Testing a patient-specific in-silico model to noninvasively estimate central blood pressure
Caterina Gallo, Joakim Olbers, Luca Ridolfi, Stefania Scarsoglio, Nils Witt
NNoname manuscript No. (will be inserted by the editor)
Testing a patient-specific in-silico model tononinvasively estimate central blood pressure
Caterina Gallo · Joakim Olbers · LucaRidolfi · Stefania Scarsoglio · Nils Witt
Received: date / Accepted: date
AbstractPurpose : To show some preliminary results about the possibility to exploita cardiovascular mathematical model - made patient-specific by noninvasivedata routinely measured during ordinary clinical examinations - in order toobtain sufficiently accurate central blood pressure (BP) estimates.
Methods : A closed-loop multiscale (0D and 1D) model of the cardiovas-cular system is made patient-specific by using as model inputs the individualmean heart rate and left-ventricular contraction time, weight, height, age, sexand mean/pulse brachial BPs. The resulting framework is used to determinecentral systolic, diastolic, mean and pulse pressures, which are compared withthe beat-averaged invasive pressures of 12 patients aged 72 ± Results : Errors in central systolic, diastolic, mean and pulse pressuresby the model are 4.26 ± ± ± ± Conclusion : The proposed modeling approach shows a good patient-specificresponse and appears to be potentially useful in clinical practice. However, thisapproach needs to be evaluated in a larger cohort of patients and could possiblybe improved through more accurate oscillometric BP measurement methods.
C. Gallo · S. ScarsoglioDepartment of Mechanical and Aerospace Engineering, Politecnico di Torino, Torino, ItalyE-mail: [email protected]. Olbers and N. WittDepartment of Clinical Science and Education, Karolinska Institutet, Division of Cardiology,S¨odersjukhuset, Stockholm, SwedenL. RidolfiDepartment of Environmental, Land and Infrastructure Engineering, Politecnico di Torino,Torino, Italy a r X i v : . [ phy s i c s . m e d - ph ] J a n Caterina Gallo et al.
Keywords central pressure · noninvasive estimation · patient-specificmodels · multiscale cardiovascular modeling · validation of cardiovascularmodels Automatic brachial BP monitoring is routinely used in clinical practice to getan easily obtainable and noninvasive measurement of arterial BP. However, it iswidely accepted that brachial BP is not a good estimation of central BP, mainlybecause of the amplification in the pressure waveforms from the ascendingaorta to the stiffer peripheral arteries [1]. Considering that target organs aremore subjected to central than brachial BP [2], simple estimation of central BPis expected to be helpful in diagnostics and clinical decision making. In supportof this, it has been demonstrated that the addition of central BP measurementto conventional brachial BP measurement may identify individuals with anelevated central BP but a brachial BP in the normal or high normal range[3]. These individuals may have an increased risk for cardiovascular eventsnot reflected by their brachial BP. Moreover, the fact that antihypertensivemedications can produce different effects on central BP but comparable effectson brachial BP [4] makes the idea to clinically use central BP attractive.Cardiac catheterization still represents the most accurate method to eval-uate central BP. However, it cannot be appropriately employed in routineclinical setting since it is an invasive procedure, technically demanding andtime consuming. Instead, a number of noninvasive devices have been proposedand tested to provide central BP estimates from distal pressure signals andthrough a variety of calibration techniques [5]. So far, the incremental value ofnoninvasive central BP compared to brachial BP in the prediction of seriouscardiovascular events has not been unequivocally demonstrated, with differ-ent studies coming up to opposite conclusions [6]. Thus, it seems that theaccuracy of current noninvasive methods for estimation of central BP is notalways sufficient to confirm superiority over brachial BP [7]. In this context,the need emerges to identify the most accurate solutions to noninvasively es-timate central BP, before further investigating if brachial or central BP is abetter prognostic parameter to be adopted in the future.We present some preliminary results about the possibility to estimate theindividual central BP by a patient-specific multiscale mathematical model ofthe cardiovascular system. In the last few decades, several models of the cardio-vascular system have been proposed and tested to shed light into the pathogen-esis of cardiac and vascular diseases [8], sustain the design of medical devices(e.g., stents and valve prostheses) [9], support teaching and training activities[10], and prognosticate the effects of potential therapeutic plans [11]. Froma clinical perspective, the modeling approach is demonstrating an attractingtool. In fact, it is less expensive than in-vivo studies and leads to reliable re-sults. Moreover, it can be used to isolate the role played by specific pathologiesand provide more information about the whole hemodynamic picture. n-silico central blood pressure estimation 3
Cardiovascular models are beginning to be tailored on each patient by theso-called patient-specific approaches, which depend on data (e.g., vascular ge-ometry, heart data, cardiac electrical activity, etc.) measured on the examinedpatient. The latter modeling approach is defined patient-specific and is typ-ically based on the adoption of the exact patient-specific vascular geometryderived from scans. In the following, we will use the term patient-specific ina more general meaning, i.e., to underline the effort to adapt, even partially,the model to a specific patient, as already presented by other authors [12,13]. Indeed, to make the model patient-specific, we did not use patient-specificvascular data, but we adopted empirical rules (extracted from measurementson large cohort of individuals) introducing the patient-specific personal andanthropometric data.This study aims at showing the potential use of the in-silico approach tononinvasively evaluate central BP on specific patients. Despite the preliminarynature of our results, they represent an invitation to continue working onpatient-specific models yielding increasingly accurate central BP estimations,apart from an extended set of patient-specific hemodynamic parameters.
