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Mechanisms of Pulsed Laser Ablation of Biological Tissues
Alfred Vogel*,† and Vasan Venugopalan
Medical Laser Center Lu¨beck, Peter-Monnik-Weg 4, D-23562 Lu¨beck, Germany, and Department of Chemical Engineering and Materials Science
and Laser Microbeam and Medical Program, Beckman Laser Institute, University of California, Irvine, California 92697
Received September 12, 2002
Contents
I. Introduction 578
II. Properties of Soft Biological Tissues 579
A. Tissue Composition and Morphology 579
B. Mechanical Properties 582
C. Thermal Denaturation 583
III. Energy Deposition and Transport 584
A. Optical Absorption Properties of Tissue 584
1. Ultraviolet Radiation (λ)180400 nm) 584
2. Visible Radiation (λ)400780 nm) 585
3. NearFar-Infrared Radiation
(λ)780 nm15 µm) 585
B. Optical Scattering Properties of Tissue 585
C. Dynamic Optical Properties in Tissue 586
IV. Linear Thermomechanical Response of Tissue to
Pulsed Irradiation 588
A. Temperature Rise and Thermal Diffusion 588
B. Thermoelastic Stress Generation and
Propagation 588
C. Implications for Precise Tissue Ablation 590
V. Thermodynamics and Kinetics of Phase
Transitions 590
A. Phase Diagrams 590
B. Surface Vaporization 591
C. Normal Boiling 592
D. Phase Explosions: Bubble Nucleation and
Spinodal Decomposition 592
E. Confined Boiling 595
F. Effects of the Tissue Matrix on the Interplay
of Phase Explosions and Confined Boiling 596
G. Effect of Stress Confinement on the Ablation
Process 596
1. Stress Confinement and Phase
Transitions 597
2. Stress Confinement and Tissue Fracture 597
3. Stress Confinement and Ablation
Threshold 598
H. Photochemical Decomposition 598
I. Interplay of Photochemical Decomposition
and Confined Boiling in Tissue 600
VI. Ablation Plume Dynamics 600
A. Plume Formation and Expansion 600
1. Plume Dynamics for Nanosecond Pulses 601
2. Plume Dynamics for Microsecond Pulses 602
3. Postpulse Ablation 604
B. Recoil Stress 604
1. Temporal Shape and Amplitude 604
2. Recoil-Induced Material Expulsion 605
3. Collateral Tissue Effects Induced by
Recoil Stress 606
C. Flow-Induced Material Redeposition 607
D. Shielding by the Ablation Plume 608
VII. Ablation Models and Metrics 609
A. Heuristic Models 609
1. Blow-off Model 609
2. Steady-State Models 610
3. Comparison of Blow-off and Steady-State
Models 611
4. Applicability of Blow-off and Steady-State
Models 611
5. Unification of Blow-off and Steady-State
Models 612
B. Ablation Metrics and Their Relationship to
Heuristic Model Predictions 612
1. Ablation Threshold 612
2. Ablation Enthalpy 613
3. Ablation Efficiency 613
C. Mechanistic Models 613
1. Steady-State Vaporization Models 614
2. Thermomechanical Models 614
D. Molecular Dynamics Simulations 615
VIII. UV and IR Ablation 615
A. Tissue Absorption Coefficients 615
B. Ablation without Stress Confinement 617
1. Temperature Rise and Thermal Diffusion 617
2. Kinetics of Tissue Decomposition 618
3. Material Ejection 618
C. Ablation with Stress Confinement 620
1. Reduction of the Ablation Threshold 621
2. Kinetics of Tissue Decomposition and
Material Ejection 621
3. Precision Achieved by Ablation under
Stress-Confined Conditions 622
D. Overall Picture 623
IX. Ablation in a Liquid Environment 623
A. Bubble Formation 623
B. Amplification of Mechanical Effects by Liquid
Confinement 625
C. Influence of the Bubble Dynamics on Ablation
Efficiency 626
* To whom correspondence should be addressed. Phone:
+49-451-500-6504. Fax: +49-451-505-486. E-mail: vogel@
mll.mu-luebeck.de.
Medical Laser Center Lu¨beck.
University of California, Irvine. E-mail: vvenugop@uci.edu.
577Chem. Rev. 2003, 103, 577644
10.1021/cr010379n CCC: $44.00 © 2003 American Chemical Society
Published on Web 02/12/2003
X. Plasma-Mediated Ablation 627
A. Kinetics of Plasma Formation in Biological
Tissues 627
B. Threshold for Plasma Formation 629
C. Plasma Formation above the Breakdown
Threshold 630
D. Plasma Absorption 631
E. Plasma Energy Density 632
F. Thermomechanical and Chemical Effects 632
G. Implications for Tissue Ablation 634
XI. Control of Precision, Thermal and Mechanical
Damage, and Ablated Mass 636
A. Control of Precision 636
B. Control of Thermal Side Effects 636
C. Control of Mechanical Side Effects 637
D. Maximizing the Ablated Mass 637
E. Selective Ablation 637
XII. Outlook and Challenges 638
XIII. Acknowledgment 639
XIV. References 639
I. Introduction
Soon after the invention of the pulsed ruby laser
by Maiman in 1960, investigators were eager to
examine the potential of pulsed laser radiation for
medical applications. It was greatly anticipated that
lasers would enable manipulation and destruction of
biological tissue with unprecedented precision and
selectivity.1,2 Within a few years, reports of the use
of pulsed lasers for precise tissue coagulation in
patients along with the development of laser systems
designed for clinical use appeared in the literature.3-6
However, a clinically viable application of pulsed
laser ablation was not reported until the early 1970s.7
It was only at the beginning of the 1980s that lasers
were routinely used for ophthalmic dissection and
ablation procedures. In other medical subspecialties,
routine laser use did not occur until the mid-1980s.8
The delay between the invention of the laser and its
successful clinical application was due largely to a
lack of understanding of the fundamental mecha-
nisms that govern laser-tissue interactions. Much
progress has been made in this regard, and now, at
the beginning of the 21st century, medical procedures
that employ pulsed lasers are present in nearly every
medical subspecialty; for many ophthalmologists and
dermatologists, lasers are considered essential tools
for medical practice.
As the understanding of laser-tissue interactions
matured in the 1990s, three books became available
and serve as a valuable resource for the field,9-11
together with the books by Ready12 and by Ba¨uerle13
that address general aspects of laser ablation. Previ-
ous survey papers include the reviews on laser-
tissue interactions by Hillenkamp14 and by Jacques;15
ultraviolet laser ablation of polymers and biological
tissues by Srinivasan,16 Srinivasan and Braren,17 and
Pettit;18 photophysics of laser-tissue interactions by
Boulnois;19 thermal processes in laser-tissue inter-
actions by McKenzie;20 medical laser applications by
Verdaasdonk;21 and laser applications in the cornea
and in ophthalmology by Marshall,22 Krauss and
Puliafito,8and by Krueger and co-workers.23 Reviews
on general aspects of tissue ablation include those of
Mu¨ller,24 Oraevsky,25 van Leeuwen,26 and Walsh.27
Specific aspects of laser ablation processes have also
been considered in comprehensive studies. Medical
applications of laser-induced plasmas were reviewed
by Gitomer and Jones,28 while ablation processes
resulting from nonlinear absorption have been con-
sidered in both a review paper29 and a monograph30
by Vogel.
Despite the increasing medical use of lasers, a
comprehensive presentation of the fundamental mech-
anisms involved in pulsed laser tissue ablation has
not appeared in the scientific literature. This is not
surprising, as the elements required for an under-
standing of the relevant processes range from non-
equilibrium thermodynamics to photochemistry to
Alfred Vogel studied physics and sociology, receiving the University degree
for high school teaching and the Ph.D. degree in physics from the Georg-
August University of Go¨ttingen, Germany. Later, he earned the degree of
Habilitated Doctor of Physics from the University of Lu¨beck. In 1988, he
joined the laser laboratory of the Eye Hospital of the Ludwig-Maximilians
University Munich, and in 1992, he moved to the Medical Laser Center
Lu¨beck, where he has been Vice-Chairman since 1999. His research
interests include lasertissue interactions in biomedical applications of
photodisruption, pulsed laser ablation, and photocoagulation as well as
laser-induced plasma formation, cavitation, and stress waves.
Vasan Venugopalan received his B.S. degree in mechanical engineering
from the University of California, Berkeley, and S.M. and Sc.D. degrees
in mechanical engineering from MIT. He held postdoctoral positions at
the Wellman Laboratories of Photomedicine, Harvard Medical School, and
the Departments of Molecular Biology and Physics, Princeton University.
He joined the University of California, Irvine, in 1996, where he is currently
Assistant Professor of Chemical Engineering, Biomedical Engineering, and
Surgery. His research focuses on applications of laser-induced thermal,
mechanical, and radiative transport processes in medical diagnostics,
therapeutics, biotechnology, and micro-electromechanical systems.
578 Chemical Reviews, 2003, Vol. 103, No. 2 Vogel and Venugopalan
plasma physics to tissue biomechanics. Consequently,
researchers who investigate the mechanisms of pulsed
laser tissue ablation originate from several disci-
plines. Moreover, the resulting scientific reports are
often narrow in scope and scattered in journals whose
foci range from the medical and biological sciences
to the physical sciences and engineering. The purpose
of this review is to collect the information to be
gleaned from these studies and organize it into a
logical structure that provides an improved mecha-
nistic understanding of pulsed laser ablation of
tissue.
We consider ablation to be any process of tissue
incision or removal, regardless of the photophysical
or photochemical processes involved. We restrict this
review to pulsed ablation (pulse durations j1 ms)
and will not treat processes in which either tissue
carbonization or dehydration/diffusive mass transfer
play important roles, as they typically result from the
use of long exposure times or low peak powers. We
further restrict the review to ablation processes
performed on a tissue level. Thus, even though it
shares the same fundamental principles and is an
area of growing importance and active research, we
do not consider explicitly pulsed microirradiation and
microdissection of cellular and subcellular targets.
However, as the fundamental principles of the laser-
material interactions are the same, many of the
insights regarding the mechanisms of pulsed laser
ablation presented here also apply to pulsed laser
microirradiation. From a phenomenological stand-
point, we examine the laser ablation process on
mesoscopic and macroscopic scales. The underlying
molecular dynamics involved in pulsed laser ablation
is treated by the review of Zhigilei and co-workers
appearing in this issue. Finally, we focus attention
on ablation of soft biological tissues (all tissues except
bone and teeth) because the extracellular matrix of
soft tissues resembles the molecular substrates that
are the primary focus of this special issue of Chemical
Reviews.
