multi-scale computationalmethod connecting these different models together to bridgedifferent spatial and temporal scales [10]. In future, we expect


heart pumpingvessel bifurcationcirculatory system

age, race, genderhealth history

macrovasculature

microvasculature

microvessel

R2

x

zy drug carrier

red blood cell

patient-specific

haematocritvascular networkshear rate

drift velocityfor each vessel

diffusion throughcirculatory system

uncertaintypropagation

of drift velocity

increasing uncertaintyinput parameters

drug clearancefor entire human body

Figure 8. Uncertainty of NP transport in the multi-scale vascular system.

fibrous cap

lipid pool

vulnerable plaque

Figure 9. A schematic of a typical vulnerable plaque with a large lipid pooland a thin fibrous cap that separates the thrombogenic components of the


11:20140301

10


that such a multi-scale model will be available, allowing for theprediction of a drug-delivery vehicle’s efficiency and speci-ficity, and hence design based on the optimal performanceacross all stages of the delivery process, as opposed to optimiz-ation for specific portions of the drug carrier’s life. Theflexibility of the method allows for rapid computational proto-typing and testing of drug delivery complexes under realisticconditions within a short time, providing new insights intothe interplay between molecular-scale interactions of intricatedelivery vehicles and their transport within a specific patient.Enhanced targeting will also alleviate patient suffering byreducing required dosage of highly toxic cancer drugs. Inaddition, medical expenses can be reduced as a result of shortertreatment durations and fewer serious side-effects.

plaque from the lumen.

2.6. Application of patient-specific computationalmodelling to detect and/or treat cardiovasculardisease

The foundations of science and engineering were rapidly, dra-matically and irrevocably changed by the advent of thecomputer. Over the past decade in particular, the exponentialgrowth of computing speed and capacity has transformedmankind’s ability to assimilate immense amounts of data,analyse them and apply them to solve global problems ofextraordinary complexity [119]. Perhaps nowhere is the scien-tific revolution sparked by computational mechanics morepromising than in the field of medicine.

This approach to problem-solving using theoretical andapplied mechanics allows us to simulate physical events andthus take much of the guesswork out of scientific researchwhile simultaneously accelerating its pace. We can test ourideas in a virtual world and, with a high degree of accuracy,predict the outcomes. How will a medical treatment work onan individual patient? How will production of a particular

energy resource affect the environment? Through the powerof simulation and visualization, we can actually predict andsee changes that are likely to occur. Thanks to these techniques,the holy grail of personalized medical treatments—those basedon an individual’s anatomy, genome, family history andenvironmental history—is now realistically in sight. Onesuch example is presented below.

Cardiovascular disease is the leading cause of death in theUSA and represents more than a half-trillion-dollar businessin research and treatment in the USA alone. Most people donot know that 70% of all fatal heart attacks are caused by ruptureof plaques with large cores of lipid and necrotic debris encasedbya fibrous cap, so-called vulnerable plaques (VPs), which oftendo not create significant narrowing of the lumen and thereforeare not detected with standard medical imaging modalities,such as computed tomography, magnetic resonance imaging,coronary angiography and external ultrasound (figure 9). Bothdetection and treatment of VPs present huge unmet clinicalneeds. It has been postulated that diseased arteries can be


(a) (b)

(c) nanoparticlesurface concentration(normalized)

drug concentration(normalized)

ligand

vascular receptor ligand receptor affinity

(d)

16

12

8

4

0

1.5 × 10–8

time: 2.31 daystime: 14.0 s

3.0 × 10–8

4.4 × 10–8

5.6 × 10–8

0

drug release from anadhered nanoparticle

Figure 10. (a) Patient-specific modelling of vascular deposition of nanoparticles from [7]. (b) Drug release from adhered nanoparticles. (c) Simulated results ofnanoparticle distribution in the targeted region (near the vulnerable plaque, VP) with a higher density of receptor expression. (d ) The corresponding drug dis-tribution pattern within an idealized VP.


11:20140301

11


diagnosed and/or acutely treated with drugs delivered locallyto rupture prone plaques using NPs in order to promote rapidplaque stabilization and/or passivation.

