Diverse forms of pulmonary hypertension remodel the arterial tree to a highshear phenotype
Roblee P. Allen,1 Edward S. Schelegle,2,3 and Stephen H. Bennett3
1Department of Pulmonary and Critical Care Medicine, University of California Davis Health System, Sacramento,California; 2Department of Anatomy, Physiology and Cell Biology, Veterinary Medicine, University of California, Davis,California; 3Respiratory Disease Unit, California National Primate Center, University of California, Davis, California
Submitted 4 March 2014; accepted in final form 17 May 2014
Allen RP, Schelegle ES, Bennett SH. Diverse forms of pulmonaryhypertension remodel the arterial tree to a high shear phenotype. AmJ Physiol Heart Circ Physiol 307: H405–H417, 2014. First publishedMay 23, 2014; doi:10.1152/ajpheart.00144.2014.—Pulmonary hyper-tension (PH) is associated with progressive changes in arterial net-work complexity. An allometric model is derived that integratesdiameter branching complexity between pulmonary arterioles of gen-eration n and the main pulmonary artery (MPA) via a power-lawexponent (X) in dn � dMPA2�n/X and the arterial area ratio � � 21–2/X.Our hypothesis is that diverse forms of PH demonstrate early decre-ments in X independent of etiology and pathogenesis, which alters thearteriolar shear stress load from a low-shear stress (X � 2, � � 1) toa high-shear stress phenotype (X � 2, � � 1). Model assessment wasaccomplished by comparing theoretical predictions to retrospectivemorphometric and hemodynamic measurements made available froma total of 221 PH-free and PH subjects diagnosed with diverse forms(World Health Organization; WHO groups I-IV) of PH: mitral steno-sis, congenital heart disease, chronic obstructive pulmonary lungdisease, chronic thromboembolism, idiopathic pulmonary arterial hy-pertension (IPAH), familial (FPAH), collagen vascular disease, andmethamphetamine exposure. X was calculated from pulmonary arterypressure (PPA), cardiac output (Q) and body weight (M), utilizing anallometric power-law prediction of X relative to a PH-free state.Comparisons of X between PAH-free and PAH subjects indicates acharacteristic reduction in area that elevates arteriolar shear stress,which may contribute to mechanisms of endothelial dysfunction andinjury before clinically defined thresholds of pulmonary vascularresistance and PH. We conclude that the evaluation of X may be of usein identifying reversible and irreversible phases of PH in the earlycourse of the disease process.
allometry; complexity; pulmonary hypertension
PULMONARY HYPERTENSION (PH) is a “silent-killer” that can leadto irreversible changes in pulmonary vascular structure andfunction, increasing pulmonary vascular resistance (PVR),right ventricular failure, and death (30). The diagnosis ofpulmonary arterial hypertension (PAH) is often difficult andconfounded by clinical entities that also may express elevationof pulmonary artery pressure as part of their clinical pheno-type. Much interest has focused on a World Health Organiza-tion (WHO)-developed nomenclature system that differentiatesPH etiology into five clinical groups. This classification doeslittle to elucidate PH etiology and pathogenesis because themultiple mechanisms and diverse triggers that exist (30). It hasbeen suggested that our continued lack of understanding of theearly stages of PH may be perpetuated by limitations inherent
in utilizing a reductionist approach to define a complex syn-drome based on end-stage pathological observations of arteri-olar vessel remodeling (5). Alternatively, for the purpose ofearly detection, treatment, and prevention, it may be beneficialto interpret the pulmonary arterial circulation globally as acomplex adaptive system to identify a vascular branchingphenotype evident in the early phases of the PH process that is,not only independent of inciting mechanism, but also suscep-tible to multiple triggers.
In the early 1900s, Richard Thoma theorized that patholog-ical processes in organ systems produce characteristic changesin branching network complexity to maintain a hemodynamic-metabolic steady state that insures the appropriate blood flowfor a given metabolic demand (44, 45). This hemodynamic-metabolic steady state is determined by the interaction betweenthe mechanical power of the heart used to perfuse the organsystem and the metabolic demands of the organ system. Themechanical power of the heart in this case is defined as theproduct of the fraction of cardiac output through the organsystem and its perfusion pressure. The minimum hemodynamicpower needed to meet the metabolic demand is adjusted byneural, humoral, and local mechanisms acting at precapillaryarterioles. Consequently, organ-system flow in health and dis-ease is distributed and adjusted via adaptations in arterial andcapillary perfusion area. The same steady-state principles canbe applied to the pulmonary circulation after birth, which is alow-pressure system that receives 100% of cardiac output.However, at rest, only a fraction of the pulmonary capillariesare recruited, and the pulmonary arterial vasculature cross-sectional area is considered to be nearly maximally vasodi-lated. In the case of maximal aerobic exercise, additionalcapillaries are recruited to meet increased gas exchange to meetmetabolic demand. Moreover, because greater than 50% vas-cular obstruction is required for a healthy lung to produce anincrease in pulmonary arterial pressure at rest (4), pulmonaryarterial cross-sectional area adjustments to cardiac output dem-onstrate a reserve that acts to limit both arterial and capillarypressures. Thoma deduced that physiological dysfunction anddisease introduce disturbing factors that chronically reduce thevascular cross-sectional area reserve to blood flow. Thesefactors include a disruption of the regulatory aspects of arterialtone and the integrity of the vascular wall by altering itsfunction and muscle thickness, which, not only encroaches onvessel cross-sectional area, but also disrupts diameter networkcomplexity by reducing the area ratio between parent anddaughter vessels. He advanced two basic hypotheses: 1) underapparent steady-state conditions, pathological processes inmammalian organ systems demonstrate the emergence of acommon phenotype of increasing network disorder between
Address for reprint requests and other correspondence: S. H. Bennett,One Shields Ave., Univ. of California, Davis, CA 95616 (e-mail: [email protected]).
Am J Physiol Heart Circ Physiol 307: H405–H417, 2014.First published May 23, 2014; doi:10.1152/ajpheart.00144.2014.
arteriolar vessels evident as a branching area reduction thatevolves toward an eventual state of daughter-vessel oblitera-tion, independent of etiology or pathogenesis; 2) the organ-system phenotype in disease is evident as a negative decreasein arterial diameter power-law slope or area ratio reduction bymorphometry and manifested via hemodynamics as a reductionin allometric scaling exponents reflecting a relationship be-tween an arterial network diameter power law and organ bloodflow or body weight. Although Thoma’s allometric theory wasnever developed or implemented in a systematic fashion, hisframework remains instrumental to the understanding of PH asa silent disease in its early phase because it predicts a commonemerging pathological pattern of network disorganization iden-tifiable by hemodynamic and/or morphometric means via sim-ilarity and power-law scaling relationships coupled to steadystates of hemodynamic-metabolic function (10).
Our hypothesis is that PH of WHO groups I-IV are charac-terized by alterations in arterial branching complexity along acharacteristic hemodynamic and morphometric trajectory,from a non-PH state characterized by low arteriolar shear stressto a PH state characterized by pathologically high shear stress.Our objective was to develop an approach for the early detec-tion of PH and the evaluation of PH progression by applyingThoma’s hypotheses of changing arterial branching complexityin disease. Using an allometric model of PH progression, wederived a power-law scaling exponent that encompasses pul-monary arterial cross-sectional area reduction and length prun-ing. When applied to retrospective hemodynamic and morpho-metric data, our model delineates early, mid, and late epochs ofPH progression. Although this approach purposely does notaddress mechanisms, we demonstrated that the most aggressiveepoch is evident early, well before clinically defined thresholdsof PH and PAH are reached, and therefore may be instrumentalin helping to identify underlying mechanisms and their inter-ventions.
MATERIALS AND METHODS
Methods summary. We formulate a predictive theoretical model(see Model) based on Thoma’s descriptive principles and hypothesesof physiological and pathological adaptation (44, 45). His principlesrepresent empirical scaling relationships, summarized as laws be-tween vessel and organ blood flow and bifurcation and vascularnetwork diameter morphology in relation to body weight (45)(Table 1). Thoma’s schema can be consolidated into a simple allo-metric power-law model of disease progression that is theoreticallyindependent of etiology, pathogenesis and species (Table 2, see Eq. 14and Model) when arterial network resistance and volume are ex-pressed in terms of diameter/length power laws (22) subject to asteady-state minimum work-rate principle (Eqs. 4–6) (Table 2 andEqs. 7–17). In this study, we use retrospective hemodynamic mea-surements to express function in terms of power �PQ-MPA, as theproduct of mean pulmonary artery pressure (PPA), and cardiac output(Q), in an allometric expression with body weight to evaluate thepower law exponent X by a simple inverse data model for the purposeof delineating the trajectory of X relative to hemodynamic steady-stateepochs during PH progression (Fig. 1) (3), where MPA is the mainpulmonary artery. We extend the data model to predict the shear-stressload in the main pulmonary artery and its amplification on terminalarterioles during PH progression for the reason that area reductionimposes increased hemodynamic stress (23), whose redistribution offorces may early on redirect metabolic pathways for proliferationand/or inflammation in a positive-feedback fashion (16, 41). We nextobtained corroborative structural evidence of X and � reduction
during PH progression by modifying a retrospective diameter power-law morphometric/stereological analysis of human tissue (Fig. 1) (16,34, 40). Last, the utility of assessing PH progression phases withinsubjects over time with superimposed clinical and experimental treat-ments is evaluated by a simple statistical approach derived from asubset of the hemodynamic data.