This review aims at providing a framework that
yields an understanding of the mechanisms of pulsed
laser tissue ablation which reaches beyond a mere
compilation of previous studies. We first present a
section regarding the material properties of soft
biological tissues that summarizes tissue composi-
tion, structure, and mechanical properties. We fur-
ther explore how these characteristics may change
as a result of pulsed laser irradiation (section II). We
then detail the mechanisms that govern radiative
transport and energy deposition resulting from pulsed
laser irradiation (section III) and consider the ther-
mal and mechanical transients produced by pulsed
laser heating (section IV). In the following section,
we focus on the key processes that drive pulsed laser
tissue ablation: the kinetics of phase transitions and
photochemical decomposition (section V). The de-
tailed consideration of these processes provides the
necessary basis for understanding the crucial role of
material ejection in tissue ablation. For ablation in
an air environment, we examine both the dynamics
of the ablation plume that consists of vaporized and
ejected material and the role of the plume in modify-
ing the amount of energy reaching the tissue (section
VI). Once the various steps constituting the ablation
process have been analyzed, we survey the theoretical
models that have been developed to describe this
process as well as the use of metrics such as ablation
threshold, ablation enthalpy, and ablation efficiency
that are used to characterize its energetics (section
VII). We end our discussion of pulsed laser ablation
in air by analyzing the elements responsible for the
observed differences between ablation produced by
pulsed ultraviolet (UV) and infrared (IR) laser sources
(section VIII). We then describe how the interplay of
the various mechanisms is modified when ablation
is performed in an aqueous environment (section IX)
and consider those ablation processes that are medi-
ated principally by nonlinear energy deposition and
plasma formation (section X). Finally, once the vari-
ous mechanisms of ablation and their range of
applicability have been established, we use this
knowledge to devise strategies to control ablative
precision, thermal and mechanical injury, and total
ablated mass (section XI) because the primary mo-
tivation for developing a mechanistic understanding
of pulsed laser tissue ablation is to enable the
rational selection of laser parameters. We end with
a summary and outlook with regard to the challenges
and opportunities that remain in the field (section
XII).
II. Properties of Soft Biological Tissues
Several properties of biological tissues are relevant
to pulsed laser ablation. Tissue composition and
morphology establish tissue optical properties that
determine the internal volumetric energy distribution
which drives the ablation process. Structure and
morphology also affect the energy transport among
tissue constituents and, together with tissue me-
chanical properties, mediate the thermomechanical
response of tissue to pulsed laser heating and phase
transformation. Here we consider the compositional,
structural, and mechanical properties of tissue, to-
gether with their modification when subjected to the
thermal and mechanical effects induced by pulsed
laser irradiation.
A. Tissue Composition and Morphology
Soft biological tissues can be viewed crudely as a
material consisting of cells that reside in and attach
to an extracellular matrix (ECM). By mass, most soft
tissues are dominated by water (55-99%) and col-
lagen (0-35%). The ECM is a complex composite
material, the principal components of which include
water, collagen, elastin, glycosaminoglycans, glyco-
proteins, and cell adhesion proteins.31-33 The ratio
of ECM components to the total tissue mass varies
significantly among tissue types. In “cell-continuous”
tissues such as liver and epithelia, the ECM fraction
is quite small and consists mostly of cell adhesion
proteins such as fibronectin. By contrast, “matrix-
continuous” tissues that include the corneal stroma,
dermis, cartilage, and tendon have a very small
cellular fraction and are almost entirely ECM. In
such matrix-continuous tissues, the collagen content
can be as high as 35%.32 A primary function of the
ECM is to maintain the structural integrity of the
Pulsed Laser Ablation of Biological Tissues Chemical Reviews, 2003, Vol. 103, No. 2 579
tissue. Thus, the ECM inhibits tissue vaporization
and material removal, which are the objectives of the
ablation process.
Collagen is the single most abundant animal
protein and accounts for approximately 25% of all
protein in humans.31,32 Collagen is a strongly hydro-
philic protein as the amount of acidic, basic, and
hydroxylated amino acid residues far exceeds the
amount of lipophilic residues. As a result, in soft
tissues, collagen exists in a highly swollen state.34
Collagen is enormously complex and displays several
levels of structural hierarchy. In fibril-forming col-
lagens, over 95% of the molecule consists of three
chains (R-chains), each of which possesses a specific
amino acid sequence. These R-chains associate in a
right-handed triple-helical structure, with each in-
dividual chain being a left-handed helix. This triple-
helical structure forms the fundamental unit known
as the tropocollagen (TC) molecule, a schematic of
which is shown in Figure 1a. The TC molecule has a
diameter of 1.51 nm, a length of 290 nm, and a helical
repeat length of 8.6 nm.34,35 The next level of struc-
tural hierarchy is related to the organization of
neighboring TC molecules to form a larger unit,
known as a microfibril. These microfibrils have a
diameter of approximately 3.5 nm and consist of six
TC molecules that organize around a common center
and are stabilized by covalent cross-links.33,35 These
covalent cross-links are critical to the mechanical and
thermal stability of collagen in vivo. The microfibrils
in turn associate with each other through lateral and
end-to-end aggregation to form collagen fibrils, the
diameters of which are specific to tissue type and can
range from 10 to 300 nm,36 as shown in Figure 1b.
Moreover, the individual TC molecules within the
microfibril are staggered by approximately one-
quarter of their length, which gives rise to structural
periodicity along the microfibrils and fibrils with a
repeat distance of 64-68 nm. This periodicity results
in a banding pattern that is apparent under trans-
mission electron microscopy (TEM) and shown sche-
matically in Figure 1b. The absence of this banding
indicates a loss in the spatial organization within the
collagen fibrils and is often used as a marker for the
onset of thermal denaturation.37
In collagen-based tissues, the individual fibrils are
embedded within a ground substance, as shown in
Figure 2 for the case of skin. The ground substance
consists largely of water, proteoglycans, glycosami-
noglycans (GAGs), and, to a much smaller extent,
nonfibrillar collagens (e.g., collagen type VI in cornea)
and globular cell adhesion proteins such as fibronec-
tin. Proteoglycans consist of sulfonated GAG side
chains that are covalently linked to a core protein.38
Although proteoglycans and GAG components are
present in connective tissues in small quantitites
(typically 1%), they are strongly hydrophilic and
sequester water in amounts equivalent to 1000 times
their own volume.32,39 Thus, nearly all the water
content of matrix-continuous tissues resides in the
Figure 1. (a) Schematic drawing of the tropocollagen (TC) molecule. (Reprinted with permission from ref 35. Copyright
1988 CRC Press.) (b) Spatial organization of collagen from the molecular to the tissue level. (Reprinted with permission
from ref 36. Copyright 1996 Springer). The staggering of the TC molecules in the collagen fibrils creates the banded structure
that is visible in electron microscopy of stained native collagen.
580 Chemical Reviews, 2003, Vol. 103, No. 2 Vogel and Venugopalan
ground substance between the collagen fibrils. While
the ground substance is not stiff, it is largely incom-
pressible and provides resistance to compressive
loading.
The individual collagen fibrils associate with each
other to form sheets known as lamellae in the corneal
stroma and collagen fibers in tissues such as tendon
and dermis (Figure 1). The lamellae have character-
istic thicknesses of 1-2µm, while collagen fibers in
tendon and dermis possess characteristic diameters
of 1-10 µm. In tendon, bundles of collagen fibers
form even larger units called fascicles. The cells in
such tissue attach to and reside between the collagen
lamellae or fibers.33
There are several types of collagen, each of which
is defined by the sequence of amino acid residues that
comprise the individual R-chains within the TC
molecule. The majority of collagen types found in the
body form fibrils (types I, II, III, V, and XI), while
other types form fibrillar networks (types IV, VII, X,
and XVII), thin beaded filaments (type VI) or serve
as links either between collagen fibrils or between
collagen fibrils and other components of the ECM
(Types IX, XII, XIV, XVI, and XIX).40,41 In fibrillar
collagens, 25% of the amino acids in the R-chain
are imino acid residues (proline or hydroxyproline)
that effectively block rotation of the collagen chain
at these sites and stabilize the triple-helical struc-
ture. This results in a fairly rigid polymer displaying
a persistence length on the order of 160 nm, or nearly
100 times its diameter.42 This rigid backbone of the
TC molecule provides for high mechanical strength.
While the spatial arrangement of amino acid residues
within each collagen R-chain precludes the formation
of bonds between the chains within the TC molecule,
hydrogen bonds and van der Waals interactions
between the R-chains are possible and further sta-
bilize the configuration and orientation of the TC
molecule in vivo.35,40,43
The collagen amount, collagen type, macroscopic
fibril size distribution and organization, and compo-
sition of the extrafibrillar space are all important in
giving rise to specific tissue characteristics. For
example, the primary mechanical function of the
dermis is to protect underlying tissues and organs
from injury. Thus, the dermis must provide both
elastic deformability and high strength in response
to compressive, tensile, and shear stresses. Collagen
provides 75% of the dry weight and 18-30% of the
volume of the dermis, which itself constitutes 15-
20% of the weight of the human body.41 Collagens I
and III are fibrillar and the most prevalent collagen
types in the dermis, constituting 70% and 15% of its
dry weight, respectively. Collagen fibril diameters in
the papillary (superficial) dermis range between 20
and 70 nm and reach up to 120 nm in the reticular
(deep) dermis.39,41,44 The collagen fibers form a loose,
nonwoven, three-dimensional network.33 The loose
network enables the collagen fibers to spatially
reconfigure and align in response to loading from a
variety of directions. Moreover, collagen fibers in the
dermis and other organs are “wavy” or “crimped”.
This provides the dermis with significant extensibil-
ity at low stresses without loading the backbone of
the TC molecule. However, once the collagen fibers
are straightened and loaded, the dermis is stiff and
can withstand high stresses before fracturing. The
ground substance between collagen fibrils in the
dermis does not contribute to more than 0.4% of the
dry weight of the skin but comprises the majority of
its volume due to its strongly hydrophilic nature.
