Artificial Intelligence and Numerical Methods Aided Design of

Patient-Specific Coronary Stents

William Solórzano-Requejo

1,2 a

, Carlos Aguilar

, Rodrigo Zapata Martínez

Oscar Contreras-Almengor

, Isabel Moscol

, Carlos Ojeda

, Jon Molina-Aldareguia

1,3 g

and Andrés Díaz Lantada

ETSI Industriales, Universidad Politécnica de Madrid, Madrid, Spain

Department of Mechanical and Electrical Engineering, Universidad de Piura, Piura, Peru

IMDEA Materials Institute, Getafe, Spain

Keywords: Machine Learning, Computational Design, Personalized Medicine, Automated Design, Additive

Manufacturing.

Abstract: The design of personalized medical devices, which are adapted to the patient’s needs, starts from a digital

model created from the advanced use of clinical imaging techniques such as magnetic resonance imaging or

computed tomography. However, this methodology has several sources of error related to the medical imaging

acquisition, segmentation and reverse engineering process, tessellation, and the selected additive

manufacturing technique. Therefore, this paper proposes a new design strategy that avoids medical image

segmentation. To demonstrate its feasibility, a patient-specific coronary stent was designed and manufactured

based on slices similar to medical images. Using artificial intelligence algorithms and numerical methods, the

ellipse that best fit the patient’s artery was obtained, and finally customized stent was generated from the

parameterization of unit cells, demonstrating that it is possible to semi-automate the design of biodevices by

removing some sources of error inherent to the conventional workflow.

1 INTRODUCTION

Cardiovascular diseases have become an increasingly

serious threat to human life. In particular, coronary

artery disease is a major health and economic burden,

and the third leading cause of death worldwide (Scafa

Udriște et al., 2021). It develops when fatty

substances, such as fat, calcium, and cellular debris,

are deposited in the arterial wall obstructing blood

flow and triggering an inadequate supply of oxygen

and nutrients to the myocardium, potentially inducing

a heart attack, brain haemorrhage or ischemic stroke

(Pan et al., 2021).

https://orcid.org/0000-0002-2989-9166

https://orcid.org/0000-0003-0291-3041

https://orcid.org/0000-0002-2611-7050

https://orcid.org/0000-0002-8166-4161

https://orcid.org/0000-0001-8959-9547

https://orcid.org/0000-0001-6163-5382

https://orcid.org/0000-0003-3508-6003

https://orcid.org/0000-0002-0358-9186

The most common treatment is the percutaneous

coronary intervention (PCI), a minimally invasive

and effective surgery used to clean the artery by

introducing a tubular metallic structure (stent) inside

it, whose objective is to restore the cardiovascular

system function through the expansion of the arterial

wall, decreasing the risk of restenosis (Saçlı et al.,

2018).

Top-class coronary stent must have mechanical

properties like high elasticity and flexibility to allow

coiling and expansion in the blood vessel; high radial

and fatigue strength to withstand periodic

physiological loads; good biocompatibility to reduce

the incidence of thrombosis and restenosis and good

Solórzano-Requejo, W., Aguilar, C., Zapata Martínez, R., Contreras-Almengor, O., Moscol, I., Ojeda, C., Molina-Aldareguia, J. and Diaz Lantada, A.

Artiﬁcial Intelligence and Numerical Methods Aided Design of Patient-Speciﬁc Coronary Stents.

DOI: 10.5220/0011639000003414

In Proceedings of the 16th International Joint Conference on Biomedical Engineering Systems and Technologies (BIOSTEC 2023) - Volume 1: BIODEVICES, pages 37-45

ISBN: 978-989-758-631-6; ISSN: 2184-4305

 2023 by SCITEPRESS – Science and Technology Publications, Lda. Under CC license (CC BY-NC-ND 4.0)

radiopacity on fluoroscopy for long-term follow-up

(Cockerill et al., 2021; Scafa Udriște et al., 2021;

Tomberli et al., 2018). Stents are prevalently

manufactured with standard dimensions and shapes.

Surgeons select the one that best fits the patient’s

anatomy. However, mismatch between the implant

and the anatomy affects its performance and lifespan.

Follow-up studies have proven that, one year after

implantation, the probability of restenosis is up to

40%, and around 10% of patients need a new

prosthesis (Pan et al., 2021; Schillinger et al., 2007).