Noninvasive patient-specific data, consisting of anthropometric and clinicalmeasures of 12 subjects, were used as model inputs to compute the individualaortic BPs. Simulated pressures were then compared with the beat-averagedvalues of the invasive ascending aorta pressure signals, quantifying the errorsproduced by the proposed modeling approach in terms of central systolic,diastolic, pulse and mean pressures.2.1 Patient-specific dataAnthropometric and clinical measures adopted as model inputs include sex ( S ),age ( AGE ), weight ( W ), height ( H ), mean heart rate ( HR ), mean left ventric-ular contraction time ( T vc ), mean and pulse brachial BPs ( P m b and P P b ). HR and T vc were extracted from the ECG, while P P b and P m b were calculatedfrom the systolic ( P s b ) and diastolic ( P d b ) brachial BPs ( P P b = P s b − P d b and P m b = P d b + P P b / Caterina Gallo et al. pressure recordings were acquired from 12 patients with sinus rhythm, usinga fluid-filled catheter system. Five French 100 cm long right coronary diag-nostic catheters, connected to a pressure transducer-equipped manifold withtwo taps (NAMIC, Navilyst Medical Inc, Marlborough, MA, USA), were used.Pressure signals were recorded using the RadiAnalyzer Xpress unit (St JudeMedical, St Paul, MN, USA) for digital storage. No data on the wave formsampling rate has been provided by the manufacturer. The catheter systemwas flushed with saline before starting the measurement for elimination ofair bubbles from tubes and connecting parts. After zeroing to air, the pres-sure transducer was adjusted to estimated left atrial level. No specific test forfrequency response of the catheter system was carried out, but the natural fre-quency of the pressure transducer itself has been specified by the manufacturerto be 200 Hz. Right radial, right brachial and ascending aorta pressure signalswere sequentially recorded by advancing a diagnostic catheter from the rightradial to the right brachial to the central site (ascending aorta). Appropriatelocation of the catheter tip was confirmed by fluoroscopy. At least 15 cardiaccycles were saved at each location for all subjects. Intra-arterial BP recordingwas initiated at the start of cuff deflation in the left arm, thus making invasiveand non-invasive BP recordings simultaneous.2.2 Patient-specific mathematical modelThe modeling approach implemented in this study is a closed-loop multiscalemathematical model of the cardiovascular system. The latter originates froma physically-based 1D representation of the systemic arterial tree [13], whichwas previously used to study the aging process [15] and the impact of atrialfibrillation [16,17]. A 1D model is adopted to reproduce the arterial tree hemo-dynamics, rather than a 0D model, because it allows us to properly describethe reflection and propagation phenomena of pressure and flow waves. Thus,much more hemodynamic information are available at a reasonable computa-tional cost. Moreover, in lumped models, vascular lengths and diameters arenot explicitly modeled, making extremely difficult to apply patient-specificadjustments on vascular geometry.The 1D model of the arterial tree is integrated with a 0D description ofthe remaining portions of the cardiovascular system, that is the systemic mi-crocirculation and venous return, the heart and pulmonary circulation, andthe short-term baroreflex mechanism to maintain homeostasis. The resulting in-silico model, which adequately describes the physiological hemodynamicbehavior of a reference healthy subject, was validated in heart pacing andopen-loop response [18], and exploited to inquire into the effects of long dura-tion spaceflights on the cardiovascular system [19]. A schematic representationof the model and a summary of the equations used to reproduce its consti-tutive parts are given in the Online Resource. Further details on the 1D-0Dmodel can be found elsewhere [13,15,16,17,18,19]. n-silico central blood pressure estimation 5
The reference multiscale model corresponds to a generic healthy subjectwith the following characteristics: HR ref = 75 bpm, T vc ref = 0 .