Model. Our proposed allometric model of PH progression centerson Thoma’s empirical diameter power-law for organ systems (Table1), where a monotonic decrease in Xd earmarks steady-state phases ofdisease progression along with the degree of arterial area reduction.Our model depends on a disease-free reference state that relies oninterspecies similarity and scaling relationships to predict commonconditions for pressure, flow, hemodynamic-metabolic steady state,and arterial-capillary network organization as a function of bodyweight (8–10) (Table 2). Here, the body-mass allometry exponents (a)represent theoretical approximations to empirically derived ones forpulmonary capillaries, arterioles, and main pulmonary artery derivedby Dawson (8–10) utilizing similarity principles for the relationshipbetween blood volume, diameter, and length in conjunction with bodydimensions, which are subject to nonuniform scaling to achievemaximum physiological vascular pressures independent of bodyweight mass.
The model delineates PH progression as a paradoxical form ofhemodynamic afterload reduction constrained to a minimum-power arterial network configuration advancing via steady-stateenergy-rate decrements in Xd and Xl from their reference condi-tions, X � Xd � X � 2.25. The steady states for capillaries (c) andthe MPA comprise:
IC � �PQ�c ⁄ �0z� M0 (1)
IMPA � �PQ�MPA ⁄ �02� M0 (2)
as defined in Table 1. PH progression is modeled by phases of Xreduction according to
�PQ�MPA�obs
�PQ�MPA�ref� 1 (3)
where early phases of PH correspond to the ratio approximately equalto 1.0. Equation 1 is assumed to be time invariant within an individualand hold within and between species (8–10). Alternatively, laterphases of PH may demonstrate observed energy rates greater than thereference for Eq. 2 but maintain a minimum-dissipation configurationwhile maintaining Eq. 1. The minimum-power dissipation conditionreflects Murray’s law (32), implemented in an alternative manner bydetermining the network value of X between the MPA and arteriolesof generation n that minimizes the energetic metabolic rate associatedwithin arterial volume Vn:
Q � km�dMPA
2 �xMPA
2n�1�3X�1�⁄2 ���MPA
Rn(4)
where
km � ��m ⁄ �8�� (5)
m � �MPA ⁄ Vn � �O2⁄ Vn (6)
Here, � denotes blood viscosity, considered independent of species(10). The constant m reflects an interspecies, intraspecies time-invari-ant steady state of energetic rates between the metabolic rate andhemodynamic power delivered to an organ system. The ratio betweenthem (IMPA � �PQ-MPA/�O2) is known as Li’s ratio (Table 1) (28) andrepresents a size-scale invariant hemodynamic-metabolic steady statebetween species. Rn is the resistance of a hemodynamic-equivalent
H406 BRANCHING COMPLEXITY IN PULMONARY HYPERTENSION
arterial bifurcating network (22) with n generations possessing diam-eter and length power laws with exponents X � Xd � Xl:
Rn � RMPA
2n�3X�1�1� � 1
2�3X�1�1� � 1(7)
where RMPA is the main pulmonary artery resistance
RMPA �8�lMPA
��dMPA ⁄ 2�4 (8)
based on Poiseuille’s relationship where lMPA is the length of theMPA and dMPA is the entrance diameter of the MPA. The correspond-ing arterial volume is given by:
Table 1. Thoma’s laws of diseasePower-Law Exponent/Area Ratio Trends
Steady-state Law (citation) [pages] Physiological Reference State ¡ Disease Progression
Concept: a disease process over time is metabolically and hemodynamically “silent” in a steady state while vascular structure-function relationshipcomplexity is progressively altered in a common direction of increasing dissipation disorder Thoma envisioned complexity change via unified scalingrelationships/laws using the premise of hemodynamic-equivalent flows coupled to morphometric-equivalent networks: i.e., the same principles apply tocascading levels of branching (vessel, bifurcation, organ system), regardless of whether or not steady-state flow is “heteronomous,” coupled toheterogeneous/asymmetric diameters, or “homonomous” in a symmetric network. His translational disease concept predicts that unspecified metabolichemodynamic work increases network complexty/disorder, by mechanisms unknown, but the process is empirically observable via xM, or xQ, coupled toan unknown relationship with arterial network complexity index Xd (x � f(Xd). �, Bifurcation or network area ratio; d, vascular diameter; dP, bifurcationor network parent diameter; d1, bifurcation major diameter; d2, bifurcation minor diameter; dn, average diameter of arterial generation, or order, n; �,daughter asymmetry ratio (d2/d1) of bifurcation or arterial network; M, body weight; Morgan, organ weight; P, arterial pressure; Q, blood flow; �PQ,hemodynamic power as product PQ; �O2, metabolic rate; Qp, entrance flow of bifurcation or organ; Q1, bifurcation major diameter flow; Q2, bifurcationminor diameter flow; Rb, branching ratio of a bifurcation n � 1, or arterial network (n � 1) that is symmetric with n generations when Rb � 2, orasymmetric with order n if Rb � 2; x, vascular diameter exponent; Xd, vascular network diameter exponent; xQ, entrance diameter blood-flow exponent;xM, entrance diameter-mass exponent for organ, or body weight.
H407BRANCHING COMPLEXITY IN PULMONARY HYPERTENSION
Under Thoma’s schema, PH progression constitutes a disease ofarterial network complexity that increases dissipation disorder via diam-eter and length pruning under apparent steady-state metabolic-hemody-namic conditions. Our assumed tree-pruning process (X decrements asvia X � Xd � Xl) represents one of many possible construed signaturecombinations of diameter and length, which impact arterial networkcomplexity via a hemodynamic-morphometric scaling condition Q �PQ
xP , analogous to Thoma’s law Q dx (45). Here, xP for a vessel, or Xp
for an organ, represents a monotonic index of dissipation intensity due toincreasing network disorder as Xl and Xd, regress from their controlvalues. The functional consequences in a network are:
XP � 1 ⁄ �2 �1 ⁄ Xl� � �4 ⁄ Xd�� (11)
(Fig. 1). Although morphometric details of the pruning process are notclear (Fig. 1), this relationship and its graphic interpretation indicatesthat when Xl and Xd change, the state of power-dissipation disorder XP
associated with flow either decreases or increases relative to thereference state XP-ref � 1.5. Exercise in the disease-free state resultsin adaptation to a state of less disorder (Xp-exercise � 1.37) accom-plished by increasing Xd � 2.33 from Xdref � 2.25 while Xl � 2.25remains constant. Paradoxical to exercise adaptation, PH progres-sion by pruning increases dissipation intensity/disorder XP by
Table 2. Thoma’s consolidated scaling laws of disease adaptation
Physiological Reference State
Stationary Allometric Relationships
Consolidating Relationships
y Ma Allometry Exponents
Function Symbol yExponent a
Rest Peak Exercise
A. Pressure (mmHg) P 0 01. Entrance, Main Pulmonary Artery (MPA) PMPA 0 02. Arterioles, (art) Part 0 03. Capillaries, (cap) Pcap 0 0
B. Cardiac Output (ml/min) Q 3/4 7/8C. Energy Rates (Watts) � 3/4 7/81. Entrance PQ, MPA �PQ�MPA � PPA · Q �PQ 3/4 7/82. Capillary PQ, cap �PQ�cap � Pcap · Q �cap 3/4 7/83. Metabolic rate: oxygen consumption �o2 3/4 7/84. Li’s ratio (28)-left ventricle: IA � �A/�o2 IA 0 05. Li’s ratio (Table 4)-right ventricle: IMPA � �MPA/�o2 IMPA 0 0
Structure
D. Network organization1. Diameter MPA dMPA 3/8 3/82. Diameter cap dcap 1/12 1/123. Length MPA lMPA 1/4 1/44. Length cap lcap 5/24 5/245. Number-arterioles (art) Nart 3/4 3/46. Number-capillaries (cap) Ncap 3/4 7/87. 1Cap:MPA diameter:Number ratio @ Max Pc ratioc � Nc
2⁄3dc2⁄3⁄dMPA
2⁄3 ratioc 1/3 1/3
8. 1Art:MPA diameter:Number ratio @ Max Part ratioart � Nart2⁄3dart
2⁄3⁄dMPA2⁄3 ratioart 1/3 1/3
Network Power-law ExponentsNetwork Adaptations to Exercise Symbol Rest a�o2 � 3/4 Exercise a�o2 � 7/8
Concept: allometric scaling laws (8–10), coupled to principle of minimum work rate for arterial network organization (Eq. 4–6), provide a quantitativeframework for consolidating Thoma’s laws for hemodynamic analysis relative to a common reference state. 1Dawson’s network constraint for maximumphysiological pressure. a, Allometric law exponent based upon body weight; I, ratio of hemodyamic power to metabolic rate; l, vessel length; N, vessel numberat generation or order n.