Another important collagen-based tissue is the
cornea. To serve its function of focusing and trans-
mitting visible light to the lens and retina, it must
retain its shape and be optically transparent to
radiation in the visible spectrum. The corneal stroma
consists primarily of fibrillar collagen types I (50-
55% dry weight), III (10% dry weight), and V (8-
10% dry weight) as well as the beaded filament
collagen type VI (25-30% dry weight) and proteogly-
cans.45 The transparency of the cornea is facilitated
by the high concentration of collagen type V that is
believed to facilitate the assembly of collagen fibrils
possessing a small and regular diameter.46 Collagen
type VI is a nonfibrillar collagen that resides in the
ground substance and is important for establishing
the regular spacing of the collagen fibrils.47 Thus,
corneal stroma, unlike dermis, has a high protein
content in the ground substance itself. The interplay
of these collagen constitutents results in a tissue in
which the collagen fibrils have a tightly controlled
range of diameters between 29 and 34 nm that are
spaced at a center-to-center distance of 64-67 nm.48
These characteristics of regular size and spacing of
collagen fibrils are the essential elements that pro-
vide the cornea with optical transparency at visible
wavelengths.46,49,50
The interaction of collagen and the other extracel-
lular matrix elements with water is important when
considering energy transport processes within the
tissue. As explained above, both collagen and the
Figure 2. Transmission electron micrograph of human
skin (dermis), showing collagen fibers sectioned both
longitudinally and transversely. Magnification 4900×. The
fibers consist of individual fibrils that are embedded in a
ground substance with high water content. (Reprinted with
permission from ref 41. Copyright 1988 Blackwell Science.)
Pulsed Laser Ablation of Biological Tissues Chemical Reviews, 2003, Vol. 103, No. 2 581
ground substance are hydrophilic and display com-
plex structural organization. At many laser wave-
lengths, only a single tissue constituent (e.g., water
or collagen) absorbs the radiation. Thus, the spatial
scales that characterize the collagen and water
“domains” within tissue are vital to understanding
potential energy-transfer mechanisms. Traditionally,
the water associated with proteins in vivo is catego-
rized as structural water, bound water, or free water.
Structural water is directly associated with the
protein and described stoichiometrically in a fashion
similar to the hydrates of inorganic salts. Bound
water is not directly associated with the protein but
possesses properties that are measurably different
than those of free water. For collagen, the amount of
structural and bound water is typically 0.35 g of
H2O/g of collagen.51 Thus, for a hypothetical tissue
comprising 35% collagen and 65% water, only 10%
of the tissue consists of structural/bound water. As
a result, the vast majority of tissue water resides in
the ground substance in which the collagen fibrils are
embedded, and the spatial scale characterizing do-
mains with different absorption properties is given
by the diameter and spacing of the collagen fibrils.
B. Mechanical Properties
The mechanical properties of biological tissues are
of great importance to laser ablation, as both the
elasticity and strength of the tissues modulate the
kinetics and dynamics of the ablation process. Figure
3 provides stress-strain curves for a variety of
collagen-based soft biological tissues. Although the
mechanical characteristics vary considerably in terms
of stiffness, extensibility at fracture, and ultimate
tensile strength, one generalization can be made.
When loaded in tension, nearly all soft biological
tissues possess a nonlinear stress-strain character-
istic with a “concave-up” shape. This is because small
strains do not stretch the collagen fibers themselves
but simply align the fibers and/or straighten them
from their normally wavy or crimped configuration.
However, once the collagen network is aligned and
straightened at larger strains, the stresses act di-
rectly on the rigid collagen fiber backbone. As a
result, biological tissues have a soft and elastic
consistency under normal physiological conditions
but become much stiffer when loaded in an extreme
fashion. Both tissue extensibility and strength are
relevant to pulsed ablation, as they provide a guide
to the stresses and deformations that must be gener-
ated when material removal is achieved via fracture
of the tissue matrix.
There is a positive correlation between tissue
strength and collagen content.52 Tissues that repre-
sent extremes of mechanical strength are the liver
and tendon. Liver is a very soft and friable tissue
possessing a very low ultimate tensile strength (UTS)
of 23 kPa but a moderate extensibility at fracture of
40%.33,53,54 Tendon, by contrast, is both strong and
stiff, with an UTS of J100 MPa and a fracture
extensibility of 10%. Liver is a cell-continuous
tissue with little ECM and collagen content. Tendon
is a matrix-continuous tissue that possesses high
collagen content. Other matrix-continuous tissues,
such as ligament and skin, have similarly high
collagen content (25-33%) and similar, albeit lower,
UTS (40 and 10 MPa, respectively) relative to
tendon.
Tissue extensibility is related to both the architec-
ture of the collagen fibrils and the content of another
ECM protein, elastin. Elastin is a strongly hydro-
phobic and very extensible protein that forms a
covalently cross-linked network of fibers within some
collagen-based tissues, such as dermis.31,33 Collagen-
based tissues with high extensibility tend to have
collagen fibrils that are wavy or crimped and can
partially reorient to align with the direction of the
applied stress. The waviness of the collagen fibrils
provides tissue extensibility simply by straightening
when loaded. The intercalation of elastin with the
collagen fibril network provides these tissues with
some additional stiffness as the collagen fibrils
straighten. As a result of the waviness of the collagen
fibrils, skin fractures at relatively large extensibilities
between 30 and 100%.
One must exercise caution when relating published
stress-strain data of biological tissue to pulsed laser
ablation. The stresses reported are often calculated
on the basis of the ratio of the applied load to the
cross-sectional area of the un-deformed sample. In
fact, the cross-sectional area of biological tissues
reduces significantly when loaded under tension.
Thus, to avoid an underestimation of the UTS, one
must determine the “engineering stress”, which is
obtained by dividing the applied load by the cross-
sectional area of the sample when loaded.33 A second
issue warranting concern is that nearly all tissue
mechanical data are acquired under “quasi-static”
loading, i.e., conditions under which the tissue is
deformed at very slow strain rates, typically on the
order of 0.1% or 10-3s-1. However, during a pulsed
laser ablation process, tissue is subjected to enor-
mously high strain rates, on the order of 105-107s-1.
Some studies have been performed to examine the
variation of tissue properties with strain rate over
the range 0.3-170 s-1.55-57 These studies indicate
that, while the tissue strain at fracture does not
Figure 3. Stress-strain curves characterizing the me-
chanical properties of various biological tissues under
uniaxial tension. The bsymbols represent the mechanical
state at which tissue fracture occurs. Data compiled from
ref 53.
582 Chemical Reviews, 2003, Vol. 103, No. 2 Vogel and Venugopalan
change significantly with strain rate, the UTS in-
creases. The increase in UTS is due to the fact that,
under conditions of rapid deformation, there is sig-
nificant viscous dissipation between the collagen
fibrils and the adjacent ground substance. The avail-
able data demonstrate that the UTS increases in
proportion to the logarithm of the strain rate. How-
ever, it is not known whether this dependence
remains valid up to the extreme strain rates pro-
duced by pulsed laser ablation. Nevertheless, the
available data suggest that the tissue UTS under
ablative conditions can be considerably higher than
that measured under ‘quasi-static’ loading conditions.
C. Thermal Denaturation
Thermal denaturation of ECM proteins resulting
from pulsed laser irradiation is of great importance,
as it affects the dynamics of the ablation process and
governs the extent of thermal injury produced in the
remaining tissue. Here we limit our discussion to the
denaturation kinetics of fibrillar collagen. Denatur-
ation of fibrillar collagen begins when a rise in
temperature increases the kinetic energy of the
constituent molecules such that they overcome the
weak hydrogen bonds and van der Waals interactions
that are responsible for stabilizing the helical con-
figuration of the R-chains in the TC molecule.43 If the
collagen is free to deform, the denaturation results
in a structural transformation of the TC molecule
from a “native” triple-helical structure to a “dena-
tured” random coil structure that is associated with
a loss of the banding pattern of the native collagen
fibrils in TEM.37 When this helix-coil transition is
accomplished, the fibrils shrink due to the presence
of the covalent cross-links that connect and maintain
the organization of the microfibrils.35 The shrinkage
occurs parallel to the longitudinal axis of the fibrils
and results in a thickening in a direction perpen-
dicular to the fibrils. However, when the collagen is
under isometric conditions, this deformation is not
allowed, and a tensile stress is developed along
fibrils.58,59 Studies of the helix-coil transition under
quasi-static heating conditions using differential
scanning calorimetry reveal that the transition has
the characteristics of a first-order phase transforma-
tion with a well-defined “melting” temperature and
enthalpy of denaturation.60,61 The melting tempera-
ture and latent enthalpy increase with the relative
amount proline and hydroxyproline residues in the
primary amino acid sequence of the R-chains. As
noted in section II.A, these imino acid residues block
rotation of the peptide backbone at these sites and
apparently contribute to the thermal stability of the
collagen triple helix.43,60,62
When the tissue is heated further, a second stage
of denaturation occurs via the hydrolysis of initially
the thermally labile and subsequently the thermally
stable covalent cross-links between the TC molecules.
This results in a stepwise disintegration of the
collagen fibrils63 and a relaxation of the stresses
developed during shrinkage.58,59,64 The dissolution of
the cross-links is termed “gelatinization” or “hyalin-
ization” and results in total mechanical failure and
disintegration of the fibrillar structure of the tis-
sue.37,43 The temperature for maximum shrinkage
and the relaxation temperature are dependent on the
density and type of covalent cross-links within the
tissue. Older tissues possess a higher density of cross-
links and thus display increased thermal stability
with corresponding increases in the characteristic
temperatures for maximum shrinkage and for stress
relaxation.35,65,66
Thermal denaturation is a rate process, as the
ability to transform a tissue from a native to a
denatured state depends not only on temperature but
also on the duration of the exposure to the elevated
temperature.67-70 If the heating time is reduced,
considerably higher temperatures are required for
denaturation.67,70-72 Often the Arrhenius rate integral
is applied to estimate the thermal injury. For a given
thermal transient, T(t), the accumulation of thermal
injury can be expressed as
where Γ(t) is a dimensionless measure of the degree
of thermal injury accumulated at time t,kBis the
Boltzmann constant, Eis the activation energy
barrier for the denaturation process, and Ais a
frequency factor.70 For fibrillar collagens, this tem-
perature-time relationship has been studied only for
relatively long (g1 s) thermal exposures. With expo-
sure times of several minutes, the onset of shrinking
of dermal and corneal collagen occurs at approxi-
mately 60 °C, regardless of collagen type and cross-
link density.58,73 Relaxation of the tissue shrinkage,
indicating gelatinization, begins at temperatures
above 77 °C in 15-month-old rat skin, with a tem-
perature of 100 °C being necessary to reduce tissue
shrinkage to half its maximal value.58 However, when
heating 52-year-old human skin, which possesses a
greater density of thermally stable covalent cross-
links, no stress relaxation was observed upon expo-
sure to temperatures up to 100 °C over several
minutes.65 These results indicate that the tissue
matrix remains mechanically intact at temperatures
of 100 °C or higher, even for long thermal exposures.
