Model-Based Pul­se Wave Ana­ly­sis (mbPWA) — Taking a new path in car­dio­vas­cu­lar diagnostics

Model-based Pul­se Wave Ana­ly­sis (mbPWA)

Taking a new path in car­dio­vas­cu­lar diagnostics

Our dis­rup­ti­ve car­dio­vas­cu­lar dia­gno­stic prin­ci­ple draws upon an arte­ri­al tree model from the 1960s. We refi­ned it cru­ci­al­ly and brought it to per­fec­tion. The con­vin­cing result: a dia­gno­stic pro­ce­du­re that mea­su­res non-inva­si­ve­ly yet direct­ly — wit­hout any detours.

With the help of a vir­tual­ly gene­ra­ted, rea­li­stic model of the human arte­ri­al vas­cu­lar tree, we deter­mi­ne the cen­tral blood pres­su­re via peri­phe­ral­ly recor­ded pul­se pres­su­re cur­ves. As pre­cise as if you were loo­king direct­ly into the arte­ries. Our dia­gno­stic approach reli­es on an algo­rithm-based simu­la­ti­on of each patient’s actu­al arterial/cardiovascular con­di­ti­on. It works enti­re­ly wit­hout any fal­si­fy­ing sur­ro­ga­te parameters.

We chall­enge pre­vious dia­gno­stic approa­ches such as arte­ri­al appl­ana­ti­on tono­me­try: Ins­tead of an under­ly­ing popu­la­ti­on avera­ge, our data are based on actu­al, indi­vi­du­al pati­ent cha­rac­te­ristics. For the first time, this enables us to obtain mea­su­re­ment results that visua­li­ze the cur­rent con­di­ti­on within the heart and the arte­ries on a 1:1 basis.

Our approach is not­hing less than a breakth­rough for dia­gno­stics and the­ra­py — and thus signi­fi­cant­ly impro­ves pati­ents’ qua­li­ty of life: Doc­tors can detect and tre­at car­dio­vas­cu­lar end-organ dama­ge much ear­lier than pre­vious­ly pos­si­ble. In addi­ti­on, the­ra­peu­tic inter­ven­ti­ons can be tra­cked with pin­point accu­ra­cy and adjus­ted with much hig­her fle­xi­bi­li­ty than ever before.

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The Hemo­dy­na­mic Background

Models are an essen­ti­al tool when­ever the goal is to sim­pli­fy com­plex pro­ces­ses and illus­tra­te under­ly­ing mecha­nisms and func­tions. When sear­ching for exem­pla­ry images of the arte­ri­al sys­tem, one encoun­ters a who­le ran­ge of dif­fe­rent expl­ana­to­ry approa­ches or constructs.

Human blood cir­cu­la­ti­on models work with tube and dis­tri­bu­ti­on models based on the human ana­to­my. Sim­pli­fied cir­cuit models are ano­ther opti­on. They trace blood flow and the pro­pa­ga­ti­on of the pres­su­re wave gene­ra­ted by the heart through pul­se waves (cur­rent pul­se and pres­su­re pul­se). Against this back­ground, the human arte­ri­al vas­cu­lar tree can be recrea­ted using so-cal­led mul­ti­com­part­ment­al models and employ­ing elec­tri­cal com­pon­ents: In ana­lo­gy to the blood flow in the cir­cu­la­to­ry sys­tem and the flow pro­per­ties of elec­tric cur­rent, one can work with the pro­per­ties of resis­tor cir­cuits R, induc­tor cir­cuits L, and capa­ci­tor cir­cuits C (RLC) to repre­sent phy­si­cal pro­per­ties of the arteries.