27 s, W ref =75 kg, H ref = 175 cm, AGE ref = 25 years, S ref =man, P m bref = 88 mmHgand P P b ref = 67 mmHg. Notice that HR , T vc and P m b appear explicitly inthe model, while AGE , W , H , S and P P b are implicit in the geometrical andcardiac/vascular mechanical properties.To make the model patient-specific, we used HR , T vc , W , H , AGE , S , P m b and P P b as model input data depending on the patient characteristics.In fact, it is widely accepted in literature that anthropometric ( W and H )and personal data ( AGE and S ) are crucial hemodynamic determinants, to-gether with time-averaged ECG parameters and pressure level, which can bedifferent among people with the same anthropometric and personal data. Co-herently to the explicit or implicit occurrence of the different model input datain the reference model, patient-specific values of HR , T vc and P m b were di-rectly introduced in the model, while individual values of W , H , AGE , S and P P b were used in empirical relationships to adapt the arterial geometry andcardiac/vascular mechanical properties to the specific patient characteristics(see Fig. 1). In this way, we were able to match the reference model to eachpatient considered. In particular, arterial lengths, diameters and thicknesses,as well as cardiac, arterial and venous compliances of the reference subject -all marked with the subscript ref and provided in a separate publication [19]- were adapted to the specific patient by suitable empirical relationships, asdescribed below. In order to compare our modelling results with pre-existingclinical data on old and not perfectly healthy patients (already measured at theDepartment of Clinical Science and Education, Karolinska Institutet, Divisionof Cardiology, S¨odersjukhuset, Stockholm, Sweden), we considered empiricalrelationships derived from large cohorts and representative of white peopleaffected by cardiovascular or cardiovascular-related problems, such as hyper-tension, diabetes and atrial fibrillation. To immediately recognize the directdependence of each vascular property to the corresponding input parameters,the following empirical relationships will be expressed in dimensional form, asthey are typically found in literature. An effort to restate them in dimension-less form will be done in future (more comprehensive) works. Arterial lengths.
Arterial path length depends on H , which then influencesthe resultant hemodynamic behavior [20,21,22,23]. In shorter people, in fact,the earlier arrival of the reflected waves to the heart during systole causes anincrease in both systolic and pulse pressures, which are responsible for a risein the left-ventricular work and stress at the same mean pressure. To take intoaccount these phenomena, we adjusted arterial lengths with H , scaling themaccording to the patient-specific H . Patient-specific arterial lengths, L art , weremodified from reference lengths, L art ref [13], as L art = L art ref HH ref + c ( AGE − AGE ref ) , (1) Caterina Gallo et al. with the term c ( AGE − AGE ref ) introducing the effect of
AGE on ar-terial lengths. In fact, some arterial tracts also elongate with
AGE , withdifferent relationships proposed in literature [24,25]. We modified the refer-ence aortic lengths with
AGE according to the regression coefficients, c , byRylski et al. [24], reported in Table 1, while maintained the other arteriallengths constant with AGE . Notice that Rylski’s coefficients (which are sex-dependent) are provided for a change in mm per year and per m of bodysurface area, BSA . Thus, coefficients c have to be multiplied for the patient-specific BSA , which we calculated from H and W with the Du Bois’s formula[26]: BSA = 0 . H . W . ( H and W are given in m and kg, respec-tively). Arterial diameters.
It is well known that diameters of elastic arteries widenwith
AGE , while muscular arteries are not subject to enlargement duringnormal aging [27]. However, if there is a general agreement about the age-induced rise in the aortic and common carotid arterial diameters, there issome controversy regarding the changes with
AGE in the diameters of somemuscular arteries, such as the brachial, radial and common femoral arteries.In fact, some authors report decreases in the diameters of these arteries [28],while others sustain the opposite trend [29]. This controversy could be due tothe existence of a transition zone between the elastic and muscular arterialbehavior at more distal arterial sites, as observed by [30], who monitored theage variations in the brachial artery diameter both proximally and distally.Considering the contrasting behavior observed at more peripheral sites, wemodeled the age effects on aortic and carotid diameters only. In particular,the role of
AGE was reproduced through the regression coefficients c , givenin Table 2, by Rylski et al. [24] along the aorta and by Kamenskiy et al.[31] for the common carotid arteries, respectively. All these coefficients aresex-dependent, and refer to a change in mm per year and per m of BSA by Rylsky et al. [24], and for a change in mm per year by Kamenskiy etal. [31]. Since an explicit dependence of the aortic diameters with
BSA wasalso considered (as described later in the text), age-dependent coefficients byRylsky et al. [24] were multiplied for the reference
BSA , BSA ref =1.90 m ,calculated through the Du Bois’s formula.Arterial diameters also change with both W and H , whose combined effectcan be taken into account by either the body mass index ( BM I = W/H ) or
BSA . In this study we used
BSA as body size variable, considering that itwas proved to be better correlated to some aortic diameters than
BM I [32].We here introduced the effects of
BSA at aortic and carotid level only, wherethe role of
BSA has been largely assessed [24,31,32,33,34,35,36]. The effectof
BSA on the aortic and common carotid arteries diameters were quantifiedthrough the regression coefficients c by Davis et al. [33] and Krejza et al.[35], respectively, both indicated in Table 2 and expressing different changesfor women and men.Thus, patient-specific carotid and aortic diameters, D ca , were determinedfrom the corresponding reference values, D ca ref [13], as n-silico central blood pressure estimation 7 D ca = D ca ref + c ( AGE − AGE ref ) + c ( BSA − BSA ref ) . (2) Arterial thicknesses.