For short thermal exposures in the nanosecond to
millisecond range, characteristic of pulsed laser abla-
tion, the temperatures required to affect mechanical
stability are certainly far in excess of 100 °C. More-
over, it is known that the application of external
tensile stresses to collagen fibrils stabilizes the helical
architecture and results in a significant increase in
the denaturation temperature.74,75 Thus, the genera-
tion of internal tensile stresses resulting from pulsed
laser heating is expected to further stabilize the
collagen ECM with respect to possible collagen
denaturation. Nevertheless, given that surface tem-
peratures approaching 400-750 °C have been mea-
sured during tissue ablation using laser pulses of
100 µs duration,76 the possibility of a modification in
the mechanical integrity of the tissue ECM during
the nanosecond to millisecond time scales that we
consider here remains likely. Moreover, when using
nanosecond laser pulses, it is possible, even at
moderate radiant exposures, to raise the temperature
Γ(t))
0tAexp
(
-E
kBT(t)
)
dt(1)
Pulsed Laser Ablation of Biological Tissues Chemical Reviews, 2003, Vol. 103, No. 2 583
in the superficial tissue layer to values exceeding
1000 °C at which point the constituent molecules of
the ECM can be thermally dissociated into volatile
fragments.
III. Energy Deposition and Transport
The spatial distribution of volumetric energy den-
sity generated by laser irradiation drives all pulsed
laser ablation processes. This distribution is con-
trolled by the incident radiant exposure, Φ0, and the
optical absorption and scattering properties of the
tissue. A survey of the photophysical and photochemi-
cal determinants of tissue optical properties has been
prepared by Hillenkamp,14 and surveys restricted to
the ultraviolet spectral region are provided by Pettit18
and by Coohill.77 A presentation of the numerous
optical methods currently used for optical property
determination can be found in the book by Welch and
van Gemert.9Tissue optical properties have also been
determined through measurement and analysis of
laser-induced mechanical and thermal transients.78-82
Here we shall provide an overview of the key com-
ponents that govern tissue optical properties and
discuss the implications for radiative transport and
the resulting spatial scales for energy deposition
within tissue. A compilation of tissue optical proper-
ties measured in vitro and in vivo has been prepared
by Cheong.83
A. Optical Absorption Properties of Tissue
The optical absorption properties of tissue are
governed by the electronic, vibrational, and rotational
structures of the constituent biomolecules.14 In non-
turbid samples, optical transmission Tis governed
by Beer-Lambert’s law according to
where Rsis the specular reflection of the sample and
Φis the radiant exposure transmitted after travel
through an optical path length lin a sample with
molar extinction coefficient (M-1cm-1) and concen-
tration c(M). Alternatively, the absorption properties
of the sample can be characterized by an absorption
coefficient µa(cm-1). Typically, in the biomedical
optics community, the absorption coefficient µais
used to express the optical absorption properties of
tissue, while is used in reference to the optical
absorption properties of specific isolated biomol-
ecules. In general, the optical absorption properties
of tissue are dominated by the absorption of proteins,
DNA, melanin, hemoglobin, and water. However, as
shown in Figure 4, the variation of their optical
activities with wavelength is quite different. In the
following sub-sections, we examine the principal
tissue chromophores in the ultraviolet, visible, and
infrared spectral regions.
1. Ultraviolet Radiation (λ)180400 nm)
The ultraviolet (UV) region of the optical spectrum
relevant for tissue ablation lies between the vacuum
ultraviolet (VUV; λ<180 nm) and visible regions.
UV radiation represents light with very high photon
energy (6.5-3.1 eV) and enables the excitation of
nfσ*and πfπ*molecular orbital transitions. UV
absorption properties of tissues have long been of
interest to the photobiology community.84 While
water displays significant absorption at λe170 nm,
its absorption throughout the UV at room tempera-
ture is negligible.85-87 The dominant tissue chro-
mophores in the UV are proteins, DNA, and melanin.
In general, UV absorption by collagen-based soft
tissues drops significantly with wavelength. Accord-
ingly, the characteristic optical absorption depth (1/
µa) of these tissues varies from j0.5 µmatλ)190
nm to 200-400 µmatλ)400 nm.
The most important chromophore at short UV
wavelengths is the peptide bond (OdCsNsH) present
in the backbone of all proteins. This absorption peak
is centered at roughly λ)190 nm and is ac-
complished through an nfσ*transition.77,88 Given
that, in human tissue, protein is the most abundant
constituent next to water, the absorption coefficients
of tissues containing large amounts of the protein
collagen, (e.g., cornea, dermis) is very high in the
wavelength region around λ)190 nm and has a
value of µa)(2-4) ×104cm-1.81,89 Although the
absorption of the peptide bond falls considerably at
longer wavelengths, its contribution to overall tissue
absorption remains significant to λ)240 nm.84
At longer UV wavelengths, deoxyribonucleic acid
(DNA), the aromatic amino acid residues, and mela-
nin become important chromophores. With respect
to DNA, both the purine and pyrimidine bases are
aromatic and responsible for the DNA absorption
peak centered at λ)260 nm. Because of this
absorption peak, DNA displays an optical absorption
that is 10-20 times higher than that for an equal
weight of protein in the λ)240-290 nm wavelength
region.84 Although DNA displays an even higher
absorption at λe210 nm, its contribution to tissue
absorption is negligible when compared to the ab-
sorption cross section and the concentration of the
peptide bond present in tissue protein. The aromatic
amino acids tryptophan, tyrosine, and phenylalanine
also exhibit broad absorption peaks centered in the
λ)250-280 nm region that are accomplished via a
πfπ*molecular orbital transition.88 It should be
Figure 4. Optical absorption coefficients of principal tissue
chromophores in the 0.1-12-µm spectral region.
T)
[
Φ
Φ0(1 -Rs)
]
)10-cl )exp(-µal) (2)
584 Chemical Reviews, 2003, Vol. 103, No. 2 Vogel and Venugopalan
noted, however, that connective tissues are relatively
acellular and do not have much DNA content. More-
over, no more than 3% of the amino acid residues in
collagen are aromatic.34,35 Therefore, even within the
spectral region where both aromatic amino acids and
DNA absorb, the absorption of collagen-based tissues
is at least 100 times lower for λ)240-290 nm than
in the λ)190 nm region.
Melanin absorption is important when considering
the optical absorption properties of pigmented tissues
such as the skin, iris, and retinal pigment epithelium.
Melanin refers to a large class of biological pigments
whose color in the visible ranges from yellow and red-
brown to brown and black. In human skin, the optical
absorption of melanin becomes important at about
λ)300 nm, and after displaying an apparent
absorption peak at λ)335 nm, its absorption
spectrum drops monotonically with wavelength from
the UV to the IR.90-92
2. Visible Radiation (λ)400780 nm)
Optical absorption properties of tissue in the visible
spectral region are dominated by the absorption of
melanin and hemoglobin. Hemoglobin itself is present
in tissue in both deoxygenated (Hb) and oxygenated
(HbO2) forms. Although Hb and HbO2do display
optical absorption in the UV, their absorption be-
comes significant relative to that of other tissue
chromophores only in the visible spectral region. Hb
and HbO2have their most prominent absorption
peaks in the violet at λ)433 and 414 nm, respec-
tively.93 Their absorption drops by more than an
order of magnitude in the violet and blue and then
increases again in the green, where HbO2presents
absorption peaks at λ)542 and 576 nm and Hb
presents an absorption peak at λ)556 nm. The
absorption of both of these chromophores drops again
by over an order of magnitude in the yellow/red.
Despite this fact, as all biomolecules have little
absorption in the red and near-infrared, both Hb and
HbO2contribute significantly to the overall optical
absorption of vascularized tissues into the near-
infrared region.93,94
In pigmented tissues such as skin, hair, and ocular
tissues, melanin plays a significant role in determin-
ing the optical absorption properties. The absorption
spectrum of melanin is featureless in the visible
spectrum, dropping monotonically with wavelength
such that its absorption at λ)780 nm is roughly
10% of that at λ)400 nm.95,96 This featureless
characteristic of the absorption spectrum of melanin
is somewhat surprising. A possible explanation may
reside in the fact that melanin naturally exists in
particulate form with a diameter of roughly 160 nm.97
Thus, the contribution of optical scattering to the
measured extinction coefficient of melanin cannot
easily be separated from the intrinsic absorption
properties of melanin.96 Recent work indicates that
the extinction coefficient of melanin is primarily due
to a large scattering coefficient that at visible wave-
lengths dominates absorption by as much as 100
times.98
3. NearFar-Infrared Radiation (λ)780 nm15 µm)
Apart from hemoglobin, which contributes signifi-
cantly to the optical absorption of vascularized tis-
sues out to approximately λ)1000 nm, water and
protein are the principal tissue chromophores in the
infrared (IR) spectral region. Water is the most
important tissue chromophore in the infrared and
begins to contribute significantly to tissue absorption
at λJ900 nm. The absorption spectrum of water is
governed by the resonance of its symmetric and
asymmetric stretch modes that are located at ν1)
3651.7 cm-1(λ)2.74 µm) and ν3)3755.8 cm-1(λ)
2.66 µm), respectively, and the resonance of its
symmetric bend mode at ν2)1595 cm-1(λ)6.27
µm).99 These vibrational modes and their combina-
tions give rise to its absorption peaks, located at λ)
0.96, 1.44, 1.95, 2.94, 4.68, and 6.1 µm.100 The optical
absorption of water in the near-infrared is initially
quite weak but rises quite rapidly with wavelength.
From the visible spectral region, the absorption of
water increases by nearly 6 orders of magnitude and
reaches a maximum at λ)2.94 µm, where the
absorption coefficient is µa)12 000 cm-1.101 Although
this absorption is high, it is nearly 3 times lower than
the optical absorption of collagen-based tissues in the
UV at λ190 nm. Optical absorption continues to
be strong (µa>500 cm-1) in the far-infrared (6-15
µm) and exhibits another maximum at λ)6.1 µm,
where µa)2740 cm-1.
The other chief chromophore in the IR is protein.