A hard­ware-based pri­mal model as the start­ing point of Model-based Pul­se Wave Ana­ly­sis (mbPWA)

A team of sci­en­tists led by Abra­ham Noor­der­graaf and, in fur­ther revi­si­on, Nico­laas Wes­ter­hof and col­la­bo­ra­tors first intro­du­ced a hard­ware-based, hand-wired approach to mode­ling the human arte­ri­al sys­tem in the 1960s in the United Sta­tes. Ear­lier, this was pri­ma­ri­ly based on mathe­ma­ti­cal or phy­si­cal models. In the final ver­si­on of the model, a total of 113 hard­ware RLC cir­cuits were inter­con­nec­ted to mimic the archi­tec­tu­re of the arte­ri­al tree. Each seg­ment repres­ents about 2 to 8 cm of a ves­sel. While seri­al­ly con­nec­ted resis­tors and induc­tors mimic the con­duc­tance of an artery and the vis­cous and iner­ti­al pro­per­ties of blood (lon­gi­tu­di­nal impe­dance), capa­ci­tors cor­re­spond to wall com­pli­ance (trans­ver­se impe­dance).

Tech­ni­cal Challenges

The ope­ra­bi­li­ty and mecha­ni­cal effort invol­ved in the manu­al pro­duc­tion of a pas­si­ve elec­tro­nic ana­log of the human arte­ri­al tree still posed a real chall­enge in the 1960s. The­r­e­fo­re, Noordergraaf’s model ver­si­on and the ver­si­on later revi­sed by Wes­ter­hof included a who­le series of tech­ni­cal con­ces­si­ons, in par­ti­cu­lar, the com­bi­na­ti­on of indi­vi­du­al wind­kes­sel ele­ments (“lum­ping”) into one sin­gle com­po­nent. Initi­al­ly, the arte­ri­al pro­per­ties (resis­tance, com­pli­ance, and blood mass iner­tia) were deter­mi­ned for 1‑cm arte­ri­al seg­ments, which would have resul­ted in more than 700 wind­kes­sel ele­ments for the model.

The ori­gi­nal cal­cu­la­ti­on base 

Noordergraaf’s solu­ti­on was to radi­cal­ly limit the immense manu­al effort that would have been invol­ved in buil­ding 700 wind­kes­sel ele­ments. He redu­ced their num­ber in the final ver­si­on to about 100 com­pon­ents the team had to assem­ble in hard­ware. Noor­der­graaf descri­bes the rela­ti­onship bet­ween the lum­ped R, L, and C values for each lum­ped size Δx ver­sus the R’, L’, and C’ cal­cu­la­ted for the 1 cm size using the fol­lo­wing formula:

L = L’ Δx, R = R’ Δx, C = C’ Δx


The pro­blem of redu­ced complexity

Howe­ver, the model setup’s redu­ced com­ple­xi­ty came at the cost of dis­tor­ted repro­duc­tion of the natu­ral flow pro­per­ties: The cou­pling of wind­kes­sel units igno­red the actu­al reso­nan­ce pro­per­ties of the arte­ri­al seg­ments and their importance for trans­mit­ting the pul­se wave. Noor­der­graaf was well awa­re of the height of the reso­nan­ce peaks’ height dis­tor­ti­on. Howe­ver, he did not attach much importance to this fact becau­se today’s modern simu­la­ti­on tools still nee­ded to be deve­lo­ped. Wes­ter­hof later adopted Noordergraaf’s so-cal­led lum­ped for­mu­las in his impro­ved model.

Our solu­ti­on: The vir­tual­ly refi­ned Wes­ter­hof model

Using sta­te-of-the-art soft­ware simu­la­ti­on tools, we could faithful­ly repro­du­ce the model crea­ted by Noor­der­graaf, later revi­sed by Wes­ter­hof and col­le­agues. During count­less test runs, we simu­la­ted various typi­cal arte­ri­al con­di­ti­ons. Thus, we gai­ned essen­ti­al insights into under­stan­ding the over­all con­text and impro­ve­ment of its behavior.

