Design and Opti­miza­tion of Ven­tric­u­lar Assist Devices

The design of ven­tric­u­lar assist devices is quite lit­er­ally a matter close to our hearts. A ven­tric­u­lar assist device (or VAD) is an electro­mechan­i­cal pump for assist­ing cardiac cir­cu­la­tion, which is used to par­tially replace the function of a weakened or failing heart. VADs are designed to assist either the right ven­tri­cle (RVAD) or the left ven­tri­cle (LVAD), or to assist both ven­tri­cles (BiVAD). Some are for short-term use, typ­i­cally for patients recov­er­ing from myocar­dial infarc­tion (heart attack) or cardiac surgery; some are for long-term use, typ­i­cally for patients suf­fer­ing from advanced con­ges­tive heart failure. Normally, the long-term VAD is used as a bridge-to-trans­plant — keeping the patient alive in rea­son­ably good con­di­tion, while being able to await the heart trans­plant outside of the hospital. In some instances, however, VADs are also used as des­ti­na­tion therapy, which is an alter­na­tive to heart trans­plant. Des­ti­na­tion therapy provides long-term support in patients who are not can­di­dates for transplant.

Ven­tric­u­lar Assist Devices: Pul­satile Pumps vs. Con­tin­u­ous Flow Pumps

The pumps used in ven­tric­u­lar assist devices can be divided into two main cat­e­gories — pul­satile pumps that mimic the natural pulsing action of the heart, and con­tin­u­ous flow pumps. Pul­satile VADs use positive dis­place­ment pumps. Con­tin­u­ous-flow VADs are smaller and have proven to be more durable than pul­satile VADs. They normally use either a cen­trifu­gal pump or an axial flow pump.

Adverse Events

Thrombus for­ma­tion, Acquired von­Wille­brand Syndrome (AvWS), and hemol­y­sis are frequent adverse events asso­ci­ated with ven­tric­u­lar assist devices. These events are pri­mar­ily depen­dent on shear stress, strain rate, and tur­bu­lent energy dis­si­pa­tion in the fluid, which can be approx­i­mated based on the velocity fields obtained from exper­i­men­tal flow visu­al­iza­tion or com­pu­ta­tional fluid dynamics (CFD). Through manip­u­lat­ing and opti­miz­ing the device’s com­po­nents, such as the rotor and casing geome­tries, these prop­er­ties can be altered and con­trolled in such ways as to minimize the adverse events men­tioned above. 

Example Case: Ven­tric­u­lar Assist Device Design with CONVERGE

This example case is part of an ongoing project carried out in the Division of Applied Bio­med­ical Engi­neer­ing at the Penn State College of Medicine. The subject of the study is a cen­trifu­gal pump intended for right heart support (RVAD), and more specif­i­cally – in this first step – its impeller. The goal is to create a flexible para­met­ric model for the impeller in CAESES® to be able to quickly and easily create design variants that, in con­nec­tion to the CFD solver CONVERGE CFD, are used to predict pump per­for­mance curves (HQ) or for CFD-driven opti­miza­tion aimed at reducing the tur­bu­lent energy dis­si­pa­tion (EPS) and recir­cu­la­tion regions in the pump. 

Geometry Setup

The baseline geometry of the impeller had pre­vi­ously been designed in SOLID­WORKS and con­sisted of a toroidal rotor body, nec­es­sary for the magnetic drive, and three straight vertical blades that are superior facing, while in vivo. While this simple design may seem crude, it proved to be rel­a­tively blood-friendly in pre­lim­i­nary trials, when compared to other poten­tial solu­tions, such as foil-shaped blades.

To further evolve this initial design, it was decided to add a fairing – basi­cally, a wedge – on the suction side of the blades in the para­met­ric CAESES® model. The suction side is of great interest, as it is believed to dictate both the mag­ni­tude and shape of the recir­cu­la­tion region behind the blade, as well as the surface effects on the rotor surface.

The inner surface of the suction side fairing is modeled with a B‑Spline curve that allows for a flexible vari­a­tion of its shape, under control of a few ded­i­cated para­me­ters. Addi­tional geometry para­me­ters control the size of the blades in radial and cir­cum­fer­en­tial direc­tion, the fillet radii on the corners of the geometry, and the number of blades.

CONVERGE Automa­tion

The impeller geometry, as well as the other parts of the pump’s fluid domain, that had pre­vi­ously been imported in CAESES®, are exported to CONVERGE CFD in its pro­pri­etary, tes­sel­lated ​“surface.dat” format that allows to identify surface patches by their color and boundary ID. This is needed for being able to replace the geometry in the opti­miza­tion process, while keeping the asso­cia­tiv­ity and auto­mat­i­cally assign­ing the correct boundary settings. Fur­ther­more, dis­tin­guish­ing dif­fer­ent bound­aries also allows for more local­ized pre­dic­tions of values such as EPS and strain rate. Sim­u­la­tion control can be admin­is­tered through CAESES® using the CONVERGE CFD input files in the Software Con­nec­tor. The boundary con­di­tions of the blood pump (such as inlet flow rates, outlet pressure, and rotor speed), sim­u­la­tion para­me­ters (such as sim­u­la­tion end time, time step sizes, and grid size), and com­pu­ta­tional power (the number of cores used) can all be turned into para­me­ters, allowing the user to adjust and run new CONVERGE CFD sim­u­la­tions – manually or auto­mat­i­cally – without the need for opening the CONVERGE CFD inter­face. Pump per­for­mance pre­dic­tion consists of creating HQ (pressure head vs. flow) curves for a given pump and rotor con­fig­u­ra­tion. The Design Assem­bler engine in CAESES® (that allows the user to pre­scribe specific com­bi­na­tions of values) was used to conduct the HQ sim­u­la­tions, allowing for multiple flow rates and speeds to be tested effi­ciently in an auto­mated fashion. The effi­ciency and volute region averaged EPS can be plotted along with the standard HQ curves to create 3D plots that allow for a more com­pre­hen­sive per­for­mance evaluation.