Infrared spectra of proteins in the IR are governed
by various vibrational modes of the peptide bond (Od
CsNsH). The most important of these are (1) the
CdO stretch, also termed the amide I band, which
for collagen is located at ν1)1640-1660 cm-1(λ)
6.02-6.10 µm); (2) the N-H in-plane deformation
with C-N stretch, also termed the amide II band,
located at ν2)1535-1550 cm-1(λ)6.45-6.51 µm)
for collagen; and (3) the C-N stretch with N-H in-
plane deformation, also termed the amide III band,
located at ν3)1230-1270 cm-1(λ)7.87-8.13 µm)
for collagen.34,102 Collagen and water share an ab-
sorption peak at λ6.1 µm, where the absorption of
collagen is larger than that of water by more than a
factor of 2. For the amide II peak at λ6.45 µm, the
absorption of water is roughly a factor of 6 lower than
that of protein.
B. Optical Scattering Properties of Tissue
Both optical absorption and scattering play impor-
tant roles in determining the spatial distribution of
volumetric energy density deposited by laser radia-
tion in tissue. When scattering is negligible or absent,
the optical penetration depth, δ, of the incident
radiation is given by the reciprocal of the absorption
coefficient and defines the characteristic depth to
which the tissue is heated. However, at wavelengths
where optical scattering is significant, δis smaller
than 1/µaand also is dependent on the diameter of
the laser beam.103
Optical scattering arises from spatial variations in
the refractive index within tissue. This variation is
dependent on the composition, size, and morphology
Pulsed Laser Ablation of Biological Tissues Chemical Reviews, 2003, Vol. 103, No. 2 585
of both cellular and extracellular tissue com-
ponents.104-109 The effect that any given scatterer has
upon the light distribution is dependent not only on
its scattering properties but also on its spatial
location and orientation relative to neighboring scat-
terers. As a consequence, even in systems with large
densities of optical scatterers, significant scattering
results only when substantial variation in the refrac-
tive index is present over length scales that are
comparable to or larger than half the wavelength of
light.50,110 For example, the microstructure of human
cornea is very regular, such that the collagen fibrils
have diameters of 30 nm and are spaced at center-
to-center distances of 65 nm. Thus, the variation
of refractive index over a spatial scale comparable
to the wavelength of visible light is very small, even
though individual collagen fibrils are strong scatter-
ers. This feature provides the optical transparency
of the cornea in the visible spectrum. Other collagen-
based tissues, such as dermis and sclera, possess
collagen fibrils with a significant variability in di-
ameter (30-300 nm), orientation, and spacing. This
variability produces significant refractive index varia-
tions over spatial scales comparable to half the
wavelength of visible light, resulting in opacity.41,49,50
Typical reduced scattering coefficients for tissues
in the green are of the order of 10-40 cm-1.83 In
addition, scattering data for tissue acquired over
significant wavelength ranges indicate that the re-
duced scattering coefficient is well characterized by
the scaling law µsλ-b, where b0.5-2.111,112 Apart
from the absolute values of the tissue optical proper-
ties, the magnitude of optical absorption relative to
optical scattering is a key determinant of the spatial
distribution of radiation generated by the laser
exposure. When absorption is dominant over scat-
tering, application of the Beer-Lambert law is ap-
propriate to determine the spatial distribution of the
absorbed radiation from a known absorption coef-
ficient. However, when scattering is dominant over
or comparable to optical absorption, one must resort
to more detailed models of radiative transport (e.g.,
using Monte Carlo simulations or approximate solu-
tions such as those provided by diffusion or random-
walk models) to obtain the distribution of the ab-
sorbed radiation.103,113,114
Figure 5 presents the relative magnitudes of ab-
sorption and scattering in skin as a function of
wavelength. For λ<450 nm, the optical activity of
the peptide bond, aromatic amino acid residues,
DNA, and hemoglobin provides for the domination
of absorption over scattering. For λ)450-1750 nm,
tissue scattering is, in general, more prevalent than
absorption, although for λ)450-600 nm, melanin
and hemoglobin provide significant absorption while
water plays a similar role for λ>1350 nm. At longer
wavelengths, water absorption picks up dramatically,
and for λ>1750 nm, tissue absorption once again
dominates over scattering. The optical scattering will
reduce the optical penetration depth, δ, of light
relative to the absorption depth. Moreover, for scat-
tering tissues, δbecomes smaller as the laser beam
diameter is reduced.15,103 In addition, when scattering
is dominant over absorption, backscattering and total
internal reflection lead to a large fluence rate proxi-
mal to the tissue surface which can exceed by several
times the delivered irradiance.15,103 It should be
noted, however, that using laser wavelengths where
optical scattering is comparable to or dominant over
tissue absorption is not conducive to precise ablation
(see section IV.C).
C. Dynamic Optical Properties in Tissue
Typically, measurement of tissue optical properties
is done under room or physiological conditions.
However, the thermal and mechanical transients
generated by pulsed laser ablation processes are
substantial and can result in a significant alteration
of the tissue optical properties. While thermal dena-
turation can result in a significant increase (as much
as 5 times) in the reduced scattering coefficient,115-117
such changes are usually of minor importance, con-
sidering that ablation is typically performed at
wavelengths where optical absorption dominates
scattering. Changes in tissue absorption, however,
are much more important. Walsh and co-work-
ers118,119 suggested in 1989 that tissue absorption
may change significantly during laser irradiation to
explain the unexpectedly large etch depths and zones
of thermal injury produced by Q-switched Er:YAG (λ
)2.94 µm) laser ablation of tissue. Subsequent
studies that investigated the thermal injury and
mass removal produced by pulsed IR laser ablation
at other wavelengths also found results that were not
fully consistent with the room-temperature absorp-
tion spectra of water.120-122
Motivated by spectroscopy literature indicating
that the absorption peak of water at λ)2.94 µm
drops and shifts toward shorter wavelengths for
increasing temperature,123,124 various researchers
investigated the reduction in the IR absorption
coefficient of tissue upon heating of the tissue.26,125-130
This reduction in optical absorption occurs due to the
weakening of the hydrogen bonds between adjacent
water molecules at higher temperature that results
in a change in the length and strength of the OH
bond. In the 2-µm region, the absorption coeffi-
Figure 5. Ratio of the reduced scattering coefficient to
the absorption coefficient of human skin. For wavelengths
below 450 nm and above 1800 nm, optical absorption,
provided by hemoglobin and protein in the UV and water
in the mid- and far-IR, dominates the optical properties.
Data compiled from refs 111 and 112.
586 Chemical Reviews, 2003, Vol. 103, No. 2 Vogel and Venugopalan
cient drops by a factor of 2 at temperatures nearing
100 °C.127,130 The 3-µm region offers the most dra-
matic change in absorption coefficient with temper-
ature. Results from a recent study by Shori and co-
workers129 for wavelengths of λ)2.94 µm, along with
data at λ)2.79 µm obtained from an earlier study
by Cummings and Walsh,125 are shown in Figure 6a.
At λ)2.94 µm, the absorption coefficient remains
nearly identical to the room-temperature value of µa
13 000 cm-1until a volumetric energy density of
0.02 kJ/cm3is reached; it then drops monotonically,
reaching µa2000 cm-1at 20 kJ/cm3. For λ)2.79
µm, the absorption coefficient remains at the room-
temperature value of µa5250 cm-1up to a volu-
metric energy density of 1 kJ/cm3, when it begins
to rise up to a maximum of approximately µa6000
cm-1as a result of the λ)2.94 µm absorption peak
shifting to shorter wavelengths. When an energy
density of 4 kJ/cm3is reached, the absorption coef-
ficient begins to fall and reaches µa1000 cm-1at
20 kJ/cm3.128
To appreciate the consequences of these findings,
we performed finite difference calculations based on
the absorption data shown in Figure 6a to determine
the variation of the volumetric energy density ab-
sorbed at the tissue surface 0with incident radiant
exposure, Φ0. The results are shown in Figure 6b.
At λ)2.94 µm, the increase of the volumetric energy
deposition with radiant exposure reduces noticeably
for Φ0>2×10-2J/cm2. This is due to the reduction
in absorption coefficient at the surface that results
in the deposition of laser energy to larger depths
within the sample. By contrast, at λ)2.79 µm, there
is an enhancement of volumetric energy deposition
at the surface over the radiant exposure interval of
0.05-1.5 J/cm2. It is only for Φ0>1.5 J/cm2that we
observe the effects of reduction of optical absorption
on the volumetric energy density.
In Figure 6c, we present the variation in optical
penetration depth as defined by the depth at which
the volumetric energy density drops to 1/e of that
delivered to the tissue surface. It is evident that for
Φ0>0.5 J/cm2, Er:YSGG radiation offers better
spatial confinement of the laser energy than Er:YAG
radiation. This is opposite to the behavior one would
expect from the absorption coefficients measured at
small radiant exposures.
The possibility of a variation in optical absorption
with temperature in the UV has also been investi-
gated. Ediger, Pettit, and co-workers reported that
the absorption of collagen targets may be enhanced
during laser irradiation at λ)193 nm and persists
for a significant time (10-4s) thereafter.131,132
Moreover, in a paper by Staveteig and Walsh,133 it is
postulated that although the absorption of UV radia-
tion by the peptide bond is a necessary first step in
the UV ablation process, the heating of the surround-
ing water results in a change in hydrogen-bonding
structure that leads to a shift of the water absorption
band located at 160 nm to longer wavelengths. The
paper provides data indicating that the absorption
of water at λ)193 nm may be raised to as much as
µa104cm-1at a volumetric energy density of
2 kJ/cm3. This raises the possibility that UV laser
ablation of tissue is driven by the optical absorption
of both collagen and water.
Figure 6. Effects of dynamic optical properties of a water
target produced by Er:YSGG (λ)2.79 µm) and Er:YAG (λ
)2.94 µm) laser irradiation. (a) Variation of optical
absorption coefficient of water with volumetric energy
density. Data compiled from refs 125 and 129. (b) Variation
of volumetric energy density at the water surface with
incident radiant exposure. Dashed lines indicate the ex-
pected variation if the absorption coefficient remained
constant. (c) Variation of optical penetration depth with
incident radiant exposure. Optical penetration depth is
defined as the location at which the volumetric energy
density drops to 1/eof the surface value. Note that for
incident radiant exposures Φ0>0.4 J/cm2, Er:YSGG laser
irradiation offers more superficial energy deposition com-
pared to Er:YAG laser irradiation.
Pulsed Laser Ablation of Biological Tissues Chemical Reviews, 2003, Vol. 103, No. 2 587
IV. Linear Thermomechanical Response of Tissue
to Pulsed Irradiation
The spatial distribution of volumetric energy den-
sity resulting from pulsed laser irradiation of tissue
generates significant thermal and mechanical tran-
sients. These thermomechanical transients are the
driving force for all laser ablation processes that are
not photochemically mediated. In this section we
describe the linear thermomechanical response of
tissue as it is a precursor to the processes that follow.