In addition to the size of the necrotic lipid core, the extentand location of plaque inflammation appear to be keyfactors in determining plaque instability [120,121]. Alongwith immune cell activation, inflammation contributes to theloss of collagen in the fibrous cap, a prelude to fibrous cap rup-ture. Inflammation is also known to induce differential surfaceexpression of specific vascular molecules such as ICAM-1,intravascular cell adhesion molecules and selectins. Blood-borne NPs, conjugated with targeting ligands and loadedwith therapeutic and/or imaging agents, can potentiallyrecognize and use these molecules as vascular docking sites,thereby helping to detect VPs and/or deliver site-specificacute therapy [121,122].

In a typical local drug delivery system, drug-encapsulatedpolymeric NPs are injected directly into the blood stream.These NPs are sufficiently small, 20–500 nm in diameter, to beadministered at the systemic level. Carried by the bloodstream, these NPs can reach any biological target. Some of theNPs marginate or drift towards the artery wall facilitatinglocal interactions with the endothelium. To enhance the specificrecognition of the biological target (NP docking sites), in thiscase receptors expressed in and around the VP at the diseasedsite, the NP surface is covered with ligand molecules and anti-bodies through nanoengineering. Through the formation ofligand–receptor bonds, the particles firmly adhere to thevessel wall, withstanding the hydrodynamic forces that tend

to dislodge them (figure 10a). From this privileged position,the NPs can release the encapsulated drug (or even smallerdrug-encapsulated particles) towards the extravascular spacein the vessel wall (figure 10b). The released molecules can thenpropagate through the artery wall to exert a therapeutic effecton the target region, the VP.

It has been previously demonstrated how a patient’s localblood flow features, such as wall shear stress, targeted receptordensity and physico-chemical properties of the NPs, includingsize, shape and surface characteristics, can influence NP depo-sition pattern and consequently therapeutic efficacy [14,123].There is therefore an overwhelming need for mathematicalmodels that can account for patient-specific attributes, alongwith NP design parameters, to ensure maximum NP targetingefficiency, thereby helping to personalize, and thus optimize,nanoparticulate therapeutic intervention in an individual patient.

To that end, a three-dimensional computational toolset hasbeen developed that uses patient-specific information (e.g.three-dimensional geometry, blood flow features, vessel wallcharacteristics) as input to analyse and predict the vasculardeposition of surface functionalized NPs within an inflamedarterial tree [14,123]. The methodology allows the simulationof NP transport through the blood stream, their adhesiononto and penetration into the vessel wall and the subsequentrelease and propagation of the encapsulated drug (or imagingagent) through the tissue in a patient-specific vasculaturewithin an isogeometric analysis (IGA) framework [13,14]. IGAis an improvement on the traditional finite-element method,which has been shown to be particularly suitable for such


extracellular matrix

REV

tumour

parent vessel

microvasculature

interstitial fluid

necrotic tumour cell

living tumour cell

healthy cells

endothelial cells

nutrient, cytokine, etc.

Figure 11. The multi-phase system within a representative elementary volume (REV) [128].


11:20140301

12


cardiovascular applications because of its precise and efficientgeometric modelling, capability to appropriately capture bothlaminar and turbulent blood flow regimes and accurate rep-resentation of stresses and near-wall quantities. Figure 10c,ddepicts simulation results for NP deposition pattern and thecorresponding drug distribution, respectively, within an ideal-ized VP when using a catheter-based nanoparticulate drugdelivery system.

The next step is to apply the computational tool in a clinicalsetting at Texas Heart Institute. The main goal was to validatethe model in vivo, then collect data from a population ofpatients and incorporate the information into the model to pre-dict the nanoparticulate drug (or imaging agent) deliverysystem that would be most efficacious. Successful realizationof this goal will lead to a robust computational frameworkthat can potentially answer critical questions such as, given adesired drug-tissue/imaging agent-tissue concentration in thetargeted region (e.g. inflammation in VPs), what would bethe optimum NP delivery mechanism, NP shape, size and sur-face properties, and drug release rate, for maximum efficacy ina patient? This computational–clinical marriage will ultimatelyenable physicians to develop a personalized treatment for indi-vidual patients and potentially predict with a high degree ofaccuracy its effects on the patient before administering it.