The results show that the HQ vs. effi­ciency surface is convex in nature, and appears to have at least a local maximum for effi­ciency (if not an absolute maximum). Running more con­di­tions at higher speeds could reveal if the most effi­cient range has already been dis­cov­ered. The HQ vs. volute average EPS surface has a positive slope pre­dom­i­nantly in the speed and delta P direc­tions, and there­fore a stronger depen­dency from these quan­ti­ties. While there also is a depen­dency from the flow rate, it is less pro­nounced. The fol­low­ing picture shows cross-sec­tional planes of the inlets/​outlet of the pump which show the presence of PlHb (plasma free hemo­glo­bin) as the sim­u­la­tion runs. PlHb levels increase with the presence of hemol­y­sis, and it is cal­cu­lated based on the tur­bu­lent energy dis­si­pa­tion user-defined function in CONVERGE CFD.

Opti­miza­tion Process and Results

Exploratory studies on the rotor design para­me­ters were con­ducted using both the Design Assem­bler and a Latin Hyper­cube Sampling. As a very broad approach meant to find the func­tional domain of the design para­me­ters, the Design Assem­bler can be used first to set larger inter­vals for the para­me­ters to be tested, before refining the para­me­ter domains, in order to be com­pu­ta­tion­ally effi­cient with limited resources. This was followed up with a DoE (Design of Exper­i­ments) process using a Latin Hyper­cube Sampling method that provides a proper sen­si­tiv­ity analysis within the refined range of the design para­me­ters. Finally, a local opti­miza­tion was started in a promis­ing region of the design space, as iden­ti­fied by the previous DoE process.

The data col­lected from the DoE studies has revealed the cor­re­la­tions of the con­sid­ered rotor para­me­ters to the EPS, which will help to drive future opti­miza­tions. Here, the length of the fairing behind the blades seemed to have the most rec­og­niz­able trend with the volute average EPS eval­u­a­tion. The effects on the rotor surface EPS eval­u­a­tion would be inter­est­ing to discover in more detail, as both EPS eval­u­a­tions appear to be inversely related. Con­tin­u­ing to uncover the effects of the suction side geometry on EPS, the local opti­miza­tion results show the same well visible rela­tion­ship between the fairing length and both EPS eval­u­a­tions, and the offset from the inner blade corner to the central hole of the toroidal rotor body seems to show a rela­tion­ship as well. However, this first opti­miza­tion was only run with 10 designs so these rela­tion­ships will be more com­pre­hen­sively under­stood once more data is collected. 

Outlook

While the inves­ti­ga­tions so far had been carried out on local resources of the Division of Applied Bio­med­ical Engi­neer­ing, future studies will move to the High Per­for­mance Com­put­ing center of the Penn State College of Medicine. With the increase in com­pu­ta­tional power, the plan is to conduct more exten­sive opti­miza­tions, includ­ing addi­tional geometry vari­ables, as well as more expen­sive eval­u­a­tions, involv­ing longer solve times, smaller grids sizes and LES com­pu­ta­tions, using a user defined EPS-based hemol­y­sis model, as well as a strain rate based model for thrombus sus­cep­ti­bil­ity poten­tial. Also, addi­tional com­po­nents of the RVAD are going to be para­me­ter­ized and con­sid­ered in the opti­miza­tion studies, such as – most promi­nently – the volute casing.

CAESES’ VAD Design Capabilities

CAESES® is being used to design state-of-the-art VADs and brings along several key capa­bil­i­ties for this task.

• CAESES® contains DoE/​optimization algo­rithms, workflow man­age­ment, inter­faces to external sim­u­la­tion codes and a highly spe­cial­ized para­met­ric CAD system. All of which are critical com­po­nents for setting up an auto­mated design process.
• Robust vari­a­tion of the VAD geometry is possible with no failed variants. As for other geome­tries, one of the most impor­tant targets of our software is 100% robust geometry vari­a­tion, obtained by smart para­me­ter­i­za­tion and depen­dency-based models.
• CAESES®’ powerful Meta Surface tech­nol­ogy – were a para­me­ter­ized cross-section is swept in a spec­i­fied direc­tion, e.g., along a path, and function curves control how the cross-section para­me­ters change during the sweep – allows for a highly flexible, while very effi­cient, para­met­ric descrip­tion of complex, free-formed, shapes (such as impeller blades or volutes).
• Arbi­trary con­straints can be built into the model or mon­i­tored. Typical examples are man­u­fac­tur­ing or pack­ag­ing constraints.
• The geometry can be exported in several dif­fer­ent formats suitable for your CFD/​meshing tools. Many of the formats support patch naming, so that the down­stream tool can cor­rectly identify surface patches for the assign­ment of indi­vid­ual mesh settings or boundary conditions.

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