In section V, we then address the kinetics of phase
transitions and photochemical processes that produce
material removal in pulsed laser ablation.
A. Temperature Rise and Thermal Diffusion
In the absence of photochemical or phase transition
processes, the energy absorbed by the tissue in
response to pulsed laser irradiation is entirely con-
verted to a temperature rise. Under adiabatic condi-
tions, the local temperature rise at an arbitrary
location r,T(r), is directly related to the local
volumetric energy density, (r), as
where Fis the tissue density and cvthe specific heat
capacity at constant volume. Once this energy is
absorbed, it is subject to spatial redistribution by
thermal diffusion.9,134 In 1983, Anderson and Par-
rish135 introduced the concept that spatially confined
microsurgical effects (selective photothermolysis) can
be achieved by the use of laser exposures that are
shorter than the characteristic thermal diffusion time
of the heated volume. For laser ablation, the heated
volume is typically a layer of tissue of thickness 1/µa,
and the characteristic thermal diffusion time, td,is
given as15,103
where κis the thermal diffusivity. “Thermal confine-
ment” is achieved when the ratio of the laser pulse
duration to the thermal diffusion time fulfills the
condition (tp/td)j1. By defining a dimensionless
measure of the laser pulse duration relative to the
characteristic thermal diffusion time, td
/)(tp/td) and
using eq 4, the thermal confinement condition can
be expressed as
The concept of thermal confinement can be ap-
preciated by considering the temperature distribution
within a water sample irradiated with a fixed radiant
exposure using different pulse durations, as shown
in Figure 7 for a planar semi-infinite target with µa
104cm-1(i.e., optical penetration depth of 1 µm). For
this case, the characteristic thermal diffusion time
given by eq 4 is td)6.9 µs. At the end of laser
exposures with duration tp<3µs, the temperature
profile is almost fully confined to the volume in which
the radiation is absorbed. However, for exposure
durations of tpg10 µs, thermal diffusion has
redistributed the energy over a larger volume and
has reduced significantly the peak temperatures
within the sample.
Water and collagen are most often the main chro-
mophores for pulsed IR and UV ablation, respec-
tively. When using a wavelength that is absorbed by
water and not collagen (or vice versa), one must
consider whether the concept of thermal confinement
applies not only to the heated volume as a whole but
also to the individual microscopic tissue structures
that absorb the radiation.136,137 As most matrix-
continuous soft tissues consist of collagen fibrils
embedded within a highly hydrated ground sub-
stance, microscale thermal confinement relates to
length scales comparable to the collagen fibril diam-
eter. Collagen fibrils in the corneal stroma and in
dermis possess diameters of 30 and 100 nm, respec-
tively, with corresponding characteristic thermal
diffusion times tdof 6.3 and 69 ns. These times are
comparable in magnitude to the duration of UV
excimer laser pulses when tp20-30 ns as well as
Q-switched IR laser pulses when tp100 ns. Thus,
while microscale thermal confinement may influence
the ablation of skin, it is unlikely to play a strong
role in the ablation of cornea unless laser pulses of
picosecond or femtosecond duration are employed.
B. Thermoelastic Stress Generation and
Propagation
Rapid heating of tissue by pulsed laser radiation
also leads to the generation and propagation of
thermoelastic stresses as the heated tissue volume
reconfigures to its new equilibrium state. The mag-
nitude and temporal structure of the thermoelastic
stresses are governed by the longitudinal speed of
sound in the medium, ca, the laser pulse duration,
tp, the depth of the heated volume, 1/µa, and an
intrinsic thermophysical property known as the Gru¨-
neisen coefficient.138-143 The Gru¨neisen coefficient is
simply the internal stress per unit energy density
generated upon depositing energy into a target under
constant volume (i.e., isochoric) conditions. Thus, its
Figure 7. Normalized temperature profiles in water
immediately following laser irradiation with a fixed radiant
exposure and optical penetration depth (1 µm) for various
pulse durations, tp.
T(r))
(r)
Fcv(3)
td)1
κµa2(4)
td
/)κµa2tpj1 (5)
588 Chemical Reviews, 2003, Vol. 103, No. 2 Vogel and Venugopalan
definition is given by the thermodynamic deriva-
tive:144
where σis the internal stress, the volumetric energy
density, vthe specific volume, Rthe coefficient of
thermal expansion, Fthe mass density, cvthe specific
heat capacity at constant volume, and κTthe isother-
mal compressibility.
Thermoelastic stresses are most prominent when
the laser pulse duration tpis smaller than or on the
order of the characteristic time for a stress wave to
propagate across the heated volume, tm)(1/µaca).
Thus, “stress confinement” is achieved when the ratio
of the laser pulse duration to the stress propagation
time, (tp/tm)j1. When the stress confinement condi-
tion is expressed in terms of a dimensionless measure
of the laser pulse duration relative to the stress
propagation time, tm
/)(tp/tm), we obtain
In this case, heating of the laser-affected volume is
achieved under isochoric conditions, and the internal
stresses generated do not propagate outside the
heated volume during the laser irradiation. The peak
thermoelastic stress σpis given by
where A)1 and the duration of the thermoelastic
stress transient tascales with the stress propagation
time (i.e. the acoustic transit time across the heated
volume) and ta(4-6)/µaca.142,145 When the stress
transient leaves the heated volume, the peak stress
drops to 0.5σp(Paltauf and Dyer, this issue).
For cases in which stress confinement is not
achieved, i.e., tm
/)µacatpJ1, significant thermal
expansion of the heated volume occurs during ir-
radiation. This has the effect of reducing the mag-
nitude of the peak stress, and thus A<1. In the limit
tm
/f, where there is no stress confinement, Af0,
and the duration of the stress transient approaches
that of the laser pulse.145 The variation of Awith tm
/
has been discussed by various authors138-141,146 and
is shown for a biexponential temporal laser pulse
shape in Figure 8. It is interesting to note that the
pressure amplitudes produced by a laser pulse with
a Gaussian temporal profile are slightly higher than
those shown in Figure 8 (see Paultauf and Dyer, this
issue).
Due to a strong variation in the thermal expansion
coefficient with temperature, the Gru¨neisen coef-
ficient of water is also strongly temperature depend-
ent. A polynomial expression that approximates this
temperature variation is given by Paltauf and
Schmidt-Kloiber.143 The effects of this temperature
dependence on the magnitude and temporal structure
of thermoelastic stress transients have been ana-
lyzed.147,148 A temperature dependence of the stress
amplitude has been recently reported for irradiation
of the retinal pigment epithelium of the eye.149
Previous measurements of the variation of ther-
moelastic stress amplitude with radiant exposure in
cornea, dermis, and aorta did not exhibit a strong
nonlinearity for radiant exposures below the ablation
threshold.78,137,150
While thermal expansion of a heated volume
generates compressive thermoelastic stresses, sub-
sequent propagation of these stresses result in tran-
sients that contain both compressive and tensile
components. Tensile stresses arise from the reflection
of the compressive stress waves at a boundary to a
medium with lower acoustic impedance (tissue-air,
tissue-water) or from the three-dimensional char-
acteristics of acoustic wave propagation.140,143,151-153
Tensile stress wave generation originating from
acoustic impedance mismatch is shown in Figure 9.
The compressive thermoelastic stress wave that
originates from the heated volume at the target
surface is almost completely reflected as a tensile
Γ)
(
σ
∂
)
v)R
FcvκT(6)
tm
/)µacatpj1 (7)
σp)AΓ0)AΓµaΦ0(8)
Figure 8. Variation of the thermoelastic stress prefactor
A(see eq 8) with the dimensionless pulse duration relative
to the stress propagation time across the heated volume
tm
/. Results are shown for a biexponential laser pulse
shape and derived from the results of ref 139.
Figure 9. (a) Development of a thermoelastic stress wave
in water calculated for Φ0)2 J/cm2,µa)200 cm-1, and tp
)8 ns. (b) Pressure as a function of time at a depth of 50
µm. (Reprinted with permission from ref 143. Copyright
1996 Springer.)
Pulsed Laser Ablation of Biological Tissues Chemical Reviews, 2003, Vol. 103, No. 2 589
stress wave at the air-target interface that propa-
gates into the bulk medium. Dingus and Scammon
first considered the possibility that tensile stress
waves formed in this manner can lead to the fracture
and “spallation” of the irradiated target.141
The second mechanism for tensile stress generation
is connected with the three-dimensional character of
stress wave propagation and arises when the condi-
tion for planar stress propagation is not satisfied.
Conservation of momentum demands that the stress
transient emitted from a heated tissue volume must
contain both compressive and tensile components,
such that the integral of the stress over time van-
ishes.153 This phenomenon has also been described
as an acoustic diffraction effect.140,142 Tensile stresses
related to the finite size of the heated volume are
most pronounced when the laser beam diameter is
comparable to the optical penetration depth. Detailed
studies have been performed for the propagation of
stress waves originating from the tip of an optical
fiber immersed in an absorbing liquid151,152 and from
the heated volume in a solid sample that was irradi-
ated in air.154-156
Studies in which optical fibers were used to irradi-
ate targets within an absorbing aqueous medium
produced significant tensile pressures with the ability
to form voids near the fiber axis close to the fiber
tip.151,152 A similar effect has been observed for the
ablation of porcine cornea in situ. Compressive recoil
stresses produced by the ejection of ablated material
from a disklike volume of finite size developed
significant tensile stresses, approaching 4 MPa after
propagation of a few millimeters into the ocular
bulb.157
In studies that considered the generation of tensile
stress by the irradiation of a solid target, attention
was given to the full stress tensor rather than the
hydrostatic pressure.82,154-156 Thus, the three normal
stress components, i.e., the axial (σzz), radial (σrr), and
circumferential (σθθ) stresses, as well as the appropri-
ate shear (σrz,σrθ,σθz) stress components were
considered. As shown in Figure 10, these studies
demonstrated that thermoelastic stress wave propa-
gation produced strong transient variations in both
normal and shear stress components with significant
tensile components at the target surface. Moreover,
significant, albeit weaker, quasi-static stresses re-
main after the cessation of the thermal expansion
and relax only after the sample has returned to a
uniform temperature. A detailed description of these
phenomena can be found in the article by Paltauf and
Dyer in this issue.
C. Implications for Precise Tissue Ablation
The achievement of precise tissue ablation requires
the use of laser wavelengths possessing a small
optical penetration depth in tissue that serves to
confine the energy deposition to a small volume.