This is the consequence of geometrical changes in a

coronary artery after surgery due to the difference in

size between the expanded stent and the blood vessel.

If the stent does not fit to the diseased artery, a strong

interaction force will be generated resulting in stress

concentration, damaging the artery, and eventually

leading to restenosis (Wang et al., 2018). This

pathology is a major challenge; therefore, the

combination of medical and mechanical design can

improve significantly the function of vascular

prostheses to meet the needs of patients and hospitals

worldwide.

Current trends around the production and design

of personalized medical devices have integrated

clinical information about the patient’s anatomy,

ranging from single-unit production using manual

techniques to fully automated manufacturing with a

rapid, non-invasive and more accurate approach

(Paxton et al., 2022).

Soft tissue reconstruction from computed

tomography (CT) or magnetic resonance (MR) slices

provides an additional view of the patient’s

pathological state that helps to optimize stent fitting.

This whole process, including the reconstruction,

personalized design, and manufacturing to get the

final cardiovascular device entails a high

computational cost and has several sources of error

(Díaz Lantada et al., 2022).

Around the slice acquisition, as consequence of

the resolution (pixels) and the thickness of the slices,

an error occurs because to reconstruct the 3D model

the designer must properly select the voxels that

compose it (segmentation). Then, it will be exported

as an STL file, which gives rise to the second error

resulting from the separation between voxels and

triangular facets due to the action of smoothing tools.

This digital artery allows the designer to model the

custom medical device and export it as an STL file,

generating the third error due to the tessellation

process (Figure 1).

Custom-made implants are generally produced

with additive manufacturing (AM) technology.

Depending on the type of AM, different layer heights

are required, creating a staircase effect. The error

associated with this effect is less significant compared

to the medical imaging acquisition, due to the

differences in the magnitudes of the layer thickness,

however, this generates the fourth source of error

(Figure 1).

All the errors described affect the final product.

Although the inaccuracy associated with medical

image and the selected manufacturing process is not

easy to avoid, the one related to segmentation can be

mitigated by capturing the patient’s physiologic

information from the image, using an algorithm that

extracts its edge and allows the designer to model on

it. This is the objective of this paper, focused on

Figure 1: Patient-specific stent workflow errors.

Figure 2: Roadmap.

BIODEVICES 2023 - 16th International Conference on Biomedical Electronics and Devices

coronary stents, which integrates artificial

intelligence, numerical methods, and computer-aided

design to produce personalized implants that reduce

the possibility of failure.

2 MATERIALS AND METHODS

This section details the basics of medical image edge

extraction (2.1), inner and outer edge separation (2.2),

algebraic fitting (2.3), and enhancement employing

the random sample consensus algorithm (RANSAC,

2.4) to obtain information from tomographic slices of

a coronary artery and design a stent that matches the

patient's anatomy (Figure 2).

2.1 Medical Images and Edge Detection

This study, as a proof of concept, does not intended

to focus on CT or MR image processing due to its

high complexity. Therefore, Chitubox

v1.9.0

(Chitubox, Zhongcheng Future Industrial Park,

Hangcheng Avenue, Baoan District, Shenzhen,

Guangdong, China 518128), an open-source program

for manufacturing 3D models with digital light

processing (DLP) technology, was used to obtain

axial tomographic images, properly setting

parameters such as number of pixels (resolution),

printing table dimensions and layer height. When the

STL file is imported into the software, black-and-

white images are generated from bottom to top, going

through the file layer by layer, producing medical-

like slices which in this research will be considered as

medical images (Moscol et al., 2022).

Edge detection plays an important role in

determining the inner radius of the artery and

adapting the stent to it. One method to recognize the

edge consists of identifying pixels with different

intensities; however, the result was not adequately

adjusted (Figure 3). Therefore, a new edge detector,

based on the partial area effect that does not assume

continuity in pixel intensity values, was used to

achieve highly accurate extraction of edge position,

orientation and curvature in challenging conditions

such as images with noise, blurred edges, low contrast

areas or very close edges (Trujillo-Pino et al., 2013).

Figure 3: Edge detection at the (A) pixel and (B) subpixel

level.