Aortic and common carotid arteries thicken with
AGE [27,37,38], while there are contrasting results at other arterial locations. Thus,only patient-specific aortic and common carotid thicknesses, h ca , were modifiedwith AGE from reference values, h ca ref [15]. Namely, h ca = h ca ref + c ( AGE − AGE ref ) , (3)where c was taken by Virmani et al. [15,39] along the aorta and accordingto Howard et al. [37] and Rashid et al. [38] for the common carotid arteries.In particular, we set coefficients c equal to 0.0040 mm/y for the ascendingaorta, 0.0092 mm/y for the descending thoracic aorta, 0.0085 mm/y for thesuprarenal abdominal aorta, 0.0144 mm/y for the subrenal abdominal aorta,and 0.010 mm/y for the common carotid arteries, neglecting any sex differenceand side-to-side effects for left and right carotids. Arterial compliance.
Elastic arteries stiffen with
AGE , leading to a decrease inarterial compliance. It was demonstrated that arterial stiffening is mainly dueto the fatigue and successive rupture of the median elastic lamellae, which areexpected to fracture after about 8 · cycles (e.g., 30 years with a mean HR of70 bpm) [40,41]. Carotid-femoral pulse wave velocity ( P W V ) is a surrogate in-dex of aortic stiffness [42], with several studies on its changes with aging avail-able in literature. However, carotid-femoral
P W V does not take into accountthe influence of proximal aorta, with only regional
P W V s adequately map-ping the differential stiffness along the aorta and at other arterial locations.Numerous authors have measured the variations in
P W V s with
AGE alongthe aorta [43,44,45] and common carotids [46,47], finding quadratic and linearrelationships, respectively. Alterations in
P W V s with
AGE at other arterialsites were found negligible or absent and were here neglected. We adapted thepatient-specific carotid and aortic compliances through the relative patient-specific pulse wave velocities (
P W V ca s). In fact, mechanical properties of 1Darteries are specified through coefficients B − of the constitutive equationfor pressure (see Eq. T3 in the Online Resource), which are function of thelocal P W V s. Aortic
P W V s (
P W V a s) were calculated from reference values, P W V a ref [13], as P W V a = P W V a ref + [ c ( AGE − AGE ref ) + c ( AGE − AGE ref )] a + b, (4)where c and c , provided in Table 1, are those by Hickson et al. [43]. Carotid P W V s (
P W V c s), instead, were evaluated from reference values, P W V c ref [13],as P W V c = P W V c ref + c ( AGE − AGE ref ) a + b, (5) Caterina Gallo et al. with c = 0 . a and term b allow one to include the role of the pressure level ( P P b and P m b ) in the patient-specific arterial compliances [48,49]. Notice that ref-erence values of local P W V s are calculated from the quasi-linear form of thesystem of equations solving the 1D arteries (Eqs. T1, T2 and T3 in the OnlineResource):
P W V a/c ref = (cid:115) Aρ ( B + 2 B A + 3 B A ) + ( β − β Q A , (6)where variables are defined in Table S2 of the Online Resource. Cardiac compliances.
Since ventricular stiffening increases with
AGE [50],we corrected patient-specific end-systolic, E es , and end-diastolic, E ed , left-ventricular elastance values, starting from the reference values [13] ( E es ref and E ed ref , respectively), as E es = E es ref + c ( AGE − AGE ref ) (7)and E ed = E ed ref + c ( AGE − AGE ref ) . (8)Coefficient c was set to have an increase of 1% and 0.5% per year for womenand men, respectively, according to Redfield et al. [50]. c was instead reason-ably taken equal to c E ed ref /E es ref . Venous compliances.