H408 BRANCHING COMPLEXITY IN PULMONARY HYPERTENSION
Fig. 1. Predictive model validation via forward-inverse modeling of diameter/length-power laws. By observation, pulmonary hypertension (PH) disease reduces diameterexponents and area ratios and also prunes their effective lengths, at the level of bifurcations, and as a population within in subtrees and the arterial tree as a whole (6, 14, 36).Thoma’s schema of maladaptive morphometric changes in branching complexity via metabolic-hemodynamic steady states leads to a simple predictive and integrativediameter/length power-law model of PH disease progression on the basis of phenotypic changes in arterial branching complexity that is, in principle, identifiable and validatedby forward (morphometric) and inverse (hemodynamic) power-law data models (3). The basic element of topological organization common to the power laws are bifurcations.As the sources of information about structure and function are disparate, forward and inverse models purposely utilize limited available information at the level of bifurcationswithin their respective approaches, to ultimately lead to a common integrated diameter power-law relationship (arterial tree). For example, the forward-morphometric model (seeRef. 16) represents an asymmetric nonuniform model morphometric tree of a PH-free and PH state when viewed at all levels of organization. However, although themorphometric distribution is nonuniform and contains more detailed information, it possesses an average value consistent with the slope of the diameter power law, which changesin a direction of area reduction for the entire arterial tree in the course of PH progression. Conversely, the inverse hemodynamic model is devoid of morphometric informationentirely. It is alternatively formulated on the basis of diameter/length adaptations subject to a principle of least work rate. The premise of xd � xl delineates an energeticrate-favorable trajectory of maladaptation for both diameter and length pruning at the level of bifurcations, bifurcation distribution, and for the arterial tree as a whole that iscoincident with Thoma’s hypothesis of disease progression and the forward model. PAH, pulmonary arterial hypertension.
H409BRANCHING COMPLEXITY IN PULMONARY HYPERTENSION
degrees depending on the interrelationship between Xd and Xl.Notably, the symmetric XP:Xd bifurcation relationship of Fig. 1illustrates that, if Xl � 2.25 remains fixed at its reference value andXd takes a progressive PH trajectory of Xd � 2.25, then greaterdissipation intensities and states of disorder for XP are experiencedin its trajectory than compared with Xd � Xl decreasing concur-rently. As the pulmonary circulation is a transducer and translatorof hemodynamic force, the extra intensity reflects additional workdelivered to remodel network complexity in a direction favorableto the organ system and organism. This suggests that the paradoxicalmaladaptive strategy associated with arterial diameter/length pruningduring PH progression represents a trade-off balancing arterial afterloadreduction to maintain metabolic-hemodynamic homeostasis (Eq. 2) andincreasing arterial dissipation to limit maximum capillary pressures fromedema formation (Eq. 1) (8–10).
Thoma proposed that the steady-state blood flow delivered to anorgan system is related to entrance diameter Q dxQ where, in turn,diameter is metabolically related to organ mass d M1/XM (45).Intended to be empirical, the entrance exponents xQ and xM becometheoretically related to the arterial network organization, X, if eachphase of reduction in X � Xl � Xd associated with the pruningprocess is subject to the minimum work condition (Eqs. 4 – 6,Table 2-Eq. 14):
xM � 4 ⁄ �2aQ � 2a�o2 3a�o2
X�1 1
4� (12)
For Thoma’s diameter-flow relationship the scaling exponent xQ is
xQ � a�o2XMPA (13)
Here, the metabolic/hemodynamic steady state of a�O2 � 3/4 andaQ � 7/8 represents an upper pressure-flow scaling limit independentof body weight that entails reference scaling laws in Table 1. Underthese circumstances, X represents an arterial tree phenotype of thestate of dissipation intensity and network complexity, predicting aunique trajectory of increasing disorder during PH progression undermetabolic-hemodynamic steady-state conditions, independent of time,etiology, pathogenesis, individual, or species.
An adverse positive-feedback effect of PH progression is associ-ated with increasing network disorder (X � 2, � � 1 ¡X � 2, � �1), which acts to progressively amplify shear stress on arterioles tountoward levels (16)
�n � �MPA2n�3X�1�1� (14)
where
�MPA �4�Q
��dP ⁄ 2�3 (15)
Hemodynamic measurements: X was calculated using the ratio
�MPA�obs
�MPA�ref�
Qobs2
Qref2
Robs
Rref�
Qobs2
Qref2
dMPA ref4
dMPA obs4
Gobs
Gref� (�Q)�2(�d)�4�g
(16)
which is based on Eq. 3, expressing it in terms of cardiac output, MPAdiameter, and resistance-gain observed/reference ratios Q, d, g, re-spectively. Observed values for �MPA-obs and Qobs
2 were taken fromretrospective clinical measurements of pulmonary pressure PPA inmmHg, cardiac output Q in ml/min, and body weight M (kg) made inPH-free and PH subjects, assumed to be in a steady state of energeticrates. The observed diameter was calculated on the basis of a pressure-distensibility relationship:
where dMPA-ref is based on the human growth estimates made bySluysmans and Colan (39) for the entrance to the pulmonary circulation.
The reference arterial distensibility, �ref � 0.02 mmHg�1 in the PH-freestate, was considered a constant that is independent of mammalianspecies and animal size (21), whereas PPA ref � 8 mmHg. The gainfunctions Gobs and Gref are derived from the resistance state dictated bythe condition of arterial network organization X � Xd � Xl
Gobs �2n�3X�1�1��1
2�3X�1�1��1(18)
Gref �2n�3⁄2.25�1� � 1
2�3⁄2.25�1� � 1� 306.38n�19 (19)
Here, X is an unknown associated with Gobs, whereas X � 2.25 isfor Gref. The number of generations, n, was evaluated from themorphometric data of Reeves and Noonan (34) (see Morphometric/stereological measurements).
X was calculated by rearranging Eq. 16 on the basis of observed/allometric ratios according to
219�3X�1�1� � 1
2�3X�1�1� � 1� Gref
�PQ obs
�PQ ref� Qref
Qobs�2�dMPA est
dMPA ref�4
� 306.38��(�Q)�2(�d)�4 (20)
and then solving for X by recursive iteration. Given X, the area ratiowas evaluated according to � � 21–2/X, and the shear stress in theMPA and amplification load on generation n � 19 arterioles wascalculated via Eqs. 14 and 15, respectively, based on the Qobs. Ineffect, a subject’s profile values for X, �, Q, and d, define anafterload-hemodynamic disease signature of the scaling distance froma hypertension-free reference state of (X � 2.25, � � 1.08, � � Q � d � g � 1).
Morphometric/stereological measurements. The number of gener-ations (n � 19) in Eq. 20 was evaluated from the PH-free controls ofReeves and Noonan (34), which measured internal diameters down to0.005 cm, along with a morphometric estimate of Xd in humanPAH-free subjects and those diagnosed with idiopathic PAH. Theirapproach measured the vessel number-diameter volume density Nv ofarterial diameters in two ranges (0.005–0.030 cm and 0.070–0.300cm). However, due to the nonrandom manner in which Reeves andNolan sampled thick lung sections, their estimates of NV density arebiased, and their number estimates based on Nv lead to nonsensicalvalues for Xd (11). Alternatively, we substituted the ratio, NA
small/NAlarge �
NVsmall/NV
large, where NA � d�NV, which represents a size, shape, anddistribution-free correction (11),
Xd logd�
smallNVsmall ⁄ d
�largeNV
large� ⁄ logd�
large ⁄ d�
small� (21)
Using this correction the values of dsmall, dlarge, NVlarge, and NV
small, weevaluated directly from Fig. 6 of Reeves and Noonan(34) and includethree PH-free and three PH subjects.
Patients. Hemodynamic data of several patients with diagnoses ofPH from WHO groups I-IV were considered from previously pub-lished data (Table 3), with additional data kindly supplied by inves-tigators (25–27, 35, 43), which included pulmonary artery pressurePPA, cardiac output Q, and body mass M, or body surface area (BSA).The study of Lucas and coworkers (29) additionally supplied corre-sponding values of oxygen consumption that was used to evaluate thehemodynamic-metabolic ratio IMPA (Table 4).