To use this algorithm (Trujillo-Pino et al., 2013),

the medical images, a 3D matrix whose rows and

columns correspond to the number of pixels, were

converted to grayscale to get a 2D array whose pixel

intensities range from 0 to 255. In addition, three

hyperparameters were defined: the threshold, which

allows the algorithm to distinguish an edge if the

difference in intensities in two adjacent regions

exceeds 120; a zero-order filter, to detect the edge

without noise; and the order of the edge to be adjusted

(second order).

2.2 Clustering Algorithm

The coordinates of the points extracted from the edge

are represented in the pixel domain, but they must be

converted into millimetres for the biodevice design.

For this, the origin is defined in the centre of the

image and an equivalence is made between the

resolution and printing table dimensions configured

in Chitubox

The image is composed of two edges: internal and

external. However, the information required by the

designer is provided by the inner part, and to separate

them automatically the density-based spatial

clustering of application with noise (DBSCAN)

algorithm was used.

The main idea of this technique is that two points

are considered neighbours if the distance between

them is less than or equal to “eps” and the minimum

number of points to define a cluster is “min_sample”.

Hence, it is implemented by setting both

hyperparameters for the images, the values of

min_samples and eps were determined as 3 and 0.7

respectively.

2.3 Algebraic Fitting

2.3.1 Elliptical

The points of the inner edge, acquired with the

DBSCAN algorithm, allow a curve to be fitted for

Artiﬁcial Intelligence and Numerical Methods Aided Design of Patient-Speciﬁc Coronary Stents

automatically taking the measurement of the artery

and adjust the design to them. The ellipses, in

particular, adapt to the shapes and sizes of complex

anatomical sections (Solórzano-Requejo et al., 2022),

so the basic principles of their algebraic fitting are

detailed. The fitted ellipse is represented by an

implicit second-order polynomial (𝑄), defined by a

vector of coefficients (𝑣=[𝐴 𝐵 𝐶 𝐷 𝐸 𝐹]



𝑄



𝑝, 𝑣



[

𝑥



𝑥𝑦 𝑦



𝑥 𝑦 1

]

⎣

⎢

⎡

𝐴

𝐵

𝐶

𝐷

𝐸

𝐹

⎦

⎥

⎤

(1)

If 𝑃=



𝑝



, 𝑝



,…,𝑝





is the set of points of the

inner edge, the vector of coefficients must be adjusted

to it, so the algebraic distance (𝐷



) is used because it

simplifies the calculations and requires less

computational resources (Fitzgibbon et al., 1999).

Mathematically, it is obtained by substituting the

coordinates of a point 𝑝



(

𝑥



, 𝑦



)

in the polynomial

𝑄, therefore, if 𝑝



belongs to the ellipse its distance

will be zero:

𝐷



(

𝑝



, 𝑣

)

= 𝐴𝑥





+ 𝐵𝑥



𝑦



+ 𝐶𝑦





+ 𝐷𝑥



+ 𝐸𝑦



+ 𝐹

(2)

The least-squares technique optimized the fit by

minimizing the square of the algebraic distance

between 𝑃 and the adjusted ellipse

𝑄, which can be

expressed as the squared norm of the product between

the design matrix 𝐷



, which contains information of

𝑃, and 𝑣.

𝐷



⎣

⎢

⎡

𝑥





𝑥



𝑦



𝑦





𝑥



𝑦



𝑥



𝑥



𝑦



𝑦



𝑥



𝑦



⋮ ⋮ ⋮ ⋮ ⋮ ⋮ ⋮

𝑥





𝑥



𝑦



𝑦





𝑥



𝑦



⎦

⎥

⎤

(3)

𝑚𝑖𝑛𝐷



(

𝑝



, 𝑣

)







= 𝑚𝑖𝑛

‖

𝐷



𝑣

‖



(4)

To avoid the trivial solution of 𝑣 = 0





, 𝑣 is

bounded with a constraint of

‖

𝑣

‖



= 1, preventing

that all coefficients are zero (Paton, 1970). Lagrange

multipliers allow to minimize the distance

considering this condition:

𝐿= 𝑣



𝐷





𝐷



𝑣 − 𝜆(𝑣



𝑣−1)

(5)

To minimize 𝐿, its gradient with respect to 𝑣 is set to 0:

𝛻



𝐿=0 ⟺ 2𝐷





𝐷



𝑣 −2𝜆𝑣=0

(6)