2.7. Multi-phase computational modelling forpredicting tumour growth and response to therapy

In transport oncophysics [124,125], cancer is defined as aproliferative disease of mass transport deregulation whichmanifests itself primarily in the disruption of the biologicalbarriers that separate body compartments [126]. The mostimportant consequences of this deregulation are invasion, theability to ‘push’ its way into host tissue; metastasis, the abilityto move to distant locations; and angiogenesis, upsetting thebalance of nutrient distribution and elimination of metabolites[126]. Tumour growth and connected nutrient and drug trans-port is a field of choice for numerical modelling. Many modelsrelated to this subject can be found in the published literature,see for instance the review papers [127,128]. Most models arefluid–fluid mixture models such as [129,130], whereas fewerare solid–fluid models. The latter of which either considerthe tumour as a solid, permeated by IF [131] or are composedof an ECM permeated by one or several fluids [132]. This lastone seems to be the most versatile and will be considered in

more detail. It can handle situations such as a melanoma grow-ing on the skin or experiments such as the one in [133] wherecells are grown in an acellular ECM. The model comprisesthe following phases: (i) the TCs, which partition into livingcells and necrotic cells, (ii) the healthy cells (HCs), (iii) theECM, and (iv) the IF (figure 11). The ECM and IF pervadethe whole computational domain, whereas the TCs and HCsare limited only to the subdomains with the tumour massand healthy tissue, respectively. The ECM is modelled as asolid, whereas all other phases are fluids. The TCs becomenecrotic upon exposure to low nutrient concentrations or exces-sive mechanical pressure. The IF, transporting nutrients, is amixture of water and biomolecules as well as nutrients,oxygen and waste products.

Existing blood vessels are modelled by line elements, andblood flow is taken into account. The governing equations areobtained via the thermodynamically constrained averagingtheory (TCAT) [128]. The resulting set of equations involvessecond-order partial differential operators and is solvedby the finite-element method to predict the growth rate ofthe tumour mass as a function of the initial tumour-to-HCdensity ratio, nutrient concentration, mechanical strain, celladhesion and geometry. TCAT provides a rigorous yet flex-ible method for developing multiphase, continuum modelsat any scale of interest [134].

Contrary to mixture theories applied in legacy models,TCAT considers the interfaces between constituents withinterfacial properties throughout the domain, and there isno need to trace sharp interfaces between constituents or tointroduce computationally expensive phase field modelswhich require higher-order partial differential operators, asin legacy models. Macroscopic interfaces arise naturallyfrom the solution of an initial-boundary value problem thatmust be composed of the mass balance equations of allphases involved. The ECM is treated as a viscoelastic solidmaterial in the finite strain regime or as an elastoviscoplasticmaterial if ECM remodelling has to be considered [135]. Thispaves the way for a better understanding of the tissue’s mech-anical properties on the development and growth of tumourmasses [136]. The model has a modular structure and furtherspecies and phases can be easily added.

As an example of the TCAT model, we show the case whereTCs grow in proximity of two otherwise healthy blood vesselsthat are the only source of oxygen. The TCs are initially locatedaround one vessel only. The volume fractions at 7 and 15 days


(a)

(c)

168 h 0.531801

0

0.2

0.4

0.495363

0

0.30.20.1

0.4

0.514534

0

0.2

0.4

0.488457 4.20 × 10–64.00 × 10–6

3.75 × 10–6

3.50 × 10–6

3.25 × 10–6

3.00 × 10–6

2.784 × 10–6

4.200 × 10–6

4.000 × 10–6

3.750 × 10–6

3.500 × 10–6

3.250 × 10–6

3.035 × 10–6

0

0.30.20.1

0.4

living tumour cells host cellsoxygen mass

fraction

360 h

(b)

0.5047748

0.4

0.2

N0

Figure 12. (a) Geometry; yellow lines show the axes of the two capillary vessels. (b) Volume fractions of the living tumour cells at 20 days; ‘N’ indicates the necroticareas. (c) Volume fractions of the living tumour cells ( first column) of the healthy cells (second column) and mass fraction of oxygen (third column) [132].