In the sub­se­quent cor­rec­tion and refi­ne­ment of the model — in con­trast to Wes­ter­hof and Noor­der­graf — we atta­ched par­ti­cu­lar importance to the pre­ser­va­ti­on of the reso­nant fre­quen­ci­es, which we belie­ved to be of dra­ma­tic importance: We pre­ser­ved them in the new model within the indi­vi­du­al 1cm arte­ri­al segments.

Thus, in the end, we com­ple­te­ly remo­ved the Noor­der­graaf-Wes­ter­hof model’s tech­no­lo­gi­cal limi­ta­ti­ons. As a result, the over­all model qua­li­ty impro­ved signi­fi­cant­ly: while the model refi­ned by Wes­ter­hof con­sis­ted of 121 Wind­kes­sel ele­ments, our refi­ned model has 711 com­pon­ents. Con­se­quent­ly, our arte­ri­al tree simu­la­ti­on pro­vi­des rea­li­stic pul­se wave­forms of the aor­ta and the bra­chi­al and radi­al arte­ries. The same is true for the true-to-life repro­duc­tion of various blood pres­su­res. 

The befo­re-and-after effect: From the Noordergraaf/Westerhof model to the vas­cu­lar avatar

Mul­ti­ple cou­pled reso­nan­ces ins­tead of a reflec­ted wave

The new arte­ri­al tree model yiel­ded new insights regar­ding the ori­g­ins of the phy­sio­lo­gi­cal aor­tic-radi­al trans­fer func­tion: We belie­ve it is attri­bu­ta­ble to the cou­pling of many small reso­nan­ce ele­ments within a com­plex arte­ri­al tree.

This enti­re­ly new insight offers an alter­na­ti­ve expl­ana­ti­on and a signi­fi­cant­ly more plau­si­ble theo­re­ti­cal approach to the cur­rent (albeit con­tro­ver­si­al any­way) doc­tri­ne that attri­bu­tes the secon­da­ry systo­lic peak to arte­ri­al pres­su­re wave reflec­tion. Our hypo­the­sis of mul­ti­ple cou­pled reso­nan­ces within the arte­ri­al sys­tem is fur­ther sup­port­ed by the fact that the refi­ned model is not enti­re­ly new. The final ver­si­on of our model mere­ly cor­rec­ted seve­ral sim­pli­fi­ca­ti­ons in the ori­gi­nal Wes­ter­hof model that had resul­ted in reso­nan­ce fre­quen­ci­es that were much too low.

As our expe­ri­ments with the refi­ned model show, the aor­tic-radi­al trans­fer func­tion evol­ves along the path from the ascen­ding aor­ta to the radi­al artery. Simi­lar­ly, the secon­da­ry systo­lic waves do not ari­se at spe­ci­fic distal sites but form along the enti­re way from the ascen­ding aor­ta to the point whe­re they are mea­su­red. Thus, for the first time, the for­ma­ti­on of the known aor­tic-radi­al trans­fer func­tion can be explai­ned and demons­tra­ted in an indi­vi­dua­li­zed arte­ri­al tree model.

The phy­sio­lo­gy of dyna­mic blood flow in caro­tid stenosis

A rea­li­stic image of the arteries

To under­stand the dis­rup­ti­ve novel­ty of the refi­ned model, we should con­sider the fol­lo­wing: The ori­gi­nal Noordergraaf/Westerhof model from the 1960s repro­du­ced the arte­ri­al sys­tem of a 26-year-old man. The­r­e­fo­re, it was mere­ly an object for visua­liza­ti­on and stu­dy. Howe­ver, the refi­ned model, per­fec­ted through modern soft­ware tools, is the exact oppo­si­te of an idea­li­zed model of any human being. In con­trast to a mere illus­tra­ti­ve model, the new model is adap­ta­ble to the arte­ri­al tree of any real person.