𝐷





𝐷



𝑣 =𝜆𝑣

(7)

Equation (7) leads to the eigenvector problem,

then λ and 𝑣 must be an eigenvalue and eigenvector

of 𝐷





𝐷



. If 𝐷





𝐷



𝑣= 𝜆𝑣, equation (4) will be:

𝑚𝑖𝑛 𝑣



𝐷





𝐷



𝑣 =𝑚𝑖𝑛 𝜆

‖

𝑣

‖



= 𝑚𝑖𝑛 𝜆

(8)

Consequently, the coefficient vector ( 𝑣) that

minimizes the distance will be the eigenvector of

𝐷





𝐷



corresponding to the smallest eigenvalue (𝜆).

2.3.2 Circular

For cardiovascular prosthesis, it may be more

interesting to fit a circle to the inner wall of blood

vessels. Therefore, this subsection describes the

theory related to its algebraic fitting (Černov, 2011).

Starting from the general equation of the circle (𝑓)

and developing it:

𝑓=

[

𝑥



𝑥𝑦 𝑦



𝑥 𝑦 1

]

⎣

⎢

⎡

−2𝑘

−2𝑚

𝑘



+ 𝑚



−𝑟



⎦

⎥

⎤

(9)

Linking equation (1) to (9), it is determined that

𝐴= 𝐶=1, 𝐵= 𝑂, 𝐷= −2𝑘, 𝐸= −2𝑚 and 𝐹=

𝑘



+ 𝑚



−𝑟



. Therefore, 𝐷



from a point 𝑝



(

𝑥



, 𝑦



)

to the fitted circle is:

𝐷



(𝐷, 𝐸, 𝐹, 𝑝



)=𝑥





+ 𝑦





+ 𝐷∙𝑥



+ 𝐸∙𝑦



+ 𝐹

(10)

To find the values of 𝐷, 𝐸 and 𝐹 defining the

fitted curve, the algebraic distance squared of the “𝑛”

points composing the inner edge is minimized:

𝐷





= 𝑚𝑖𝑛

(

𝑥





+ 𝑦





+ 𝐷∙𝑥



+ 𝐸∙𝑦



+ 𝐹

)







(11)

For this purpose, 𝐷





is partially derived with

respect to 𝐷, 𝐸 and 𝐹, equating to 0 and rewritten in

matrix form:

⎣

⎢

⎡

𝑥





𝑥



∙𝑦



𝑥



𝑥



∙𝑦



𝑦





𝑦



𝑥



𝑦



𝑛

⎦

⎥

⎤

. 

𝐷

𝐸

𝐹



⎣

⎢

⎡

−

(

𝑥





+ 𝑦





)

∙𝑥



−

(

𝑥





+ 𝑦





)

∙𝑦



−

(

𝑥





+ 𝑦





)

⎦

⎥

⎤

(12)

Solving the linear system, the coefficients of the

fitted circumference are obtained.

2.4 RANSAC Algorithm

The random sample consensus algorithm

(RANSAC), published by Fischler and Bolles

BIODEVICES 2023 - 16th International Conference on Biomedical Electronics and Devices

(Fischler & Bolles, 1981), is an iterative method for

estimating the parameters of a mathematical model

from a dataset containing outliers. RANSAC

proposes to create a cost function that sums the

distance of the points to the fitted curve and

iteratively select some of them to fit again and choose

the one that produces the lowest cost.

Due to the iterative nature of the algorithm, it is

not deterministic, and the model obtained may not be

the best. Nevertheless, it is a useful tool to integrate

with the elliptical and circular fitting, presented in the

previous sections, since in personalized implant

design it is required that the fitted curve adapts as well

as possible to the inner edge without exceeding it. If

only the algebraic fitting is used, the result does not

meet this condition, so it is necessary to integrate this

procedure to RANSAC (Figure 2).

Compared to the algebraic fitting that squares the

distance to make the function convex and ensure that

a minimum exists, the modified RANSAC algorithm

takes advantage of the sign of the algebraic distance

(cost function) to determine whether the adjusted

curve is inside or outside the edge. This innovate

approach is interesting and can be applied to image

processing and computer vision tasks.

Figure 4: (A) Web application. (B) Coronary artery slice fits. Comparison between (C) the fit provided by the application and

(D) another possible solution. (E) Output of the web application.