In the case of reports reporting only BSA, body mass M wasapproximated by the Meeh formula M � 10·BSA3/2. The groupsincluded controls free of PH (C); mitral stenosis (MS WHO group II);chronic obstructive pulmonary disease (COPD WHO group III);chronic thromboembolism (CTEPH WHO group IV); and congenital(CHD-PAH), idiopathic (IPAH), familial (FPAH), collagen vasculardisease (CVD-PAH), and methamphetamine exposure (METH-PAH)(all from WHO group I).
H410 BRANCHING COMPLEXITY IN PULMONARY HYPERTENSION
Statistical analysis. For between-subjects analysis, ANOVA wasused to evaluate trends of PH progression on the basis of averagedecrements in X in relationship to afterload and hemodynamic state,where only one hemodynamic sample was available. Values of X wereranked and stratified from largest to smallest value irrespective ofdiagnosis on the basis of 12 incremental phases of PH progression(Table 5). ANOVA was then performed with phases as categories forvariables X and � under the hypothesis that they are theoretically fixedand independent of hemodynamic conditions (16). If significant,multiple comparisons were then made by repeated t-tests at P � 0.05significance using a Bonferroni correction for the number of compar-isons (17). The subsequent phase for each subject was then used forother variables as a means of profiling the afterload and hemodynamicstate during progressive phases of PH branching complexity. Thepulmonary afterload variables considered were X, the d, along withthe external work-rate power ratio for the right ventricle, �. Thehemodynamic data analyzed included pulmonary artery pressure (PPA
in mmHg), the flow ratio Q, and the shear stress in the MPA �MPA
(Eq. 14), along with its amplification factor in generation n � 19arterioles as �n (Eq. 15).
For within-subjects analysis, ANCOVA was used to comparetemporal changes in phases from retrospective data of PH treatmentswithin individuals obtained from the FREEDOM-C trial (43). TheFREEDOM-C trial involved subjects with continuing treatments ofendothelin-1 receptor antagonist and/or phosphodiesterase type 5inhibitor, which were also unresponsive to previous treatments of PH.They were subsequently randomly assigned to treatment groups, givena daily dose of either a placebo or treatment (oral Trepostinil), andrestudied 16 wk later. X before and after the study was calculatedaccording to Eq. 20, and the values were categorized according tophase (Table 5). The difference in phase within a subject over thestudy period was calculated as Phase/16wk � Phase after � Phase
before. The change in phase for the study groups (placebo vs.treatment) was evaluated in conjunction with ANCOVA with refer-ence to the baseline state variable (Var � X) that was adjusted forunspecified within-subject adaptations, categorized as either beingworse defined by a phase increase Phase/16wk � 0, or designatedbetter as defined by a phase decrease Phase/16wk 0. The origins ofthe adaptations were not specified and were assumed either due tochance, previous treatments, the treatment itself, or an uncon-trolled progression not responding to concurrent therapy. Theoverall prediction expression in terms of intercept b, slope m, anddummy variables is:
�Phase
16wk� b m (22)
b � b0 �bGIG �bAIA �bAGIAG (23)
m � m0Var �mGIG�Var � cG� �mAIA�Var � cgA� (24)
where the dummy variables for the group (G), adaptations (A) andtheir interaction (AG) are defined as
IG �
�1 Treatment
1 Placebo
0 Else
(25)
IA � ��1 better � �Phase ⁄ 16wk 0
1 worse � �Phase ⁄ 16wk � 0
0 Else
(26)
IAG � IAIG (27)
If the overall covariance relationship was significant, then the adjustedtreatment slope was tested for significance �mG � 0 as evidence of atreatment-placebo trend that was dependent on the magnitude of X.
Reported results were summarized by their mean values and 95%confidence intervals, unless otherwise noted. Statistical analyses wereperformed using SAS Jump version 10 (Cary, NC).
RESULTS
X-model morphometry. The values of Xd evaluated in sixcases from Reeves and Noonan (34) include the following:
Table 3. Hemodynamic data sources (PPA, Q, M)
PH-Condition/Diagnosis WHO Group N Source
Control 44 (29)10 (25)10 (27)
CTEPH IV 10 (25)10 (26)
CG I 7 (25)2 (42)
COPD III 7 (25)CVD I 9 (43)FPAH I 6 (25)IPAH I 31 (26)
9 (25)18 (43)8 (26)
METH I 5 (43)MS II 35 (35)
Concurrent hemodynamic and metabolic measurements available from ref-erences to calculate �O2 and IMPA for Table 4. PH, pulmonary hypertension;CTEPH, chronic thromboembolism; CG, congenital; COPD, chronic obstruc-tive pulmonary disease; CVD, collagen vascular disease; FPAH, familialpulmonary arterial hypertension; IPAH, idiopathic pulmonary arterial hyper-tension; METH, methamphetamine exposure; MS, mitral stenosis.
Table 4. Empirical allometry for human reference state
Table 5. Phase categorizations of PH progression via X
Phase X Range
1 2.25 X 3.002 2.0 X �2.253 1.95 X �2.04 1.90 X �1.955 1.85 X �1.906 1.80 X �1.857 1.75 X �1.808 1.725 X �1.759 1.70 X �1.72510 1.675 X �1.7011 1.65 X �1.67512 1.50 X �1.65
H411BRANCHING COMPLEXITY IN PULMONARY HYPERTENSION
case 1, control (male, 10 mo old) Xd � 2.12; case 2, control(female, 52 yr old) Xd � 2.18; case 3, control (male, 32 yr old)Xd � 2.13; case 4, PH-congenital defects (female, 11 mo old)Xd � 1.65; case 5, PH-IPAH (female, 29 yr old) Xd � 1.58;case 6, PH-CTEPH (female, 18 yr old) Xd � 1.87. Additionalmorphometric data include Horsfield and Woldenberg (19)estimate of a PH-free control derived from three sources Xd �2.3. For vessel lengths in PH disease, Moledina and coworkers(31) evaluated Xl within WHO functional classes I-IV asfollows: class I, Xl � 1.55; class II, Xl � 1.56; class III, Xl �1.47; class IV, Xl � 1.3; overall average Xl � 1.46. Themorphometric-derived values X � 1.55 are plotted as whiteboxes in Fig. 2.
The number of generations for the bifurcating tree model inEq. 20 was calculated as n � 19, evaluated according to n �Xdlog(dMPA/0.005)/log(2). Here, Xd � 2.14 represents the av-erage of the three case values of the Reeves-Noonan controls.The MPA diameter was assigned dMPA � 2.6 cm, drawn froman allometric-derived value for a 75.4-kg adult via (dMPA-ref �0.514M0.375) (39), consistent with the average mass of theadults of this study (75.4 � 14.0 SD, N � 178).
X-model: between subjects. In the afterload shown in Fig. 2,ANOVA for X was significant (X: F � 592, R2 � 0.96, P �0.0001), which demonstrated 12 statistically independentphases of progression. The frequency of diagnosis associatedwith each phase is summarized in Fig. 2E. Morphometricanalyses of the Reeve’s-Noonan data from three control andthree PH subjects demonstrated corresponding phases consis-tent with hemodynamic-derived values of Xd and �.
There were significant changes in afterload with progressivephases in X (Fig. 2, B–D). The diameter ratio (Fig. 2B)demonstrated monotonic increases from the baseline referencestate, except during three epochs where d � constant while Xwas concomitantly decreasing (early: phases 3–4, mid: phases5–6, and late: phases 9–10). The power ratio (Fig. 2C) dem-onstrated three epochs of constant power dissipation while Xwas decreasing significantly, with the greatest decrement ratein X observed early. The respective epochs (early, mid, andlate) demonstrated statistically distinct slopes and intercepts[early: phases 1–4, X � �0.136 � phase 2.43, R � 0.88,95% CI slope (�0.152, �0.119), intercept (2.39, 2.46); mid:phases 5–8, X � �0.047 � phase 2.11, R � 0.96, 95% CIslope (�0.052, �0.04), intercept (2.09, 2.13); late: phases10–12, X � �0.031 � phase 1.99, R � 91, 95% CI slope(�0.034, �0.027), intercept (1.96, 2.03)].