This is a revo­lu­tio­na­ry, com­ple­te­ly new approach, which con­se­quent­ly goes hand in hand with an equal­ly inno­va­ti­ve mea­su­re­ment method. As descri­bed abo­ve, the initi­al focus in the deve­lo­p­ment of the new mea­su­re­ment method was on gene­ra­ting rea­li­stic pul­se wave­forms. Once this was achie­ved, the cli­ni­cal bene­fits of the new model were imme­dia­te­ly obvious: The arti­fi­ci­al arte­ri­al sys­tem of the arte­ri­al tree model can now be adapt­ed to a real pati­ent. Thus, the new­ly crea­ted model pro­vi­des valuable sup­port in car­dio­vas­cu­lar dia­gno­stics and pre­ven­ti­on in a varie­ty of ways. The high­light: What could not be mea­su­red in real life wit­hout inva­si­ve mea­su­res (e.g. high-risk car­diac cathe­ter exami­na­ti­ons), can now be read wit­hout pro­blems in simu­la­tio­ne, i.e. based on the image of a living per­son — in the vas­cu­lar avatar.

Abnor­mal or patho­lo­gi­cal vas­cu­lar con­di­ti­ons may mani­fest in increased con­duc­tion resis­tance R (e.g., steno­sis, throm­bo­sis, vas­cu­lar tone dys­func­tion), increased iner­ti­al pro­per­ties of blood L (e.g., high hema­to­crit), or low arte­ri­al com­pli­ance C (e.g., stiff or infla­med arte­ries due to arte­rios­cle­ro­sis or atheros­cle­ro­sis). The indi­vi­du­al mul­ti­pli­ers dMult, lMult, and cMult obvious­ly cor­re­spond very well with an individual’s spe­ci­fic arterial/cardiovascular health status.

Eva­lua­ti­on of a Model-based Pul­se Wave Ana­ly­sis (mbPWA) measurement

Cli­ni­cal Applications 

Our insights con­cer­ning the reso­nant natu­re of the aor­tic-radi­al trans­fer func­tion qua­li­fy for rese­arch and edu­ca­tio­nal pur­po­ses. In addi­ti­on, the indi­vi­dua­li­zed trans­fer func­tion deri­ved from our refi­ned model incor­po­ra­tes dif­fe­rent pati­ent cha­rac­te­ristics. The­r­e­fo­re, one can also app­ly it to deter­mi­ne central/aortic blood pres­su­re (cBP) values.

Cen­tral vs. bra­chi­al: visua­li­zing medi­ca­ti­on effects, adjus­ting therapies

Non-inva­si­ve mea­su­re­ments of cen­tral blood pres­su­re are signi­fi­cant­ly instru­men­tal in the cli­ni­cal con­text. Our fin­dings are of par­ti­cu­lar ele­van­ce when trea­ting hyper­ten­si­ve pati­ents: Upon deter­mi­ning their cen­tral blood pres­su­re values, striking dif­fe­ren­ces in the mode of action bet­ween dif­fe­rent anti­hy­per­ten­si­ve drugs beco­me appa­rent. For ins­tance, the anti­hy­per­ten­si­ve effect of beta-blo­ckers is often ove­re­sti­ma­ted. This ove­re­sti­ma­ti­on may be due to chan­ges in arte­ri­al pro­per­ties cau­sed by bra­dy­car­dia, incre­asing cen­tral systo­lic pres­su­re, and pul­se pres­su­re. While fur­ther mecha­ni­stic stu­dies are still pen­ding in this regard, the­re is no doubt that our indi­vi­dua­li­zed arte­ri­al tree model is of gre­at use for pro­s­pec­ti­ve, soft­ware-based inves­ti­ga­ti­ons of various drug effects.