Venous compliances, as arterial ones, reduce with
AGE [51,52]. We evaluated the patient-specific venous compliances, C v , from thereference values, C v ref [19], through the C v = C v ref + c ( AGE − AGE ref ) , (9)with c chosen in order to have a linear reduction in C v ref of 50% from 25 to80 years [52].2.3 Sensitivity analysisIn order to quantify the role of the different patient-specific input data tothe individual central pressure values, we performed a sensitivity analysis.Considering an input parameter X and an output parameter Y , the sensitivityof Y to X is defined as s = (cid:18) Y (cid:48) − YY (cid:19) (cid:18) XX (cid:48) − X (cid:19) , (10)where Y (cid:48) is the modified output parameter obtained with the modified inputparameter X (cid:48) [53]. Based on this definition, negative values of s imply that an n-silico central blood pressure estimation 9 increase in X causes a decrease in Y and a decrease in X causes an increasein Y . Moreover, | s | values higher (smaller) than 1 indicate that the inputvariability introduced through X is amplified (damped) in Y . Here, we imposedan increase of 25% to all the patient-specific input data, that is X (cid:48) = X +0 . X .Fig. 2 shows the sensitivities of central systolic (sys), diastolic (dia), mean(mean) and pulse (pp) pressures to AGE , W , H , HR , T vc , P m b and P P b for men. Results for women are very similar to the ones for men (they arereported in Table S4 in the Online Resource). From Fig. 2, it emerges that P m b is the only input parameter having a not negligible impact on all the outputparameters, and H and P P b are the input parameters with the greatest impacton central pp. The sensitivity of central pp to H is negative (-0.94), while thesensitivity of central pp to P P b is positive (1.40). The other input parameters( AGE , W , HR and T vc ) result to be less effective on the output parameters,with the smallest sensitivities for central mean and the highest for central pp.From Fig. 2 it also appears that the variability introduced through P m b isamplified in central dia and mean (and damped in central sys and pp), andthe variability introduced through P P b is amplified in central pp (and dampedin central sys, dia and mean). The variability associated to all the other inputparameters results to be damped. Thus, according to Fig. 2, specific brachialBPs and H measurements are the most influential input data on the modeloutputs, although the majority of the chosen patient-specific input data areproven to be important to match central pp. Anthropometric and clinical data, presence of comorbidities, like diabetes andischemic heart disease (IHD), and smoking status of patients are reported inTable 3.Mean, µ , standard deviation, σ , and coefficient of variation ( cv = σ/µ ) val-ues of systolic and diastolic pressures recorded at the three measurement sitesfor all the patients are indicated in Table 4. Based on systolic BP transmissionfrom central-to-peripheral sites, Picone et al. [54] individuated four BP phe-notypes: (phenotype I) both central-to-brachial and brachial-to-radial systolicBP increase ( ≥ µ p ( t ) , (and thestandard deviation, σ p ( t ) ) of the central pressure per beat over the recorded cardiac cycles. Then signal µ p ( t ) was compared against the correspondingsimulated average waveform, µ p ( t ) comp . The latter was obtained through thepatient-specific multiscale model, which received as model inputs the patient-specific noninvasive data ( S , AGE , W , H , HR , T vc , P P b and P m b ).Fig. 4 displays measured central pressure signals ( µ p ( t ) , continuous thinblue line, and µ p ( t ) ± σ p ( t ) , dotted thin blue line) and the corresponding sim-ulated average signals ( µ p ( t ) comp , continuous thick red line) for all patients.All signals are reported as a function of the non-dimensional mean heartbeatperiod, RR . Visually, one can appreciate that the simulated signals well matchthe average measured signals, despite dissimilarities between the measured andcomputed shapes of the central pressure waveforms.To better quantify the accuracy of the model, we also determined, for eachpatient, the errors introduced by both the reference model (the one withoutthe patient-specific adjustments) and the patient-specific model in estimatingcentral systolic, diastolic, mean and pulse pressures with respect to the meanvalues of the related measured pressures indicated in Table 4. These results arereported in Table 5. It emerges that the reference model leads to higher meanerrors in central systolic (26.12 mmHg), mean (10.43 mmHg) and pulse (28.46mmHg) pressures compared with the patient-specific model (4.26, 4.98 and3.51 mmHg for systolic, mean and pulse pressures, respectively). Differently,slightly smaller mean errors occur in central diastolic pressure (5 mmHg) withrespect to the patient-specific model (5.86 mmHg). Based on these results, itis apparent that the adaptations to make the reference model patient-specificare effective in reproducing the patient-specific characteristics. For diastolicpressure, however, the mean error by the reference model is moderately lit-tler than by the patient-specific model. The reference model does not lead tosmaller errors in central diastolic BP for all the patients but for only five ofthe twelve patients, for which the error is drastically reduced. Since these fivepatients belong to three over the four recognized BP phenotypes (see Table4), it is difficult to identify clear correlations between the error in central di-astolic BP and one or more BP phenotypes. Thus, it should be verified ona greater number of patients whether (i) central diastolic pressure is smallerwith the reference than with the patient-specific model, and (ii) potential cor-relations between one or more BP phenotypes and the individual errors incentral diastolic BP exist.By adopting the patient-specific model, differences between measured andmodeled mean pressures appear quite acceptable. In fact, mean error is al-ways ≤ ≤ n-silico central blood