Hemodynamics are shown in Fig. 3. The average � de-creased significantly and progressively from one phase toanother, (Fig. 3A) (�: F � 316, R2 � 0.94, P � .0001), whichdemonstrated 12 statistically independent phases that mono-tonically decreased from one to another. Similar to X, � alsodemonstrated statistically distinct epochs (early, mid, and late),composed of linear trends in slope and intercept during steadystates of constant hemodynamic power (Fig. 3D) as follows:[early epoch: phases 1–4, � � �0.043 � phase 1.14, R �0.89, 95% CI slope (�0.048, �0.039), intercept (1.12, 1.14);mid epoch: phases 5–8, � � �0.0187 � phase 1.04, R �0.96, 95% CI slope (�0.020, �0.017), intercept (1.039,1.056); late epoch: phases 10–12, � � �0.0133 � phase 1.01, R � 90, 95% CI slope (�0.015, �0.011), intercept(0.994, 1.03)]. In general, as area decreased, epochs of constantpressure were observed that subsequently became elevated in
successive phases (Fig. 3B). During the early epoch (phases3–4), the slope of � vs. phase (Fig. 3D) decreases in a constantfashion while pulmonary artery pressure PPA remains constantbetween phases, which is statistically equivalent to the clinicaldefinition of PH [PPA � 25 mmHg, 95% CI (21, 28)]. A midepoch of elevated, but constant, pressure follows [phases 5–6,where PPA � 35 mmHg, 95% CI (32, 39)], is characterized bya different statistically distinct slope of � decrease than theearly epoch, and is coincident with mid epoch power ratio (Fig.
Fig. 2. A–E: afterload responses during PH progression. Points in plotsrepresent phases of progression corresponding to average values � 95% CI.Statistically insignificant differences between adjacent phases are highlightedby shaded boxes. Statistically significant differences between phases are notshaded. A: hemodynamic- and morphometric-derived values of X demonstratemonotonic decrements during steady states of constant energy-rate deliveryduring PH progression independent of diagnosis, confirming Thoma’s predic-tion in humans for PH disease that organ system pathology demonstratesevolving patterns of arterial network complexity. B: d responses in PH, as theexpected main pulmonary artery (MPA) diameter increases during PH pro-gression relative to a reference state (Eqs. 16 and 17). This ratio reflects theMPA afterload adjustment of a hemodynamic-equivalent network that mini-mizes arterial power dissipation. C: � is the energy rate ratio of entrance topulmonary circulation reflecting steady-state metabolic-hemodynamic condi-tions relative to a baseline PH-free state. D: statistical equivalent steady statesof constant energy rate delivery designated by similar shades of gray thatdemonstrate statistically different decrements/stage, early, mid, and late.E: distribution of diagnosis for each stage of disease. C, control; MS, mitralvalve disease; COPD, chronic obstructive pulmonary disease; CTEPH, chronicthromboembolic pulmonary hypertension; IPAH, idiopathic pulmonary hyper-tension; CG, congenital defects; CVD, collagen vascular disease; FPAH,familial PH; METH, methamphetamine PH.
H412 BRANCHING COMPLEXITY IN PULMONARY HYPERTENSION
3C). The late epoch of PH [phases 9–10, PPA � 56 mmHg95% CI (53, 59)] was also associated with concomitant signif-icant decreases in X and � that were significantly different fromthe early and mid epochs. Figure 3C indicates that the progres-sive phases of � are associated with a significant decline incardiac output but is earmarked by a cyclic pattern of alternat-ing epochs of constant flow as follows: a significant decrease,then subsequent increase in the next phase, followed by areduction and sustained average covering more than one phase.This pattern is evident in phases 3–5, 5–7, and 8–12.
The shear stress calculated in the MPA and terminal gener-ation arterioles demonstrates contrasting trends during arearatio regression (Fig. 3, A, D, and E). Significant attenuation in
�-MPA during the early epoch is evident, based on concomi-tant increases in MPA diameter (Fig. 3B) and decreases inrelative cardiac output (Fig. 3C). After phase 4, �-MPA wasnot significantly different between phases. In contrast, progres-sive amplification characterized the state of shear stress ongeneration in 19 terminal arterioles during PH progression(Fig. 3E) in conjunction with phases of area reduction (Fig.3A). The amplitudes in the early epoch (phases 2–4) areassociated with thresholds consistent with endothelial dysfunc-tion, whereas the mid epoch (phases 5–6) is associated withthresholds and levels earmarking the transition from endothe-lial dysfunction to a broad range consistent with endothelialdamage. The late epoch (phases 9–10) coincides with progres-sive decreases in X and � and a maximum peak-power ratio.
X-model. Within subjects, the covariance analysis demon-strated a significant regression (F � 14.8, R2 � 0.76, P �0.0001) along with significantly different trends (t-ratio �6.17, P � 0.0195) between the treatment and placebo groupscharacterized by �phase/16wk � �5.46 3.49X IG [5.56(X � 1.752)].
Figure 4A indicates that the placebo group demonstrated themost aggressive advancement in PH progression at the begin-ning of the study, (phase/16wk � 3) and were identified asthose subjects categorized as being at an earlier phase of thedisease process (X � 2). In contrast, those subjects at advancedphases produced smaller phase increments over time [(phase/16wk) � 0.6 for X � 1.75]. Alternatively, the treatment groupdid not demonstrate a change in phase at X � 2 but crossedover to the same phase as the placebo group at X � 1.75.
DISCUSSION
Our allometric model of pulmonary arterial branching com-plexity offers novel insight into the PH disease process. Unlikethe interpretation of PVR, it utilizes a diameter/length power-law relationship to elucidate a common morphometric-hemo-dynamic phenotype that delineates PH progression in relation-ship to apparent hemodynamic steady-state conditions. Thisstudy demonstrates five important findings: 1) diverse forms ofPH share a common phenotype progression characterized byphases of a monotonic reduction in X (X � 2 ¡ X � 2) andarterial area ratio (� � 1 ¡� � 1) that is independent ofetiology and pathogenesis; 2) three epochs of progression areevident (early, mid, and late), each of which takes place underconcomitant conditions of hemodynamic homeostasis betweenphases (pressure, flow, shear stress, and/or power dissipation);3) the early epoch (phases 1–4 where X � 1.90) demonstratesthe largest magnitude of reduction in X and � under steady-state conditions; 4) arterial area reduction to � � 1 constitutesa pathophysiological positive-feedback process to blood flowin which shear stress in arterioles is incrementally amplified tomagnitudes that may initiate/exacerbate endothelial dysfunc-tion and injury before the onset of PH; 5) Trepostinil interven-tion forestalls progression when administered at earlier phases(X � 1.75) compared with later ones (X � 1.75).
PH progression demonstrates a functional-morphometric af-terload signature composed of advancing phases of X reduction(Fig. 2A) that are associated with early, mid, and late epochs(Fig. 2D). Corresponding values of X and MPA diameter ratio( d) identifies an underlying normalized diameter power lawdn � dMPA2�n/X representing a hemodynamic-equivalent bi-
Fig. 3. A–D: hemodynamic responses during PH progression. Shaded andunshaded boxes follow the same convention as Fig. 2. A: � decreasessignificantly with each stage in several stages before the emergence ofclinically defined pressures (B) for PH ({) and PAH (Œ). C: cardiac outputdemonstrates significant reductions early in progression along with variableshort-term and longer-term steady states with changes in stage. D: attenuatedshear stress in main pulmonary artery. E: amplified shear stress on generationof 19 arterioles. Statistical significant increases to thresholds consistent withendothelial dysfunction occur in first phase and hold a steady state up to phase4, consistent with PAH diagnosis. Later phases demonstrate elevated levelsconsistent with endothelial and cellular injury. Statistical equivalent steadystates are designated by similar shades of gray.
H413BRANCHING COMPLEXITY IN PULMONARY HYPERTENSION
furcating network of n � 19 generations (Fig. 2B). Each epochis associated with a constant energy-rate ratio at the entrance tothe pulmonary circulation ( �) (Fig. 2C) with the early epochoccurring before clinical definitions of PH and PAH are evi-dent (Fig. 3). This process is not one of an increase in PVR butone of unspecified hemodynamic-metabolic work performedon arterial and arteriolar network organization under steady-state conditions ( � � constant), in accord with minimumwork-rate/dissipation principles dictated by Eqs. 4–6 and 17.In this schema, PH progression decreases the negative diameterpower-law slope X and increases dMPA, as inferred via a rising d under an apparent constant hemodynamic energy rate � �1 (Fig. 2, B and C). This reduction in slope predicts that thelarger arterial vessels will undergo chronic dilation (42) and amorphometric pattern of vascular pathology within smallerarterioles that will concomitantly diminish their diameter andbranching topology via area reduction (Fig. 1). The predictedbaseline and borderline PH values for dMPA are consistent withobserved values. In the disease-free state, the model MPAdiameter power law adheres to a 3/8 power law (Table 1),which is consistent with the empirical 3/8 scaling law for MPAdiameter in cm (dMPA-ref � 0.514M0.375) evaluated duringgrowth (39). For a 70-kg adult, the average value for MPAdiameter in the disease-free state as observed in a large popu-lation (46) is dMPA � 2.51 cm � 0.28 cm (N � 3,171). Thepredicted early significant increases in MPA diameter (Fig. 2B,phases 2–4) are consistent with empirical findings of MPAdilation observed via CT in borderline (24) and progressivestages of PH (13). Lange and coworkers (24) demonstrated thatsignificant MPA diameter dilatation is evident in border-line-PH subjects, exhibiting an average diameter of 3.16 �0.53 SD, which would correspond to a d � 1.26 and phase 3in Fig. 2, and their suggested cutoff to categorize borderline PHof dMPA � 2.9 is consistent with a d � 1.16 and phase 2. Thusour allometric-hemodynamic model (Eq. 16) is consistent witha spectrum of morphometric deviations of X in several epochs
of PH (early, mid, and late) and consistent with the approach ofLange et al. (24) as a means for discriminating early phases ofPH progression, which may be useful for purposes of earlydetection and therapeutic intervention (24, 31, 42).