11:20140301

13


of the HC phase and of the living TC phase are shown infigure 12. The HCs are almost completely displaced by theTCs and necrosis occurs in locations within the tumourwhich are further from the left blood vessel.

From a more complete understanding of the growth andresponse dynamics of cancer, one may indeed expect to identifypromising clues for the development of more effective treatments.

3. Biomedical device design3.1. Rapid and simple preparation of nucleic acids using

micro- and nanostructuresRapid and simple preparation of nucleic acids is important fordisease diagnosis, DNA sequencing and forensic investigations.The challenge for rapid DNA preparation is to purify and con-centrate DNA without compromising the performance of largelaboratory equipment. The current methods are based oncentrifugation, microfiltration, toxic buffers and skilled person-nel. Microscale and nanoscale mechanics can offer ampleopportunity to replace the complex functions of equipment.

Electric fields can be combined with capillary action forpreparation of microscale and nanoscale objects in liquid.When microscale or nanoscale tips are immersed in solution,the forces induced from capillary action and viscosity, in com-bination with an attractive electric-field-induced force, cancapture or release the particles (figure 13a). The size-selectivecapture can purify DNA molecules in a sample matrix, repla-cing the function of centrifugation. Figure 13b shows a DNAextraction device designed for processing four DNA samplesin one batch. Four chips are loaded onto a plastic coupon

(figure 13c). Each individual chip has five microtips, whichare made of a 1 mm thick silicon nitride layer supported on a500 mm thick silicon layer. The top sides of the microtips arecoated with a 20 nm thick gold layer for electrical connectionand preservation of DNA. Metallic rings are used to suspendsample solutions by surface tension (figure 13d ). The devicecan yield similar performance to a commercial kit, but it cansimplify the operation and requires no toxic reagent. A nanotipalso showed similar performance with a more straightforwardoperation, which demonstrates the application of microscaleand nanoscale mechanics for novel biodevices.

Towards commercialization of similar microscale andnanoscale devices, the remaining challenges are (i) scalable pro-duction of microscale and nanoscale structures, (ii) integration ofsuch small structures into a device, and (iii) quality control of thedevices for uniform and reproducible performance. In thefuture, novel working principles in small-scale mechanics willlead to a revolution in the field of biomedical devices. The roleof numerical simulation in commercial applications is to clarifythe mechanics in the multi-scale regime, which will explain thebehaviour of nanoscale objects and uncover underlying mech-anisms which can be used for novel device design. In practice,numerical approaches have explained the sophisticated inter-action of molecules in liquid [139], which will shorten theincubation time for device applications.

3.2. Point-of-care diagnostics using nanosensorsPOC diagnostic systems are a rapidly growing segment ofbiosensors that will eventually lead to home-diagnostic sen-sors. To date, many methods have been developed for POCdiagnosis: assays based on polymerase chain reaction,


small particles

withdrawaldirection

microtip

viscous force

dielectrophoreticforce

solution

capillary force

~large particle

Dtip

hand-held device

10 mm

10 mm 100 µm

(a)(b) (c)

(d)

Dparticle

Figure 13. (a) Force mechanics on a nanotip and microtip surface in the capturing process [137]. (b) A portable prototype device [138]. (c) Magnified view showingfour chips in the holders. The inset shows a scanning electron microscopy image of a single microtip. (d ) An array of wells containing the solution. The inset showsthe immersion of the chip into the solution.