pressure estimation 11 ( R ). The latter are equal to 0.95 and 0.67 for systolic and diastolic pressures,respectively, thereby reflecting a good correlation between measured and sim-ulated pressures, as well as larger errors by the model for diastolic pressuresthan for systolic pressures.Bland-Altman plots of the central systolic and diastolic pressure errors bythe model are depicted in Fig. 6. The coefficients of determination, R , for therelations between the central pressure error and the mean central pressure are0.035 for the systolic pressure and 0.11 for the diastolic pressure. Thus, thepresent data suggest that the error magnitude does not depend on the systolicpressure, even if it is slightly correlated to the diastolic pressure. In the present study, we propose a patient-specific mathematical model tononinvasively evaluate central BP, and test it against the invasive central BPmeasurements of twelve patients.Taking into account that this computational method does not require in-vasive pressure signals as input data, and it is just based on systolic/diastolicautomatic oscillometric brachial pressures and generic anthropometric pa-rameters, the comparison between computed and measured central pressurewaveforms seems satisfying. More in details, errors (absolute mean errors ± standard deviation) in systolic, diastolic, mean and pulse pressure for thetwelve patients are 4.26 ± ± ± ± ± ± ± ± ± ± patient-specific method to an oscillogram. The technique by Natarajan et al.yields errors in central systolic, diastolic and pulse BP between -0.6 and 2.6mmHg and corresponding standard deviation in the range 6.8-9 mmHg. Thus,despite the proposal by [58] produces extremely reduced mean errors withrespect to our model, standard deviations double compared to ours. Basedon this comparison, our model produces competitive results with respect tothe SphygmoCor and the generalized transfer function by Shih et al. [56,57],despite leading to larger mean errors than the physiology-based technique byNatarajan et al. [58]. However, considering a wider picture of medical devicesto estimate central BP, the modeling approach here proposed gives comparableresults. In fact, according to Papaioannou et al. [59] - which took into account22 validation studies of 11 medical devices involving a total of 808 subjects- the error in aortic systolic BP through noninvasive brachial BP calibrationis between -7.79 and -3.84 mmHg. Our patient-specific model, which leads toa mean error in central systolic BP of -4.26 mmHg, results among the best11% of the methods considered by [59] and adopting noninvasively measuredbrachial BP values for calibration. Even if this study is not able to providea definitive answer about the best prognostic parameter between central andbrachial BP, it offers a promising preliminary view of the in-silico approachin providing patient-specific central BP estimations, and represents a stimulusto exploit similar models to estimate additional individual hemodynamic mea-sures. Patient-specific models, in fact, apart for central BP evaluation, can beexploited to obtain further cardiac and vascular parameters, which can enrichthe hemodynamic picture of each patient.It is clear that the errors by our modeling approach largely depend on theerrors associated to the brachial oscillometric measurement, from which thebrachial mean and pulse BPs ( P m b and P P b ) adopted in the patient-specificcalibration of the reference model were extracted. The importance of these twoparameters in making the reference model patient-specific is, in fact, provedby the sensitivity analysis reported in section 2.3. Considering the latter, it ispredictable that any error associated to the input data P m b and P P b is trans-mitted (with the same order of magnitude) to the output data, namely thecentral BP values. Despite the automatic oscillometric device we adopted toassess brachial systolic and diastolic BP is widely used in clinical practice, nopeer-reviewed clinical validation information is available on this technology.It follows that a direct comparison between the input errors in the values of P m b and P P b and the output errors in the estimations of central BP for the 12patients is not possible here. Together with the brachial oscillometric measure-ments, also invasive BP recordings could be affected by bias. In fact, we didnot perform any specific assessment of the frequency response of our pressuremeasuring system, possibly introducing bias to our invasive BP measurements.As previously mentioned, no information on the wave form sampling rate ofthe pressure signal recording system has been provided by the manufacturer,that represents another potential source of bias in invasive BP values.As next steps in successive studies, we first recognize the need to increasethe number of test patients, which would allow one to estimate the actual n-silico central blood pressure estimation 13 model errors in central BP, and identify potential correlations between centralpressure errors and impacting factors, in order to further reduce the modelerrors. Then, a direct comparison between input and output errors should beexecuted, and output errors could be possibly reduced through more precisepatient-specific oscillometric BP measurement methods, like the one proposedby Liu et al. [60] and adopted by Natarajan et al. [58]. The proposed modeling approach exhibits a good patient-specific response.Despite it is not demonstrated to be superior to all the other methodologies tononinvasively estimate central BP, it shows acceptable approximation levels forcentral systolic BP evaluation with noninvasive brachial BP calibration, andcould be adopted not only for central BP but also for other central cardiacand vascular hemodynamic parameters on specific subjects. Further efforts areneeded to test the reliability of the present method, by extending the wholeprocedure to a larger cohort of individuals, and possibly reducing the inputerrors through more accurate oscillometric BP measurements techniques.