Artiﬁcial Intelligence and Numerical Methods Aided Design of Patient-Speciﬁc Coronary Stents

3 RESULTS AND DISCUSSION

3.1 Web Application and Virtual

Model

In order to integrate the explained algorithms and to

encourage the symbiotic use of computer aided

design, artificial intelligence and numerical methods

in the design of personalized biodevices, a web app

has been developed with the Streamlit library

(Streamlit, n.d.) of Python

3.7.14 (Phyton Software

Foundation) as it allows the deployment of apps in a

simple way.

As mentioned above, two different approaches

were used to assist the parametric design of

personalized coronary stents. The circular algebraic

fitting which, in most cases, does not appropriately

adjust the patient’s coronary topology and a new

innovative and more suitable approach, the elliptical

one.

To prove the effectiveness of both methods, a

virtual STL model of a patient's artery has been used.

The STL file (Model ID 3DPX-012589), based on a

CT scan and segmented by researchers at the

University of Toronto and Toronto General Hospital,

has been downloaded from the NIH 3D Print

Exchange repository (Phantom Coronary Artery

Models | NIH 3D Print Exchange, n.d.) and imported

into Chitubox

by setting up the resolution, print plate

dimensions and layer height as 512 512 pixels,

101022 mm and 1 mm respectively. Finally, the

3D model was sliced, and each image has been stored

in a general .ZIP file.

The .ZIP archive has been uploaded in the web

application (Figure 4A) by introducing the

parameters configured in Chitubox

to transform

pixel into coordinates and compute the algebraic

distance, used as cost function to get the circle or

ellipse that best fits the arterial wall to cause minimal

long-term restenosis (Figure 4C & D). The app

outputs, for each slice, the circular and elliptical

algebraic fitting (Figure 4B), the average radius or

radii and length of the artery, parameters that will be

introduced into the parametric design (Figure 4E).

3.2 Parametric Design of Coronary

Stents

The stent designs are based on a geometry unit cell

(Figure 5C) that is repeated bidirectionally, resulting

in a 2D mesh (Figure 5D) that folds back on itself to

form the stent (Figure 5E) and then deforms to obtain

the elliptical cross-section (Figure 5F). The modelling

of these unit cells is parameterised according to the

web app outputs, the average radius (𝑅) and length

( 𝐿), in addition, for the elliptical adjustment, the

major (𝑅



) and the minor average radius (𝑅



). The

number of unit cell repetitions (𝑁



and 𝑁



) in the

transversal (𝑋) and radial (𝑌) axes, and the thickness

(𝑡) can be modified as the designer requires.

Figure 5: (A) Macroscopic and (B) microscopic view of

coronary stent model. (C) Unit cell and (D) mesh

construction. (E) Circular and (F) elliptical parametrized

stent.

As an example, the entire parametrized design

workflow can be seen in Figure 5. Macroscopically,

the unit cell, in most cases, is a 𝑎𝑏 rectangle that

will repeat 𝑁



and 𝑁



times in the 𝑋 and 𝑌 axis,

respectively. When figuring 𝑎 and 𝑏 measures, the

thickness of the stent must be considered. In this

example, unit cells connectors must be also taken into

consideration, resulting in a

(

𝑎+ 𝑐

)

𝑏 rectangle.

Therefore, the width of the mesh will be 2 𝜋

(

𝑅−0.5 ⋅𝑡

)

and the dimension of 𝑏:

𝑏=

2𝜋

(

𝑅−0.5𝑡

)

𝑁



(13)

The relation between the mesh and unit cell length is

(Figure 5A):

𝐿−𝑡= 𝑁



(

𝑎+ 𝑐

)

−𝑐

(14)

Microscopically, the unit cell has a specific shape

bounded by the 𝑎𝑏 rectangle, hence, the

mathematical relation between macroscopic and

microscopic parameters must be established. To

simplify the parametrization, the length of the unit

cell ( 𝑎) and the connector length (𝑐) was set as

follows (Figure 5B):

BIODEVICES 2023 - 16th International Conference on Biomedical Electronics and Devices

𝑐=

𝑎

(15)

Introducing (15) into (14), the value of 𝑎 is defined as

a function of 𝐿, 𝑁



and 𝑡:

𝑎=

𝐿−𝑡

𝑁



−

(16)

The curve 𝑓

(

𝑥

)

used in the unit cell follows the

sinusoidal equation parametrized as a function of 𝑏

and 𝑐. Where





is the amplitude and the vertical

offset,





the period and





the phase shift (Figure 5B).