11:20140301

14


immunoassays, etc. These methods are more sensitive andrapid than the traditional detection methods; however, theperformance is still not satisfactory. In addition, owingto the low analyte concentration in the actual samples, apre-concentration step is critical. Currently available con-centration methods use centrifugation, microfiltration ormagnetic beads. However, the methods are limited by cum-bersome preparation steps, low yield and low throughput.To address the challenge, electric-field-induced concentrationhas the potential for application in highly sensitive detectionof molecular biomarkers for disease diagnosis and drug dis-covery. Using a nanostructured tip, a high-strength electricfield can be generated to concentrate molecules larger than2 nm in size with high efficiency. However, designing a tipthat reliably concentrates a specific target molecule requiresa detailed understanding of the physical interactions govern-ing the separation process. Mechanics has already influencedthe design process of mechanical and aerospace applications[140–144], as well as biosensors through the immersed finite-element technique [20–23,25,145,146], which is capable ofaccurately modelling the various forces experienced by abiomolecule during separation such as fluid–structure inter-action (FSI) of arbitrarily shaped structures, large structuraldeformations, electrokinetics, temperature-dependent thermalfluctuations and molecular interactions [21]. The developednumerical tool accurately predicts the efficacy of pre-concen-tration of molecular targets, in agreement with experimentalresults [32]. Once pre-concentrated, the detection can be carriedout by fluorescence and electrical measurement [147]. Suchan amplification-free platform can show a high sensitivityequivalent to polymerase chain reaction but with a shortassay time [148]. The nanostructured tip offers a simpleconfiguration for POC diagnosis as well as a convenienthome-diagnostic platform, and mechanical analysis plays animportant role in rapid development of novel tip designs forspecific problems. Furthermore, the numerical methods estab-lished in this context are ripe for further development and

application to other important processes involving complexinteractions with biomolecules, both in vitro and in vivo.

3.3. Developing model organ or multi-organ (in vitro)microdevices for the rapid and effective screeningof pharmaceuticals

During the past decade, the capabilities of microfluidics,enabled by the development of soft lithography [149], haveexpanded dramatically and now encompass a broad rangeof medical and biological applications ranging from single-molecule measurements to single-cell or cell-populationstudies. Indeed, the recent development of techniques thatenable the co-culture of multiple cell types in two- or three-dimensional co-culture has led to breakthroughs in ourcapability of recreating many aspects of organ function in asingle microfluidic chip. This has numerous applications,among which are the abilities to replicate certain biological orpathological processes outside the body and to create modelorgan or tissue systems that can be used to screen for new thera-peutics. Because these innovative microfluidic platforms arecapable of capturing multi-cell-type interactions, they bettermimic the real physiological situation. In addition, and impor-tantly, they have the potential to take advantage of rapidadvances in cellular reprogramming to produce human,induced pluripotent cells (iPSCs) [150]. By using the iPSCsfrom a particular patient, the prospect of patient-specificscreening is brought one step closer to being a reality.

What are our current capabilities for producing these‘organs-on-a-chip’ technologies? Over the past several years,research has emerged demonstrating the capability to reproducesome functions of a variety of organs (figure 14) [151]. Whilethese vary in their ability to truly reproduce or mimic organfunction, they clearly reach far beyond the ability of single-cell-type drug screening in well-plate systems, which is stillthe standard approach used by the pharmaceutical industry.


(a)100 mm

400mm

lung on a chip

blood vessel on a chip

muscle on a chip

BBB on a chip

heart on a chip

liver on a chip

tissue perfusion

air (alveolar)

liquid(vascular)

membraneepitheliu

m

cyclic

vacuum endothel

ium

GI tract on a chip

electrodes

APD data collectedfor each field

of view

field of viewbelow film

(g)

(e) (i) (ii) (iii)( f )

(b)(c)

(d )

Figure 14. The spectrum of model systems (‘organs on a chip’) is being developed for drug screening purposes. Systems have been developed for (a) lung, (b) theblood – brain barrier, (c) heart tissue, (d ) liver, (e) the gastrointestinal tract, ( f ) muscle and (g) the microcirculation. Reproduced from [151], adapted from [152]with permission.


11:20140301

15


One example is illustrated in figure 14a, the ‘lung-on-a-chip’[153]. Designed to simulate conditions in the gas exchange oralveolar region of the lung, it incorporates multiple cell types(e.g. both endothelial and epithelial cell monolayers), allowschemical signalling between them and subjects the cells tocyclic stretch by varying the air pressure inside channels, therebystretching the elastic substrate on which the monolayers aregrown. It also includes an air–liquid interface, which is necess-ary for the epithelial cells to take on the right morphology,and also stimulates the synthesis and secretion of pulmonarysurfactant, which is critical for many lung functions.