DeclarationsFunding
Not applicable.
Conflict of interest/Competing interests
The authors declare no competing interests.
Availability of data and material/Code availability
Data and material/code produced and analyzed during this study are availableon reasonable request.
All procedures followed were in accordance with the ethical standards of theresponsible committee on human experimentation (institutional and national)and with the Helsinki Declaration of 1975, as revised in 2000 (5). Informedconsent was obtained from all patients for being included in the study. Noanimal studies were carried out by the authors for this article.
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Figure legendsFig. 1
Schematic representation of the procedure adopted to make the refer-ence mathematical model patient-specific. HR , T vc and P m b are directly intro-duced to the model, while H , BSA (which is function of H and W through theDu Bois’s formula [26]), AGE , S and P P b are used in the empirical relationsto adapt the model parameters - arterial lengths, L art , aortic/carotid arterial n-silico central blood pressure estimation 17 diameters, D ca , aortic/carotid arterial thicknesses, h ca , aortic/carotid pulsewave velocities, P W V ca , end-systolic/end-diastolic left-ventricular elastancevalues, E es/ed , and venous compliances, C v - to the patient characteristics,starting from the reference values (subscript ref ) Fig. 2
Sensitivities of central systolic (sys), diastolic (dia), mean (mean)and pulse (pp) pressures to the input model parameters (age,
AGE , weight, W , height, H , heart rate, HR , mean left ventricular contraction time, T vc ,and mean and pulse brachial BPs, P m b and P P b ) for men Fig. 3
Schematic representation of the procedure implemented to test thepatient-specific multiscale model
Fig. 4
Measured central pressure signals ( µ p ( t ) , continuous thin blue line,and µ p ( t ) ± σ p ( t ) , dotted thin blue line) and corresponding simulated averagesignals ( µ p ( t ) ,comp , continuous thick red line). Time is made dimensionless bythe heartbeat period, RR Fig. 5
Scatter plots between computed (subscript comp) systolic (sys)and diastolic (dia) pressures and measured (subscript mea) values. R is thecoefficient of determination and continuous/dotted lines are the those of linearregression/equality Fig. 6
Bland-Altman plots of the central systolic (sys) and diastolic (dia)pressures errors by the model (sys err and dia err, respectively). µ and σ standfor the mean and standard deviation values of the pressure errors Figures
Fig. 1 -1-0.500.511.5 s AGE W H HR P m b PP b T vc Input parameters sysdiameanpp
Fig. 2 N o n i n v a s i v ed a t a I n v a s i v e da t a 𝑆, 𝐴𝐺𝐸,𝑊, 𝐻, 𝐻𝑅,𝑇 !" , 𝑃𝑃 , 𝑃 $ ! Patient-specificmultiscalemodel
MODEL INPUTSPRESSURE RECORDING AVERAGED SIGNAL MODEL OUTPUTSERROR EVALUATION
Fig. 3 n-silico central blood pressure estimation 19 P a sc ao r [ mm H g ] Patient 1 a) Patient 2 b) Patient 3 c) P a sc ao r [ mm H g ] Patient 4 d) Patient 5 e) Patient 6 f) P a sc ao r [ mm H g ] Patient 7 g) Patient 8 h) Patient 9 i) P a sc ao r [ mm H g ] Patient 10 j) Patient 11 k) Patient 12 l) Fig. 4
110 120 130 140 150 160 170 180 sys mea [mmHg] sys c o m p [ mm H g ] R =0.95 a)
55 60 65 70 75 80 85 dia mea [mmHg] d i a c o m p [ mm H g ] R =0.67 b) Fig. 5
110 120 130 140 150 160 170 180 sys mea [mmHg] -15-12-9-6-30369 sys e rr o r [ mm H g ] +2-2a)
55 65 75 85 dia mea [mmHg] -15-10-5051015 d i a e rr o r [ mm H g ] +2-2b) Fig. 6 n-silico central blood pressure estimation 21
Tables
Table 1
Regression coefficients expressing the variations in aortic lengths ( c ) - for bothwomen (subscript ,w ) and men (subscript ,m ) - and pulse wave velocities ( c linear coeffi-cients and c quadratic coefficients) with AGE according to Rylski et al. [24] and Hicksonet al. [43], respectively. Results are given for 4 different aortic tracts; 1: from the aortic valveto the origin of the brachiocephalic artery, 2: from the end of tract 1 to the the origin of theleft subclavian artery, 3: from the end of tract 2 to the origin of coeliac artery, and 4: fromthe end of tract 3 to the aortic bifurcation.