𝑓

(

𝑥

)

𝑐

⋅sin 

2𝜋

𝑏

𝑥−

𝑏

+

𝑐

;

𝑥 ∈

[

0, 0.5𝑏

]

(17)

This geometry has been designed and

parametrized in Solidworks

2021 (Dassault

Systèmes SolidWorks Corporation, UK). To validate

its suitability, the web outputs has been introduced in

the parametric file described above where 𝑁



, 𝑁



and

𝑡 has been set as 4, 5 and 0.2 mm respectively. Then,

the patient-specific stent has been exported in STL

format to manufacture prototypes using AM

techniques such as stereolithography (Figure 6B),

selective laser sintering (Figure 6C) and selective

laser melting (Figure 6D).

Figure 6: (A) Library of parameterized coronary stents.

Prototypes manufactured by (B) stereolithography, (C)

selective laser sintering and (D) melting.

The main objective of this methodology is to

promote the creation of a parametrized coronary stent

library (Figure 6A). Therefore, physicians will have

several options to select the one that best suits to the

clinical and mechanical patient needs (Martínez

Cendrero et al., 2022). Moreover, it will ensure a

more personalized and simplified workflow by

directly using the medical image and avoiding its

segmentation.

4 CONCLUSIONS

The increasing demand of personalized biomedical

solutions poses a major healthcare challenge. This

proposal is a useful tool that aids custom stent

modelling by adapting its cross-section to the internal

artery cavity improving its fit and filling.

Furthermore, this proof-of-concept avoids

segmentation, as the arterial edge is extracted directly

from the medical image, reducing the inherent errors

of conventional workflow.

The integration of artificial intelligence and

numerical methods in the web application has shown

that elliptical sections are better adapted to the

coronary artery and, from these fitted curves patient-

specific stents can be designed. The web application

transforms the designer`s work into an inspector to

ensure that the solution proposed by the application

meets quality standards.

The main problems of personalized medicine are

time-consumption and high economic cost.

Therefore, the web application and parametric

models, automatization tools, could be the solution

related to the first issue, as they reduce the delivery

times being the personalized protheses competitive in

emergency situations. Moreover, by using 3D

printing, the price of personalized medical devices

will be decreased significantly. Consequently, the

combination of medical imaging, automatization

tools and 3D printing could lead to new competitive,

affordable, and accessible high-quality patient-

specific implants.

5 FUTURE LINES

To balance the medical demand for personalized

solutions, advances in computer vision,

computational design and artificial intelligence will

be critical to achieve full automatization of the

implant’s workflow (Figure 1). This will help

designers produce a more aesthetic morphology and

precise fit, as well as a higher level of customization

and a comforting patient experience. This symbiosis

of computational, mechanical, and biomedical

Artiﬁcial Intelligence and Numerical Methods Aided Design of Patient-Speciﬁc Coronary Stents

technologies will result in a new generation of

customized prostheses that will improve clinical

outcomes for millions of patients worldwide. This

new methodology could be extrapolated to many

clinical cases, such as aortic valves and hip prostheses

(Solórzano Requejo et al., 2022).

ACKNOWLEDGEMENTS

The research presented has been supported by the

project: "iMPLANTS-CM: impresión de

metamateriales empleando aleaciones con memoria

de forma y gradientes funcionales para una nueva

generación de implantes inteligentes", funded by the

"Convocatoria 2020 de ayudas para la realización de

proyectos sinérgicos de I+D en nuevas y emergentes

áreas científicas en la frontera de la ciencia y de

naturaleza interdisciplinar" financed by Comunidad

Autónoma de Madrid (ref. del proyecto: Y2020/BIO-

6756).

The authors express their gratitude to Mar

Cogollo, Adrián Martinez, Francisco Franco, Miguel

Clavijo, Pedro Ortego, Javier Tuesta, Nicolás Kuroki,

Leandro Velásquez and Daira Mena for inspiring and

supporting us to conduct research that benefits

society.

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