Other systems incorporate the capabilities to grow cellson a two-dimensional surface, appropriate for cellular mono-layers, but in many cases also within three-dimensionalgels that mimic the microenvironment essential for natural func-tion of cells embedded in the interstitial space. Examples ofthree-dimensional gel microenvironments include the ‘liverbioreactors’ produced by several groups [154] and model gastro-intestinal tracts [152], blood–brain barriers and muscles, bothcardiac or skeletal. In these systems, simultaneous two- andthree-dimensional cultures allow cells to interact in a naturalway, exchanging signalling factors via the interstitial spaces ofthe gel, and allowing for a more realistic, cell-specific mor-phology. The enormous flexibility of these systems is only nowbeing fully realized as the models become increasingly complexand more realistic. This poses new opportunities to the researchcommunity, especially in terms of creating computationalmodels that capture the transport characteristics through chan-nels, gels and within more complex tissues, while alsoincorporating the increased complexity of the biology.

Of particular note, efforts have recently been launched,under the support of substantial government programmesfrom the Defense Advanced Research Projects Agency and

National Institutes of Health, to combine single-organ modelsof this type to produce ‘body-on-a-chip’ systems in which mul-tiple ‘organs’ can interact in a realistic way. One of the majordriving forces behind this effort is the need to understand andbe able to anticipate off-target effects of drugs, deleterious effectson organs other than the one for which the drug is targeted.

An important feature of many tissue models is the capa-bility to incorporate vascular perfusion and the exchange ofvarious metabolites throughout the tissue space. Previousinability to do so has also been one of the major limitationsin the development of engineered organs, with the exceptionof those tissues, such as cartilage or cornea, for which bloodcirculation is not essential. Recently, several groups havedemonstrated methods in model systems to produce a vascu-lar network that can be perfused. Two approaches have beendeveloped. In one, the vessels are either etched onto the sur-face of the device, or cast into it [155] or created by othermeans [156], inside a three-dimensional gel that may ormay not be biodegradable. The channels produced are thenseeded with endothelial cells that adhere to and form a con-fluent monolayer over the walls of the gel channels. Thesesystems tend to be limited at present to channels that arelarger than natural capillaries, but new methods are constantlyemerging that are sure to reduce vessel diameter further.An alternative method that has been used by several groups[112,157,158] is to induce the vascular cells to bore intothe hydrogel from a monolayer and form new vessels by the pro-cess of angiogenesis [159,160]. Another approach is to drawupon the natural capabilities of the cells to form networkswhen dispersed uniformly within the three-dimensionalmatrix, termed vasculogenesis [112,157,158]. Either approachproduces networks with morphologies that are both controllableand have dimensions closer to those of normal capillaries.


air inlet

blood outletblood inlet

(a) (b)

Figure 15. (a) The Berlin EXCOR PVAD. (b) Geometrical model of the PVADcontaining the blood and air chamber with the corresponding inlets and out-lets. The model is used in fluid – structure interaction simulations in [165].


11:20140301

16


Numerous challenges exist in the design of systems thatpossess the same transport and mechanical properties ofliving tissue. Matrix materials are needed that replicate boththe chemical and mechanical characteristics of normal humanECM. Abundant evidence exists supporting the critical role ofmatrix mechanics in behaviours ranging from cell migration[161], to cytoskeletal functions [162], to stem cell differentiation[163], and the biomechanics community has made considerableprogress in understanding these effects.

However, much of the design currently is based ontrial and error, and a need exists to meld a fundamentalunderstanding of biology with a sound approach to themechanical issues. Computational approaches rely now pri-marily on agent-based models [164], in which the cellbehaviour is described by a collection of rules that are largelydetermined empirically. Few if any models can be found thatare based on first principles, although the mechanical proper-ties and transport characteristics of cell and ECM have beenreasonably well characterized. Flows, both intravascularand interstitial, exert important influences on tissue function,and these can be modelled by conventional means. The great-est challenge is to meld these more traditional models withthe intrinsic biology of the systems in order to create trulypredictive simulations.