Asi­de from the fact that it is often neces­sa­ry and in the patient’s best inte­rest to reas­sess the pre­scrip­ti­on of beta-blo­ckers, the­re is also an over­ar­ching, gene­ral bene­fit. Doc­tors can tail­or any medi­cal hyper­ten­si­on the­ra­py to the indi­vi­du­al needs and poten­ti­al com­or­bi­di­ties of pati­ents much more effec­tively than would be pos­si­ble with purely bra­chi­al data by using the cen­tral, signi­fi­cant­ly more meaningful blood pres­su­re values. Repea­ted con­trol mea­su­re­ments during tre­at­ment allow phy­si­ci­ans to ensu­re that desi­red the­ra­peu­tic effects occur as expec­ted — in the case of purely phar­ma­co­lo­gi­cal inter­ven­ti­on, for exam­p­le, by chan­ging drug clas­ses, incre­asing or redu­cing doses, or using com­bi­na­ti­on the­ra­py. Mea­su­re­ments of aor­tic blood pres­su­re also pro­vi­de infor­ma­ti­on on whe­ther pati­ents at an ear­ly stage of car­dio­vas­cu­lar impair­ment can at least redu­ce an exis­ting medi­ca­ti­on after con­sul­ta­ti­on with the phy­si­ci­an purely through effec­ti­ve life­style chan­ges or even dis­con­ti­nue it enti­re­ly after some time. Pro­vi­ded pati­ents stick to a health-pro­mo­ting life­style, they can often avo­id taking an anti­hy­per­ten­si­ve medi­ca­ti­on altog­e­ther for a long time. Cen­tral blood pres­su­re data (coll­ec­ted at regu­lar inter­vals) are of cru­cial importance here, as they reflect the actu­al con­di­ti­on and hence, the heart’s func­tion­a­li­ty, in con­trast to bra­chi­al-deter­mi­ned values.

Hemo­dy­na­mic Para­me­ters and Vas­cu­lar Age

Inva­si­ve deter­mi­na­ti­on of cen­tral hemo­dy­na­mic para­me­ters show­ed an asso­cia­ti­on bet­ween fle­xi­on time and aug­men­ta­ti­on index of the ascen­ding aor­ta and the risk of coro­na­ry artery dise­a­se in sym­pto­ma­tic high-risk pati­ents. The­se fin­dings were con­firm­ed non­in­va­si­ve­ly by appl­ana­ti­on tonometry.

Howe­ver, the­se con­ven­tio­nal para­me­ters repre­sent mere­ly indi­rect indi­ca­tors of arte­ri­al pro­per­ties. We pos­tu­la­te that the adap­ti­on fac­tors used in the refi­ned model direct­ly cor­re­spond to the total arte­ri­al con­duc­tion resis­tance (dMult), blood iner­tia (lMult), and arte­ri­al wall com­pli­ance (cMult) of an indi­vi­du­al pati­ent. They repre­sent dif­fe­rent health sta­tes. The­r­e­fo­re, they are bene­fi­ci­al for esti­mat­ing bio­lo­gi­cal vas­cu­lar age (often devia­ting signi­fi­cant­ly from the actu­al age).

An ear­ly war­ning sys­tem for endo­the­li­al damage

The abili­ty to con­trol vas­cu­lar tone is impai­red by aging and by endo­the­li­al dys­func­tion. This leads to hyper­ten­si­on and atheros­cle­ro­sis. We hypo­the­si­ze that such a dys­ba­lan­ce of vas­cu­lar tone is also pre­sent at rest. This, in turn, is the basis of our hypo­the­sis that increased con­duc­tion resis­tance detec­ted with the refi­ned model could be an ear­ly indi­ca­tor of endo­the­li­al imba­lan­ce and atheros­cle­ro­sis. This working hypo­the­sis should be vali­da­ted in a cli­ni­cal tri­al, e.g. by mea­su­ring flow-media­ted dila­ti­on (FMD) as the accept­ed gold standard.

In addi­ti­on, we recom­mend fur­ther stu­dies to eva­lua­te the poten­ti­al of the arti­fi­ci­al artery model for risk pre­dic­tion. Among other things, it could be used to gui­de the inva­si­ve assess­ment of pati­ents at risk for pre­ma­tu­re coro­na­ry artery dise­a­se.