Aortic tract c ,w c ,m c c [mm/y/m ] [mm/y/m ] [mm/y] [mm/y ]1 0.22 0.21 1.8986 10 − − − − Table 2
Regression coefficients for women ( c ,w /c ,w ) and men ( c ,m /c ,m ) expressingthe variations in aortic and carotid diameters with AGE / BSA . Dependencies with
AGE are formulated according to Rylski et al. [24] (in [mm/y/m ]) and Kamenskiy et al. [31](in [mm/y]) for the aortic and carotid tracts, while dependencies with BSA according toDavis et al. [33] and Krejza et al. [35] (both in [mm/m ]) for the aortic and carotid tracts,respectively. Results are given for 6 different arterial tracts; 1: from the aortic valve to theorigin of the brachiocephalic artery, 2: from the end of tract 1 to the the origin of the leftsubclavian artery, 3: from the end of tract 2 to the origin of coeliac artery, 4: from the endof tract 3 to the aortic bifurcation, 5: along the right common carotid artery, and 6: alongthe left common carotid artery. Arterial tract c w , c w c ,m , c m Table 3
Anthropometric and clinical data, presence of comorbidities, like diabetes (d) andischemic heart disease (IHD), and smoking status (s) of patients. Averages and standarddeviation values of
AGE , W , H , HR , T vc , P P b and P m b are reported in bold in the lastrow. Patient
S AGE W H HR T vc P P b P mb d IHD snumber [years] [kg] [cm] [bpm] [s] [mmHg] [mmHg]1 m 72 61 170 63 0.38 63 75 x x2 f 68 81 175 65 0.39 50 94 x x3 m 73 81 170 80 0.34 62 1014 f 83 68 163 61 0.39 63 745 m 65 99 193 54 0.39 83 116 x6 f 81 69 167 63 0.36 74 93 x x x7 m 75 91 172 55 0.41 82 96 x x x8 m 62 77 175 61 0.41 55 829 f 72 60 167 51 0.39 78 91 x10 m 74 97 182 71 0.32 60 92 x11 f 73 64 162 62 0.39 88 9912 m 62 82 179 61 0.36 61 93 ± ± ± ± ± ± ± n-silico central blood pressure estimation 23 Table 4
Mean and standard deviations values of systolic (sys) and diastolic (dia) invasivepressures along the ascending aorta (AA), right brachial (RBA) and radial (RRA) arteries.Coefficients of variation are provided in percentage. The phenotype associated to each pa-tient (I, II, III, or IV, see text), identified as indicated by Picone et al. [54], is reported inbrackets below the Patient number.
Patient number AA RBA RRAsys dia sys dia sys dia[mmHg] [mmHg] [mmHg] [mmHg] [mmHg] [mmHg]1 114.54 58.21 124.38 59.53 154.59 64.41(I) ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± Table 5
Errors ([mmHg]) in simulated central systolic (sys), diastolic (dia), mean (mean)and pulse (pp) pressures through both the general (superscript G) and patient-specific (su-perscript PS) models, evaluated with respect to the mean values of the same invasive pres-sures along the ascending aorta (AA). Moduli of mean errors ± standard deviation arereported in bold in the last row. Patient General model Patient-specific modelsys G dia G mean G pp G sys PS dia PS mean PS pp PS ± ± ± ± ± ± ± ±±