3.4. Fluid – structure interaction modelling, simulationand optimization of paediatric pulsatile ventricularassist devices

Heart failure is a common condition in the USA, with morethan 600 000 cases diagnosed annually [165]. Cardiac trans-plantation remains the preferred treatment; however, a lackof suitable donors restricts this option for many patients,and the median survival with this condition is only 2–3years after initial diagnosis. Ventricular assist devices(VADs) pump blood in parallel with the native heart functionand provide full or partial mechanical circulatory support toone or both ventricles of the heart. They are used clinically ina range of adult and paediatric diseases, including congenitalheart disease, cardiomyopathy and post-infarction heart fail-ure. They were first developed as a bridge to transplant, inorder to prolong life of critically ill patients awaiting organavailability. However, as designs have evolved to becomesmaller and even fully implantable, they can now be usedas destination therapy, supporting one or both ventricles.More recently, there has also been success, most notably inpaediatric patients, with use of VADs in bridge to recoveryscenarios, allowing sufficient offloading for myocardialremodelling and recovery.

The need for reliable and safe mechanical circulatory sup-port is also growing in the paediatric population [166];however, the number of available donor hearts for this popu-lation has remained fixed at approximately 500 each year.VAD usage has thus increased in this population, althoughpaediatric VADs have a notably poorer performance thanavailable adult models. Development of VAD technologyhas taken place almost exclusively for the adult population.The Berlin EXCOR (figure 15), a pulsatile device, remainsthe only US Food and Drug Administration-approveddevice for children. However, adverse clinical effects occurin these devices at an alarming rate. Particularly troublingis the consistently high rate of thromboembolic events (22%).

With the increasing prevalence of VADs in clinical use, thereis now focus on improving design performance to reduce comor-bidities, reducing device size and allowing patients a more activelifestyle. Computational-mechanics simulations, coupled withoptimization techniques, can be used to accelerate the designprocess and optimize current and future designs. Simulationsoffer a promising means to cheaply and efficiently test and opti-mize competing device prototypes, thereby reducing time tomarket and identifying potential performance enhancements.Computational-mechanics modelling and simulation is anintegral part of the design process in many industries (e.g. aero-space, automotive). Almost every automobile manufacturermakes use of detailed, large-deformation structural-mechanicssimulations to model car crashes in an effort to assess vehiclesafety for the passengers. Aircraft manufacturers use compu-tational fluid mechanics coupled to rigorous optimizationalgorithms as a crucial and cost saving part of the designchain for all major aircraft. However, despite its demonstratedsuccess in these large-scale applications, adoption of simula-tion tools has lagged behind in the medical device industry.This is due in part to initial success with designs identifiedthrough trial and errorand experimentation as well as challengesassociated with complicating factors of blood biochemistry,mechanobiology and physiological response, which make simu-lations challenging. While simulations have been applied morerecently, particularly in the design of the HeartMate II andHeartAssist 5 blood pumps, there remains a need for increa-sed adoption of simulation technology and formal designoptimization algorithms.

To model pulsatile VADs (PVADs), dynamic interaction ofair, blood and a thin membrane separating the two fluids needsto be considered. Coupled FSI simulations at full scale areessential for realistic and accurate modelling of PVADs. Thisis because the motion and deformation of the thin membranedepend on the flow in the device blood and air chambers,and the flow patterns, in turn, depend on the motion and defor-mation of the membrane. As a result, the fluid and structuralmechanics equations need to be solved simultaneously, withappropriate kinematic and traction coupling at their interface.The computational challenges for FSI of PVADs includelarge, buckling motions of a very thin membrane, the needfor periodic remeshing of the fluid mechanics domain (owingto the large motions of the membrane, which induce verylarge changes in the blood and air flow domain geometryduring the cycle), and the necessity to use tightly coupledFSI solution strategies owing to the very strong addedstructural-mass effect present in the problem.

The state of the art in FSI modelling and simulation is ableto address these challenges (see a recent book on FSI [167]


(a) (b)

(c) (d)

Figure 16. Top: snapshots of the blood flow velocity during the fill (a) andeject (b) stages of the PVAD operation. Bottom: snapshots of the deformedconfiguration of the thin structural membrane during the fill (c) and eject (d )stages of the PVAD operation. The FSI simulations shown are from [168].


11:20140301

17


and references therein); however, there is currently no readilyavailable, off-the-shelf commercial software where these tech-niques are implemented and that may be robustly deployedfor this class of problems. The successful, one-of-a-kind,physiological FSI simulations of PVADs, as accomplished inthe recent work (see [168] and figure 16), present an impor-tant first step towards computer-aided engineering designof these devices.