However, this condition alone is not sufficient. Ther-
mal confinement is also required for precise ablation
in order to limit the spatial extent of thermal diffu-
sion during irradiation and maximize the tempera-
tures in the absorbed volume. Stress confinement
may provide for a more efficient ablation process as
there is ample evidence that it serves to reduce the
volumetric energy density required for material
removal. This results in an increase of the ablation
efficiency and a reduction of the thermal injury in
the tissue that remains. These issues will become
clearer in the next section, where we consider the
thermodynamics involved in phase transition and
material removal processes.
V. Thermodynamics and Kinetics of Phase
Transitions
Ablative cutting or material removal requires the
fracture of chemical bonds. The breakage of bonds
leads either to the removal of molecules, molecular
fragments, and molecular clusters or to the formation
of voids within the bulk of the material. Void (i.e.,
bubble or crack) formation results in the ejection of
non-decomposed material fragments upon mechani-
cal failure of the material. Vaporization, molecular
fragmentation, and void formation are all phase
transitions and can be accomplished via photother-
mal, photomechanical, or photochemical mechanisms.
Given the central role of phase transitions in the
ablation process, this section is devoted to a system-
atic analysis of their thermodynamics and kinetics.
In sections V.A-G, we consider the generation of
phase transitions via photothermal and photome-
chanical phenomena and their modifications in the
presence of a tissue matrix. We then treat photo-
chemical mechanisms to achieve bond dissociation in
section V.H and discuss their interplay with photo-
thermal and photomechanical processes for tissue
ablation in section V.I.
A. Phase Diagrams
Consider a schematic of the pressure versus tem-
perature projection of the phase diagram for liquid
and gaseous water shown in Figure 11. The solid
curve A-C represents those pressure/temperature
pairs in which liquid and gaseous water are in
equilibrium with one another and is known as the
“binodal”.158-160 The curve B-C-D in Figure 11
denotes a locus of states representing the intrinsic
Figure 10. Time evolution of radial thermoelastic stresses
on a tissue surface as a function of radial position at
different times following the laser pulse. In the case shown,
the laser beam diameter is 1200 µm and the optical
penetration depth 860 µm. All stresses are normalized to
the initial compressive stress at the surface. (Reprinted
with permission from ref 156. Copyright 1995 National
Academy of Sciences, U.S.A.)
590 Chemical Reviews, 2003, Vol. 103, No. 2 Vogel and Venugopalan
stability limit of the liquid or vapor phase (i.e., (T/
s)p)0 and (p/v)T)0) and is known as the
“spinodal”. At the spinodal, the superheated liquid
phase or subcooled vapor phase is no longer stable
with respect to the random density fluctuations that
occur in all materials at nonzero temperatures. Thus,
the segment of the spinodal denoted B-C represents
the limit to which metastable liquids can be super-
heated, while the segment D-C represents the limit
to which metastable vapor can be subcooled.158-163
The binodal and spinodal curves intersect at the
critical point C, above which no thermodynamic
distinction can be made between liquid and vapor
phases. As ablation is often driven by a phase
transition from the liquid to the vapor state, we focus
our attention on segment B-C of the spinodal and
future depictions of the pvs Tphase diagram will
omit segment D-C of the spinodal for clarity.
Figure 12 provides the pressure versus specific
volume projection of the phase diagram with equi-
librium and van der Waals isotherms shown. In this
diagram, the liquid-, vapor-, and mixed-phase regions
are clearly demarcated. The boundary of the mixed-
phase region encloses the range of specific volumes
in which liquid and gaseous phases coexist for a given
pressure and temperature and is often referred to as
the ‘vapor dome’. The apex of the vapor dome (point
C) denotes the critical point which for water is located
at Tc)374.14 °C and pc)22.09 MPa. The dashed
curve within the mixed phase region represents the
spinodal, where segment B-C specifies the stability
limit of superheated liquid and segment D-C speci-
fies the stability limit of subcooled vapor. In both
Figures 11 and 12, additional locations have been
indicated that are pertinent to the discussion that
follows. Point 1 represents ambient conditions, i.e.,
T1)25 °C and p1)101 kPa; point 2 denotes
saturated liquid at atmospheric pressure, i.e., the
“boiling temperature”, T2)100 °C and p2)101 kPa;
point 3 is the location of the spinodal at ambient
pressure, T3)305 °C and p3)101 kPa; and point 4
provides the equilibrium vapor pressure and specific
volume for saturated liquid corresponding to the
spinodal temperature, i.e., T4)305 °C and p4)9.2
MPa. Points 4, 5, and 5lie on the binodal in the
mixed phase region and possess the same specific
enthalpy as liquid at ambient pressure heated to the
spinodal limit. Their significance, along with the
curve of constant enthalpy (isoenthalp) shown in
Figure 12, is discussed in section V.D.
B. Surface Vaporization
Equilibrium vaporization takes place at a liquid-
vapor interface, where liquid water at a free surface
is transformed to vapor at the saturation tempera-
ture and pressure.154,155 Thus, equilibrium vaporiza-
tion can occur when the liquid is in any thermody-
namic state that lies on the binodal. As a result,
vaporization does not occur at a predetermined
temperature and all theoretical models that adopt a
fixed “vaporization temperature” violate the basic
physics of the process. The rate at which energy is
supplied to the system dictates the vaporization rate.
Many investigators have developed fluid dynamic
models of surface vaporization driven by the absorp-
tion of laser radiation that are consistent with the
thermodynamics of the process.166-171
Enhanced rates of vapor formation from the free
surface of a liquid can be achieved at the start of
pulsed laser radiation via the process of nonequilib-
rium interphase mass transfer.172 Consider a liquid
system located at point 1 in the phase diagram,
where the surface of the liquid is in equilibrium with
the ambient vapor at a temperature below the
saturation temperature. An enhancement in the rate
of vapor formation occurs when the liquid surface
temperature is raised rapidly (to a value that may
still be below the binodal), the liquid surface is no
longer in equilibrium with the surrounding vapor.
This results in a very high net mass flux from the
liquid surface to the surroundings that persists until
the ambient vapor pressure reaches the equilibrium
vapor pressure corresponding to the new surface
Figure 11. Pressure vs temperature projection of the
thermodynamic phase diagram including the spinodal
curve. Specific states of interest are (1) ambient temper-
ature and pressure, (2) boiling temperature under ambient
conditions, (3) spinodal temperature at ambient pressure,
and (4) saturated conditions corresponding to the ambient
spinodal temperature. The importance of points 4and 5
are discussed in section V.D.
Figure 12. Pressure vs specific volume projection of the
thermodynamic phase diagram including the spinodal
curve along with equilibrium and van der Waals isotherms.
Points 1-4 correspond to those shown in Figure 11. The
importance of points 4,5,5and that of the isoenthalp is
discussed in section V.D.
Pulsed Laser Ablation of Biological Tissues Chemical Reviews, 2003, Vol. 103, No. 2 591
liquid temperature. Once the vapor pressure returns
to equilibrium, the balanced exchange of the evapo-
ration of liquid molecules into the vapor phase and
the condensation of vapor molecules back into the
liquid phase is restored. Such a process also mediates
the initial vapor flow from a liquid surface when
rapidly heated to extreme temperatures; even those
in excess of the critical point. The impact of nonequi-
librium interphase mass transfer on pulsed infrared
laser ablation has been considered by Yablon and co-
workers.173
C. Normal Boiling
Normal boiling refers to a process that, like surface
vaporization, occurs at a thermodynamic state on the
binodal, as indicated by point 2 in Figure 11. Thus,
for a given pressure, the binodal defines the corre-
sponding “boiling temperature”, which is 100 °C for
water at atmospheric pressure. Normal boiling relies
on the presence of cavities of dissolved gas or other
heterogeneities within the liquid that catalyze the
nucleation and growth of vapor bubbles. The energy
is deposited into the system at a rate sufficient to
drive the growth of pre-existing vapor nuclei at such
heterogeneous locations.158,160,164,165,174,175 The rate of
volumetric energy deposition provided by the laser
irradiation is balanced by the energy of the vapor
leaving the system. In a normal boiling process
driven by laser irradiation of a free surface, the
transition from saturated liquid to saturated vapor
necessarily occurs in a finite layer of mixed phase at
the sample surface. The thickness of this ‘vapor-
liquid’ layer is comparable to the optical penetration
depth of the incident radiation and its composition
varies from that of saturated liquid at the base to
saturated vapor at the surface.164,176 As a result, the
surface temperature is fixed to the saturation condi-
tions corresponding to the pressure at the target
surface and there is no temperature gradient within
the vapor-liquid layer.
The temperature and pressure at which boiling
occurs is influenced by the rate of mass removal from
the target surface. The recoil associated with a rapid
rate of mass removal increases the pressure at the
target surface beyond ambient conditions. In such
cases, if the ambient pressure is atmospheric, the
boiling temperature of water will exceed 100 °C.
While normal boiling has provided the basis for
models used to investigate the various aspects of
laser ablation of tissue,176,177 the density of hetero-
geneous bubble nucleation sites is likely insufficient
to provide a boiling process sufficiently vigorous to
balance the high rates of energy deposition achieved
in most pulsed ablation processes.137,164,165 Another
factor limiting the role of normal boiling in pulsed
laser ablation is the requirement that the bubbles
move to the target surface on a time scale set by the
propagation velocity of the ablation front. Miotello
and Kelly165 showed that this is not possible for
irradiation of pure water with submicrosecond laser
pulses. In tissue, the mobility of vapor bubbles is
further inhibited by the presence of the ECM.
It is important to note that once a normal boiling
process is established, the presence of volumetric
energy densities infinitesimally higher than that
corresponding to the saturation temperature results
in the formation and growth of a vapor bubble. Thus,
normal boiling always involves the partial vaporiza-
tion of a liquid volume through the growth of vapor
bubbles. In studies that consider the ablation of
biological tissues, one sometimes finds the concept
that vaporization occurs only once the entire latent
heat of vaporization is deposited into a specified
volume of water. This concept is not tenable, as it
would lead to the superheating of liquid to temper-
atures far beyond the limit of stability.