The pruning process of PH, visually apparent in radiographsand CTs in various phases of PH (Fig. 1) (12, 31), is evident inour model as a functional reduction in Xd � Xl operating tominimize hemodynamic power dissipation to match the meta-bolic rate (Fig. 1). A question arises as to whether the pruningprocess we proposed represents a common morphometric-hemodynamic coupled modality universal to all diverse formsof PH over all phases. Our initial rationale for assuming X �Xd � Xl reduction in the hemodynamic model was that thetheoretical predicted reference state identifies this condition asone for maximum pressures in a disease-free state independentof body weight and species (Table 2, Eqs. 10, 12 at rest). Underphysiological conditions, the assumption Xd � Xl does not holdstrictly for transient acute vasomotor changes, such as thoseinduced by intense abnormal vasoconstriction via endothelin-1,where diameter is affected first, decreasing the bifurcationexponent to x � 2, whereas the exponent for length remainsunchanged (18). However, as indicated by Fig. 1, if thiscondition remains imposed in a chronic way while Xd de-creases, the overall work rate for a given flow at the entranceis elevated compared with an alternative adaption had theeffective daughter lengths been compensated instead by ob-struction. Alternatively, as this figure also illustrates, diameter-length obstruction together mitigates hydraulic power-dissipa-tion intensity if daughter and lengths scale together to achieveminimum dissipation for the network xl � xd or xl � (2/3)xd.This suggests that pruning of combined length/diameter net-work elements together represents a paradoxical afterload-adaptive strategy that diverts blood flow to low-resistancepathways in an effort to optimize ventilation/perfusion match-ing, while also minimizing the rate of energy dissipation whileregulating capillary pressures (8–10). Unfortunately, morpho-
Fig. 4. A–B: influence of Trepostinil and placebo on PH progression. A: covariance trends (Trepostinil, thick line; placebo, thin line) summarize PH progressionover 16 wk as a function of baseline starting value of X and demonstrate statistical profiles between groups. Phase advancement (�phase/16wk, earmarksdisease worsening, -�phase/16wk, phase reversal). Placebo trend indicates that subjects with baseline values of X � 2.00 demonstrated the most rapidadvancement in phase progression (3 phases) over the course of the 16-wk study. Placebo subjects starting the study at later phases (X � 1.75) did not significantlyadvance further. Unlike the placebo group, the Trepostinil-exposed subjects beginning with a X � 2.00 baseline phase did not change, but those with moreadvanced phases at the start of the study advanced only 1 phase by 16 wk. B: covariance trends were controlled for statistically similar intragroup variations thatmay have arisen from prior treatment, classified as either worse (increase in phase) or demonstrated improvement (decrease in phase). There was a significantdifference between the combined group of demonstrating progression (worse) and responders (better), which was not affected by placebo or treatment (NS).
H414 BRANCHING COMPLEXITY IN PULMONARY HYPERTENSION
metric methods and necessary data to evaluate concomitantsamples of Xd and Xl in humans are nonexistent to verify thispremise at present. However, separate analysis of diameter andlength power laws provides insight. Figure 2 summarizes therange of morphometric-derived Xd in the PH-free subjects, andalternative origins of PH morphometric-derived reductions inXd are supported by Reeve and Nolan’s (22) diameter powerlaw data measured in the lungs of patients who have died fromPH. Recently, Moledina and coworkers (31) demonstratedreductions in the topological fractal dimension of CTs ofpediatric patients with congenital heart diseases (31), whichwere skeletonized to vessel lengths. Their dimension, evalu-ated with respect to lengths distributed in the pulmonaryvascular volume, is theoretically consistent to our Xl. Althoughdisease-free controls were not evaluated, they demonstratedthat WHO class I-II patients exhibit similar dimensions,whereas class III-IV patients showed significant reductionsto values comparatively smaller than those we observed fordiameter morphometrically. Thus both diameter and lengthare reduced, consistent with the radiological appearance ofvascular pruning during PH progression but likely at differ-ent rates in the tree remodeling process. Despite this limi-tation, our assumption of Xd � Xl represents an approxima-tion that is an energetic rate-favorable one, applicable toearly phases (Fig. 1).
Our results indicate that the most significant epoch of arterialarea reduction appears early before the emergence of theclinical definition of PH (Fig. 3A). In this regard, changes innetwork topological organization and complexity represent amore sensitive functional index of PH progression. This reso-lution into phases of PH progression is based on arterialbranching complexity and Thoma’s framework of a metabolic-hemodynamic steady state (Table 1), whose underlying powerlaws are likely more functionally sensitive to arteriolar arearatio changes, as opposed to arteriolar diameter changes whenevaluated by pulmonary artery pressure or PVR. For example,PH is confirmed by right heart catheterization on the basis of aPPA � 25 mmHg, for subjects where cardiac output is consid-ered normal. In contrast, the diameter-length power-lawschema classifies this threshold as phase 3 (early epoch) whosemean value was X � 1.97 within a 95% confidence interval(1.95, 2.00). Additional criteria for the diagnosis of PAHincludes a PPA of 25 mmHg plus a transpulmonary arterypressure gradient �P � PPA � Pwedge of 20 mmHg and apulmonary PVR � �P/Q equal to three Wood units. Again incontrast, the diameter-length power-law schema classifies thisthreshold as phase 4 (1.90 � X 1.95). A PVR threshold forPAH classification was later added to the clinical definition ofPH because PVR was considered a more robust criterionbecause it reflects both �P and Q and is elevated only whenvascular obstruction occurs within the precapillary pulmonarycirculation. However, by the time the hemodynamic statereaches a clinical state of PH or PAH via a PVR-definedclinical defined threshold, our analysis indicates that the dis-ease process may already be in a relatively advanced phase.
One reason for this increased sensitivity to area ratio changein our model is that, if length reductions do occur via resistancevia Eq. 15, as a reduction via Xd � Xl or other deviations fromthis assumption, then their functional influence does not undulyaffect the magnitude of X. Krenz, Linehan, and Dawson (7, 22)demonstrated that the scaling properties of Xl and Xd on the
resistance Rin are influenced primarily by X via diameter Xd
raised to the fourth power and not as much as their ratio Xd/Xl
when both vessel diameter and length are concerned (7, 22).More importantly, as Thoma predicted from his early studies(44, 45), there is morphometric evidence that the earliest phaseof a pathological disease process appears as a reduction of thearea ratio in small arterioles. Indeed, Ghorishi and coworkers(11) demonstrated in an experimental model of surgicallyinduced congenital PH that vascular remodeling before PHemergence alters arteriolar diameter complexity in a nonuni-form manner in accord with our allometric model (11). Theyshowed by morphometry that the local average values of Xd
and � between large arteries and arterioles are nonuniform inthe PH state, and the value of Xd is significantly reducedrelative to the control (shunt Xd � 1.73, � � 0.897, vs. controlXd � 2.02, � � 1.007). The significance of the power law-based PH process revealed in their study was that the globalreductions evident in Xd are due to the impact of regional localaverage ones occurring in arterioles via increased smoothmuscle thickness encroaching on the corresponding area ratios� before PH was evident. Thus it is important to emphasizethat the area ratio reductions by vascular remodeling appearbefore PH emergence.