Thrombus formation (i.e. blood clotting) is the majorproblem in VADs and, in particular, PVADs. However, deter-mining thrombotic risk factors in these devices is challenging.Thrombus formation is the result of a complex sequence ofchemical reactions in the bloodstream, resulting in plateletactivation and aggregation and the formation of fibrinnetworks around these aggregations. Thus, it is desirable tonot only model the FSI in PVADs, but also the process ofblood coagulation in order to understand the source of theproblem, and to propose device design modifications to miti-gate it. Some research has been dedicated to this, althoughdetermining an appropriate blood coagulation model forour purposes is quite challenging. As a result, we exploreother surrogates for thrombotic risk that may be directlycomputed from FSI simulation data. Long residence timesand areas of blood recirculation or stagnation may lead toincreased risk of thrombosis in PVADs [169]. A method forcalculating particle residence time for flows in moving spatialdomains was proposed in [170], and the developments forPVAD FSI and residence time computations were used to per-form a shape-optimization study of a paediatric device, as in[171]. The optimization using a derivative-free surrogatemanagement framework (SMF) [172] was carried out for afull-scale three-dimensional device, with time-dependentFSI simulations performed under physiologically realisticconditions (figure 17).

Despite recent progress, challenges remain to increase therelevance and utility of VAD simulations in the device designprocess and in the clinic. First, complete modelling of bloodbiochemistry remains computationally intractable owing tohigh computational cost. There is therefore a need for contin-ued development and validation of reduced-order models tomeasure the risks of thrombosis and haemolysis. Second,there is a need for integration of the advanced simulationand formal optimization methods outlined above to acceler-ate the design process in the presence of constraints anduncertainties. As the optimization process identifies new

designs, the need will also arise for rapid prototyping ofsimulation-derived designs for experimental testing. Third,as simulation methods mature, there is an increased needfor validation of simulated risk of thrombosis and haemolysisagainst clinical data in VAD patients and animal models.Finally, one cannot ignore the underlying physiology of thepatient, and VAD models should be coupled to lumpedparameter network models of circulatory physiology to eluci-date the interplay between the device and physiologicalconditions. This is particularly compelling in paediatriccardiology owing to the complex physiology and unusualanatomy in congenital heart disease patients.

4. Cell mechanics4.1. Mechanosensing and mechanotransductionAs the basic unit of life, living cells perform an enormous var-iety of functions through synthesis, sorting, storage andtransport of biomolecules; expression of genetic information;recognition, transmission and transduction of signals; andconversion between different forms of energy. Many ofthese cellular processes can generate, or be regulated by,mechanical forces at the cellular, subcellular and molecularlevels. For example, during cell migration, contractile forcesare generated within the cell in order for the cell body tomove forward. These contractile forces, in combination withthe adhesion of cells to ECM through focal adhesion com-plexes, enable cells to sense the stiffness of the surroundingsubstrate and respond to it. Many normal and pathologi-cal conditions are dependent upon or regulated by theirmechanical environment. Some cells, such as osteoblastsand vascular cells, are subjected to specific forces as part oftheir ‘native’ physiological environment. Others, such asmuscle and cochlear outer hair cells, perform their mechan-ical function either by converting an electrical or chemicalstimulus into mechanical motion or vice versa.

Of particular importance is the ability of cells to sensemechanical force or deformation and transduce these mechan-ical signals into a biological response. For example, endothelialcells can recognize the magnitude, mode (steady or pulsatile),type (laminar or turbulent) and duration of applied shear flow,and respond accordingly, maintaining healthy endothelium orleading to vascular diseases, including thrombosis and athero-sclerosis. Vascular smooth muscle cells in the arterial wallremodel when subjected to pressure-induced wall stress. Fibro-blast cells ‘crawl’ as an inchworm by pulling the cell bodyforward using contractile forces. Bone alters its structure toadapt to changes in its mechanical environment as occurs,for example, during long bed rest. Stem cells sense the elasticityof the surrounding substrate and differentiate into differentphenotypes accordingly. These and other examples demon-strate the ability of cells to sense

usnctam perspectives on mechanics in medicine · body. although they obviously obey the general...

Documents