D. Phase Explosions: Bubble Nucleation and
Spinodal Decomposition
When the rate of volumetric energy deposition
provided by laser radiation is more rapid than the
rate of energy consumed by vaporization and normal
boiling, the tissue water is driven to a metastable
superheated state. The liquid can remain metastable
until the spinodal temperature is reached (point 3
in Figures 11 and 12). At the spinodal temperature,
the stability limit is violated, and the liquid under-
goes “spinodal decomposition”, a spontaneous process
by which a thermodynamically unstable liquid re-
laxes toward equilibrium.158,160 Unique features of the
spinodal temperature can be appreciated by viewing
a plot of the Gibbs free energy versus specific volume
at ambient pressure, such as that shown in Figure
13. For equilibrium saturation conditions (T)Tsat),
the Gibbs free energy displays two local minima of
equal magnitude located at specific volumes corre-
sponding to saturated liquid and saturated vapor
states.144 For temperatures greater than Tsat, the
vapor state is favored, and thus the local minimum
corresponding to the specific volume of the vapor is
lower than the local minimum corresponding to the
liquid state. However, the presence of the local
minimum corresponding to the liquid state indicates
Figure 13. Gibbs free energy vs specific volume of a pure
substance for several temperatures starting at the satura-
tion temperature, Tsat, where the liquid and gaseous states
are in equilibrium, up to the spinodal temperature, Tspin.
Note that the local minimum corresponding to the liquid
phase disappears at the spinodal temperature, effectively
forcing conversion of the substance to the vapor phase.
592 Chemical Reviews, 2003, Vol. 103, No. 2 Vogel and Venugopalan
that the liquid, while not globally stable, resides in
ametastable state. Accordingly, the transition from
liquid to vapor requires that a free energy barrier be
overcome. Larger temperature differences from satu-
ration conditions result in a shallower local minimum
for the liquid state and a reduction in the free energy
barrier. At the spinodal temperature, Tspin, the Gibbs
free energy minimum corresponding to the liquid
phase disappears, the superheated liquid becomes
unstable, and the transition to the vapor phase via
spinodal decomposition is spontaneous.158
Thus, unlike bubble nucleation, spinodal decom-
position is not an activated process and is not
impeded by the presence of a free energy barrier. This
results in a phase transition with a fundamentally
different character. While bubble nucleation results
in the formation of large density fluctuations of small
spatial extent, spinodal decomposition involves the
rapid spontaneous growth of small density fluctua-
tions that extend over large spatial scales.158,178 The
result is a process of phase separation that encom-
passes the entire unstable liquid volume. The super-
heated, unstable water at atmospheric pressure
spontaneously “relaxes” by separating into an equi-
librium state of mixed phase composed of saturated
liquid and vapor at pressures that can approach the
saturation pressure corresponding to the spinodal
temperature (i.e., p)9.2 MPa; for water at atmo-
spheric pressure). This “relaxation” process thus
involves an impressive pressure rise.
For the phase diagram shown in Figure 11, the
deposition of an amount of energy just sufficient to
produce spinodal decomposition first produces a
heating phase that corresponds to the path 1 f3.
The spinodal decomposition process initially results
in an isochoric transition from point 3 on the spinodal
to point 4in the mixed phase region possessing the
same enthalpy. If this pressure jump results in tissue
fracture, the liquid-vapor mixture will be exposed to
atmospheric pressure and be ejected as saturated
vapor and saturated liquid droplets. As this mixture
expands, its thermodynamic state will follow roughly
the curve of constant enthalpy (isoenthalp) as shown
on Figure 12 until it reaches atmospheric pressure
at point 5. However, if the pressure jump does not
result tissue fracture, the tissue will expand slightly
and relax to an intermediate temperature and pres-
sure represented by point 5. In this latter case, the
precise location of point 5 depends on the stiffness
of the tissue and additional energy deposition is
required to further increase the internal temperature
and pressure to produce ablation (see section V.F).
To provide a complete description of the phase
transformation process, we must also consider the
contribution of homogeneous nucleation as the liquid
is heated to the spinodal limit.137,165,179-181 For a
superheated liquid, homogeneous nucleation refers
to the spontaneous formation of vapor inclusions
within the bulk liquid, solely from thermodynamic
fluctuations and not catalyzed by the presence of
impurities or dissolved gas. While the formation of
such vapor “nuclei” is spontaneous, their growth is
not ensured and depends strongly on superheat
temperature. Thus, the transformation of super-
heated (metastable) liquid to an equilibrium state of
mixed phase may involve both bubble nucleation and
spinodal decomposition, and we refer to the collective
phase transition processes as a “phase explosion”.
Let us consider the process of homogeneous bubble
nucleation more closely. In the framework of classical
nucleation theory initially formulated in the 1920s,
the driving force for growth of vapor “nuclei” is
supplied by the difference in chemical potential
between the superheated liquid outside the bubble
and the vapor inside, and it is necessary to overcome
the surface tension separating the vapor from the
liquid. Because the chemical potential difference that
drives bubble growth scales with the bubble volume
(i.e., r3) while surface tension scales with the bubble
surface area (i.e., r2), small vapor nuclei that form
due to thermodynamic fluctuations spontaneously
collapse, while larger vapor nuclei will grow. The
Gibbs free energy, G, that describes the thermody-
namics of bubble formation is given by
where µvand µlare the chemical potentials of the
vapor and liquid states, respectively, ris the size of
the vapor nuclei, and σis the surface tension of the
surrounding liquid.160,175 Nuclei grow only if they are
larger than a critical radius, rcr, such that the
chemical potential difference exceeds the barrier
posed by surface tension.160 An increase in the
superheat temperature increases the chemical po-
tential difference between the superheated liquid and
the vapor inside the bubble and results in a reduction
in the critical embryo size that can spontaneously
grow. Note that for bubble nucleation, the intrinsic
stability of the superheated liquid phase is not at
issue; instead, it is the difference in chemical poten-
tial of the superheated liquid relative to the vapor
that drives the growth of vapor nuclei. This is
illustrated in Figure 14, where the variation of the
Figure 14. Schematic of the Gibbs free energy vs bubble
radius required for the formation of a vapor inclusion
coexisting with a superheated liquid phase for various
superheat temperatures. The maximum of these curves is
the critical Gibbs free energy, Gcr, and represents the
energy barrier that impedes vapor bubble growth. The
critical bubble radius, rcr, is the bubble size corresponding
to the critical Gibbs free energy. Note that both Gcr and
rcr decrease with increasing superheat temperature.
G)4πr3
3(µv-µl)+4πr2σ(9)
Pulsed Laser Ablation of Biological Tissues Chemical Reviews, 2003, Vol. 103, No. 2 593
Gibbs free energy required for the formation of vapor
nuclei with a given size within water is shown for
different superheat temperatures. Vapor nuclei
smaller than the size corresponding to the peak Gibbs
free energy in these curves are called “embryos” and
will spontaneously collapse because their growth is
not favored energetically. However, vapor nuclei with
size rcr (or larger), corresponding to the maximum (or
critical) Gibbs free energy, Gcr, are called bubbles
and will grow spontaneously. Figure 15 shows the
dependence of this critical Gibbs free energy and
critical radius on superheat temperature for water.
Note that although both Gcr and rcr become very
small for large superheat temperatures, they remain
finite even at the spinodal temperature, and thus
nucleation remains an activated process with a finite
free energy barrier.158 The strong reduction of Gcr
and rcr results in a dramatic rise in the nucleation
rate, J, with the superheat temperature that attains
a large, but finite, value at the spinodal temperature,
as shown in Figure 16. The energy barrier that must
be overcome for the conversion from the liquid to the
vapor phase disappears only when surface tension
disappears, and this occurs at the critical point.
At first glance, these results appear to be at odds
with the expectation that the phase transition must
occur once spinodal conditions are reached. However,
we must recall that classical nucleation theory is not
a general formalism that includes spinodal decom-
position as a possible mechanism for phase separa-
tion. The first general formalism for phase separa-
tion, the van der Waals-Cahn-Hilliard theory of
inhomogeneous fluids, was developed later in the
1950s. Using the theory of interfaces, this approach
unifies the thermodynamics and kinetics of bubble
nucleation and growth with those of spinodal decom-
position and sharply distinguishes metastable states
(from which phase separation occurs by the activated
process of nucleation and growth) from unstable
states (from which phase separation occurs sponta-
neously by spinodal decomposition). The analysis
shows from first principles that the “expense” of free
energy involved in the formation of a critical vapor
“bubble” vanishes at the spinodal rather than at the
critical point. It also provides a framework to describe
the kinetics of the phase explosion once the spinodal
is reached.158
Theoretical estimates for the spinodal temperature
of water at atmospheric pressure are in the range
Tsp )305 °C.160 When heating is done on time scales
of several seconds to minutes, the superheat limit of
water at ambient pressure has been measured as T
)279.5 °C,181 while for heating conditions on the
microsecond time scale, superheat temperatures in
excess of 300 °C have been reported.182 Taking Tsp )
305 °C and considering the strong temperature
dependence of the specific heat capacity of super-
heated water,160,183 one can determine that the volu-
metric energy density necessary to heat water from
room temperature to the spinodal limit is 1.27 kJ/g,
which comprises only 49.6% of the sum of the sensible
and latent heat of vaporization for water. Thus, in
cases where the phase explosion produces tissue
fracture and material removal, less than half of the
superheated liquid is transformed to saturated vapor,
and the remaining saturated liquid is ejected in the
form of liquid droplets.
Upon examination of Figure 11, one can infer that
the spinodal limit can be reached through either a
rapid increase in temperature or a rapid reduction
Figure 15. (a) Variation of the critical Gibbs free energy
necessary for vapor bubble growth with superheat tem-
perature. Note that the critical Gibbs free energy goes to
zero at the critical temperature. (b) Variation of the critical
bubble radius required for spontaneous vapor bubble
growth with superheat temperature. Note that the critical
bubble radius goes to zero at the critical temperature.
Figure 16. Variation of vapor bubble nucleation rate with
superheat temperature.
594 Chemical Reviews, 2003, Vol. 103, No. 2 Vogel and Venugopalan
in pressure. The latter path is significant when
considering the effect of tensile thermoelastic stresses
on the ablation process (section V.G). In this context,
it is important to know the tensile strength of water
at room temperature, as this defines the onset of a
tensile-stress-induced phase explosion. The tensile
strength of macroscopic samples of water has been
measured to be -27.7 MPa at 10 °C,184 while more
recent measurements using microscopic samples of
ultrapure water have been successful in obtaining
metastable liquid water at pressures up to -140 MPa
at room temperature.185,186 Theoretical considerations
of the equation of state for water yield predictions
for the spinodal limit of room-temperature water in
the range from -110 to -200 MPa,186-188 while
classical nucleation theory and molecular dynamics
approaches predict fracture limits of -140 and -27
MPa, respectively.186,189
Thus far, we have focused on processes tracing a
path indicated by 1 f2f3f4f5or5in Figure
11. This path corresponds to the extreme case in
which no vapor nuclei are present in the liquid, or
the heating occurs extremely rapidly. There are,
however, instances in which heter