PH progression by branching complexity and arterial net-work disorder, regardless of cause, exacerbates an unstablepositive-feedback influence that likely contributes to endothe-lial dysfunction, disruption, and injury by concomitantly atten-uating shear stress in large arteries and amplifying shear stressin small arterioles (Fig. 3, D and E). Vascular remodelingleading to PH is thought to result from a “multiple hit” modelof cause, where a genetic susceptibility is first required, that isthen followed by mechanistic pathways leading to arteriopathythat reduce diameter and increase PVR (30). Recently, epige-netic mechanisms that are responsive to shear stress andinflammation (47) have been implicated in the regulation ofvascular tone and the pathogenesis of PH (20). Our resultsemphasize that the afterload changes we observed utilizing thismodel, as discussed earlier (large artery dilation and arteriolararea ratio reduction), represents a progressive positive-feed-back disturbance to the endothelial-shear stress environment ofthe pulmonary circulation for which epigenetic mechanismswould be expected to exacerbate PH progression (Figs. 2–3)(47). For example, Fig. 3D indicates that the shear stressexperienced in the MPA and large arteries is significantlyreduced in the early phases of progression (phases 1–3) andreaches a steady state by phase 4. Tang and colleagues (42)recently inferred the same phenomena in the left and rightpulmonary artery, with amplification to small artery vessels,utilizing their analysis of the branching geometry captured bythe MRIs of controls and PH subjects. In essence, the largeartery afterload reduction in PH subjects significantly reducedthe average arterial shear stress to near stagnant levels, whichwhen combined with endothelial dysfunction and damage, maycontribute to a positive-feedback inflammation-injury processakin to atherosclerosis (37). In contrast, the arteriolar area ratiodecrease with progressive PH transforms arterial network or-ganization into a high-gain shear stress amplifier (1, 3, 16), inwhich the magnitude of arteriolar shear stress loaded ontoarterioles demonstrates critical thresholds before dysfunction,followed by endothelial damage (33) (Fig. 3C). In the contextof our analysis, shear stress does not represent an initiating
H415BRANCHING COMPLEXITY IN PULMONARY HYPERTENSION
factor of PH (23); instead the amplitude of arteriolar shearstress should be interpreted as an index of the integrativepositive feedback inherent in PH progression. For example,Dereddy and coworkers (28) recently found that the smallarterioles in infants with PH arising from high-flow/low-flowcongenital heart disease, bronchopulmonary dysplasia, or re-spiratory distress exhibit discriminatory patterns of endothelialdysfunction, injury, and smooth muscle proliferation and weredependent on the hemodynamic stimulus of elevated shearstress and/or inflammation. Consequently, increasing arterialnetwork complexity/disorder chronically redistributes forces inlarge and small arteries, in which early transduction maytranslate into metabolic processes promoting proliferationand/or inflammation (40, 41).
The principal limitation of the power-law approach in itscurrent form is that it is based on invasive hemodynamicmeasurements of pulmonary pressure and flow obtained viaright heart catheterization in a limited number of PH-free andPH subjects (N � 221). Improved clinical discrimination andresolution between phases with greater statistical power wouldbe facilitated by including data from registries composed ofthousands of PH-free and PH subjects. However, invasivemeasurements are presently used to confirm PH diagnosis onlyand not intended for early screening. In this study, the intent ofour method was to interpret the PH adaptive/maladaptiveprocesses in terms of a simple allometric predictive modelbeyond PVR that could be applied to retrospective studies inwhich morphometric-hemodynamic data were already avail-able. Despite these shortcomings, our model emphasizes andsupports that global principles of steady-state physiology gov-ern pathological processes masked in branching complexityand arterial scaling (8, 9, 44, 45), which apply to, not onlyhumans, but also experimental mammalian models of thedisease, independent of PH etiology and pathology. Alterna-tively, noninvasive inferences of diameter/length power-lawbehavior via impedance or flow waveform reflection measure-ment in the pulmonary artery, which enable values of X orarterial area ratio to be similarity calculated via inverse-scat-tering models, may fill this gap (2, 3). In this regard, retro-spective and prospective studies utilizing a greater number ofsubjects that compare both invasive and noninvasive hemody-namic methods, in combination with morphometric/stereologi-cal approaches that delineate power-law relationships on thebasis of vasculopathy populations earlier in the disease process(40) remain necessary to establish the discriminatory capabilityand resolution for early clinical detection (24).
The analysis of hemodynamic data from patients with PHobtained from the Trepostinil trial (Freedom-C trial) (43)suggests advantages of our model for early diagnosis andintervention (Fig. 4B). Our statistical analysis allowed us todetermine whether an observed increase or decrease in X overthe 16-wk trial period was present on the basis of prior therapy,the present therapy, or due to chance via �bAIA. This analysisindicates that patients characterized as having early phases ofPH progression (phase 3: 1.90 � X 1.95) are the mostresponsive to treatment. Placebo-treated subjects demonstratedan aggressive progression by two to three phase incrementsover 16 wk, whereas Trepostinil-treated subjects from the sameinitial baseline did not change phase at all, indicating a pro-tective-staving effect. However, both placebo and treatmentgroup subjects starting the study at more advanced phases
(phase 7: 1.75 � X 1.80 or greater) demonstrated little or nochange in phase. This apparently contradictory behavior isconsistent with the PH phases delineated in Figs. 2A and 3A;earlier epochs of PH progression demonstrate phase changes ofsignificantly greater area reductions than those demonstratedby later epochs. Thus, whereas the previous analysis of theFreedom-C study did not demonstrate a functional significantend point defined by an improvement of the 6-min walk (43),the reinterpretation of the clinical hemodynamic data suggestsa significant drug action on arterial network organizationwhose effectiveness is enhanced in slowing disease progres-sion by interventions at earlier phases of diagnosis. Figure 4Bindicates that, despite the overall trend of subjects that weremost likely to advance to progressive phases of the disease(Fig. 3A), there was a significant difference over the 16-wktime period when the treatment and placebo groups wereclassified into subgroups as either improving or becomingworse. Of those that became worse, the placebo group with thegreatest increase in phase progression occurred in those sub-jects starting the study at earlier phases. In contrast, for thosetreatment and placebo subgroups that were classified as better,thereby increasing their area ratios, their response may repre-sent a different baseline state of endothelial function andinflammation. This suggests a simple method to profile re-sponders and nonresponders to therapy in PH progression inthe early epochs; the direction of change in area ratio inducedby a perturbation, such as exercise, associated with prolifera-tion/inflammation biomarkers may be predictive of down-stream positive-feedback mechanisms (12, 20, 40, 41).
In conclusion, our study suggests a common trajectory forarterial vascular remodeling in diverse forms of PH. This novelparadigm may alter our classification, intervention, and diag-nostic approach with clinical populations that, to date, have notbeen thought of to share a common ground. The ability todiagnose at-risk populations at a stage of disease that isclinically silent offers the hope of preventing clinical deterio-ration, as suggested by the results of the early trial (15, 38).Last, our analysis of the data from the Trepostinil trial (Free-dom-C trial) (43) offers a new understanding that interventionsmay have quite variable effects depending on the severity ofdisease of the study population that is not apparent throughtraditional hemodynamic techniques. This may serve as avaluable end point to guide future trial development.
ACKNOWLEDGMENTS
The authors thank Drs. Jan-Willem Lankhaar, Nico Westerhof, and AntonVonk-Noordergraaf for providing the patient hemodynamic data. We alsothank Hank Harrison and Paula Montibeller-Bennett for reviewing the manu-script at various stages.
GRANTS
This work was supported by National Institute of Health grantP51OD011107.
DISCLOSURES
No conflicts of interest, financial or otherwise, are declared by the authors.
AUTHOR CONTRIBUTIONS
Author contributions: R.P.A., E.S.S., and S.H.B. conception and design ofresearch; R.P.A., E.S.S., and S.H.B. analyzed data; R.P.A., E.S.S., and S.H.B.interpreted results of experiments; R.P.A., E.S.S., and S.H.B. edited and
H416 BRANCHING COMPLEXITY IN PULMONARY HYPERTENSION
revised manuscript; R.P.A. and E.S.S. approved final version of manuscript;S.H.B. prepared figures; S.H.B. drafted manuscript.
REFERENCES
1. Bennett SH, Eldridge M, Zaghi D, Zaghi S, Milstein J, Goetzman B.Form and function of fetal and neonatal pulmonary arterial bifurcations.Am J Physiol Heart Circ Physiol 279: H3047–H3057, 2000.
2. Bennett SH. Modeling methodology for vascular input impedance deter-mination and interpretation. J Appl Physiol 75: 455–484, 1994.
3. Bennett SH, Goetzman BW, Milstein JM, Pannu JS. Role of arterialdesign on pulse wave reflection in a fractal pulmonary network. J ApplPhysiol 80: 1033–1056, 1996.
4. Burrows K, Clark A, Tawhai M. Blood flow redistribution and ventila-tion-perfusion mismatch during embolic pulmonary arterial occlusion.Pulm Circ 1: 365–376, 2011.
5. Chan S, Loscalzo J. Pathogenic mechanisms of pulmonary hypertension.J Mol Cell Cardiol 44: 14–30, 2008.
6. Cool C, Groshong S, Oakley J, Voekel N. Pulmonary hypertension:cellular and molecular mechanisms. Chest 128: 565–571, 2005.
7. Dawson CA, Krenz GS, Karau KL, Haworth ST, Hanger CC, Line-han JH. Structure-function relationships in the pulmonary artery tree. JAppl Physiol 86: 569–583, 1999.
8. Dawson T. Modeling of vascular networks. J Exp Biol 208: 1687–1694,2005.
9. Dawson T. Scaling laws for capillary vessels of mammals at rest and inexercise. Proc Biol Sci 270: 755–763, 2003.
10. Dawson T. Similtude in the cardiovascular system of mammals. J ExpBiol 204: 395–407, 2001.
11. Dehoff R. Measurement of number and average size in volume. In:Quantitative Microscopy, edited by Dehoff R and Rhines F. New York,NY: McGraw Hill, 1968, pp. 130–147.
12. Dereddy N, Huang J, Erb M, Guzel S, Wolk J, Sett S, Gewitz M,Mathew R. Associated inflammation or increased flow-mediated shearstress, but not pressure, disrupts endothelial caveolin-1 in infants withpulmonary hypertension. Pulm Circ 2: 492–500, 2012.
13. Edwards P, Bull R, Coulden R. CT measurement of main pulmonaryartery diameter. Br J Radiol 71: 1018, 1998.
14. Evans W, Short D, Bedford D. Solitary pulmonary hypertension. BrHeart J 19: 93, 1957.
15. Galiè N, Rubin L, Hoeper M, Jansa P, Al-Hiti H, Meyer G, Chiossi E,Kusic-Pajic A, Simonneau G. Treatment of patients with mildly symp-tomaticpulmonary arterial hypertension with bosentan (EARLY study): adouble-blind, randomised controlled trial. Lancet 371: 2093–2100, 2008.
16. Ghorishi Z, Milstein J, Poulain F, Moon-Grady A, Tacy T, Bennett S,Fineman J, Eldridge M. Shear stress paradigm for perinatal fractalarterial network remodeling in lambs with pulmonary hypertension andincreased pulmonary blood flow. Am J Physiol Heart Circ Physiol 292:H3006–H3018, 2007.
17. Glantz S. Primer of Biostatistics. New York, NY: McGraw-Hill, 1997.18. Griffith T, Edwards D, Randall M. Blood flow and optimal vascular
topography: role of the endothelium. Basic Res Cardiol 86: 89–96, 1991.19. Horsfield K, Woldenberg MJ. Diameters and cross-sectional areas of
branches in the human pulmonary arterial tree. Anat Rec 223: 245–251,1989.
20. Kim G, Ryan J, Marsboom B, Archer S. Epigenetic mechanisms ofpulmonary hypertension. Pulm Circ 1: 347–356, 2011.
21. Krenz GS, Dawson CA. Flow and pressure distributions in vascularnetworks consisting of distensible vessels. Am J Physiol Heart CircPhysiol 284: H2192–H2203, 2003.
22. Krenz GS, Linehan JH, Dawson CA. A fractal continuum model of thepulmonary arterial tree. J Appl Physiol 72: 2225–2237, 1992.
23. Kulik T. Pulmonary blood flow and pulmonary hypertension: is thepulmonary circulation flowphobic or flowphilic? Pulm Circ 2: 327–339,2012.
24. Lange T, Dornia C, Stiefel J, Stroszczynski C, Artz M, Pfeifer M,Hamer O. Increased pulmonary artery diameter on chest computedtomography can predict borderline pulmonary hypertension. Pulm Circ 3:363–368, 2013.
25. Lankhaar J, Westerhof N, Faes T, Gan T, Marques K, Boonstra A,Berg Fvd Postmus P, Vonk-Noordergraaf A. Pulmonary vascular re-sistance and compliance stay inversely related during treatment of pulmo-nary hypertension. Eur Heart J 29: 1688–1695, 2008.
26. Lankhaar J, Westerhof N, Faes T, Marques K, Marcus J, Postmus P,Vonk-Noordergraaf A. Quantification of right ventricular afterload inpatients with and without pulmonary hypertension. Am J Physiol HeartCirc Physiol 291: H1731–H1737, 2006.
27. Laskey W, Ferrari V, Palevsky H, Kussmaul W. Pulmonary arteryhemodynamics in primary pulmonary hypertension. Am Coll Cardiol 21:406–412, 1993.
28. Li J. A new similarity principle for cardiac energetics. Bull Math Biol 45:1005–1014, 1983.
29. Lucas R Jr, St. Geme J Jr, Anderson R, Adams P Jr, Ferguson D.Maturation of the pulmonary vascular bed: a physiologic and anatomiccorrelation in infants and children. Am J Dis Child 101: 467–475, 1961.
30. McLaughlin V, Archer S, Badesch D, Barst R, Farber H, Linder J,Mathier M, McGoon M, Park M, Rosenson R, Rubin L, Tapson V,Varga J. ACCF/AHA 2009 Expert Concensus Document on PulmonaryHypertension: A Report of the American College of Cardiology Founda-tion Task Force on Expert Consensus Documents and the American HeartAssociation Developed in Collaboration with the American College ofChest Physicians; American Thoracic Society, Inc; and the PulmonaryHypertension Association. J Am Coll Cardiol 53: 1573–1619, 2009.
31. Moledina S, Bruyn Ad Schievano S, Owens CM, Young C, HaworthSG, Taylor AM, Schulze-Neick I, Muthurangu V. Fractal branchingquantifies vascular changes and predicts survival in pulmonary hyperten-sion: a proof of principle study. Heart 97: 1245–1249, 2011.
32. Murray C. The physiological principle of minimum work. I. The vascularsystem and the cost of blood volume. Proc Natl Acad Sci USA 12:207–214, 1926.
33. Rabinovitch M, Bothwell T, Hayakawa B, Williams W, Trusler G,Rowe R, Olley P, Cutz E. Pulmonary artery endothelial abnormalities inpatients with congenital heart defects and pulmonary hypertension: acorrelation of light with scanning electron microscopy and transmissionelectron microscopy. Lab Invest 55: 632–653, 1986.
34. Reeves J, Noonan J. Microarteriographic studies of primary pulmonaryhypertension. Arch Pathol 95: 50–55, 1973.
35. Reuben S. Compliance of the human pulmonary arterial system in disease.Circ Res 29: 40–50, 1971.
36. Robertson B, Rosenhamer G, Lindberg J. Idiopathic pulmonary hyper-tension in two siblings. Acta Med Scand 186: 569–577, 1969.
37. Scheleithoff S, Voelter-Mahlknecht S, Navina-Dahmke I, MahlknechtU. On the epigenetics of vascular regulation and disease. Clin Epigenetics4: 1–13, 2012.
38. Simonneau G, Galiè N, Meyer G, Al-Hiti H, Kusic-Pajic A, Lemarié J,Hoeper M, Rubin L. Long-term results from the EARLY study ofbosentan in WHO functional class II pulmonary arterial hypertensionpatients. Int J Cardiol 172: 332–330, 2014.
39. Sluysmans T, Colan S. Theoretical and empirical derivation of cardio-vascular allometric relationships in children. J Appl Physiol 99: 445–457,2005.
40. Stacher E, Graham BB, Hunt JM, Gandjeva A, Groshong SD,McLaughlin VV, Jessup M, Grizzle WE, Aldred MA, Cool CD, TuderRM. Modern age pathology of pulmonary artery hypertension. Am JRespir Crit Care Med 186: 261–272, 2012.
41. Sutendra G, Mechelakis E. The metabolic basis of pulmonary arterialhypertension. Cell Metab 19: 2014.
42. Tang B, Pickard S, Chan F, Tsao P, Taylor C, Feinsten J. Wall shearstress is decreased in the pulmonary arteries of patients with pulmonaryarterial hypertension. Pulm Circ 2: 470–476, 2012.
43. Tapson V, Torres F, Kermeen F, Keogh A, Allen R, Frantz R, BadeschD, Frost A, Shapiro S, Laliberte K, Sigman J, Arneson C, Galie N.Oral Trepostinil for the treatment of pulmonary arterial hypertension inpatients on background endothelin receptor antagonist and/or phosphodi-esterase type 5 inhibitor therapy (The FREEDOM-C Study). Chest 142:1383–1390, 2012.
44. Thoma R. Text-Book of General Pathology and Pathological Anatomy.London, UK: Black, 1896.
45. Thoma R. Uber den Verzweigungsmodus der Arterien. Arch Entwick-lungsmechanik 12: 352–413, 1901.
46. Truong Q, Massaro J, Rodgers I, Mahabadi A, Kriegel M, Fox C,O’Donnell C, Hoffman U. Reference values for normal pulmonary arterydimensions by noncontrast cardiac computed tomography. Circ Cardio-vasc Imaging 5: 147–154, 2012.
47. Yan M, Matouk C, Marsden P. Epigenetics of the vascular endothelium.J Appl Physiol 109: 916–926, 2010.
H417BRANCHING COMPLEXITY IN PULMONARY HYPERTENSION
