Patent Publication Number: US-2022211523-A1

Title: Laser dimpled stent for prevention of restenosis

Description:
This application is a continuation-in-part of and claims priority to U.S. patent application Ser. No. 16/494,953, filed on Sep. 17, 2019, entitled “Laser Dimpled Stent for Prevention of Restenosis,” which is a 371 application of PCT/US2017/59753, filed Nov. 2, 2017, entitled “Laser Dimpled Stent for Prevention of Restenosis,” which claims priority to U.S. Provisional Patent Application Ser. No. 62/475,574, filed on Mar. 23, 2017, entitled “Laser Dimpled Stent for Prevention of Restenosis,” the entire contents of which are hereby incorporated by reference. 
    
    
     BACKGROUND 
     The present invention relates generally to a stent designed to prevent tissue build-up after placement. In particular, the stent is subjected to laser processing to introduce one or more dimples that increase localized turbulence inside the stent and reduce the potential for tissue build-up and restenosis. 
     Angioplasty is a safe and effective way to unblock coronary arteries. Initially, angioplasty was performed only with balloon catheters, but technical advances have been made and improved patient outcome has been achieved with the placement of small metallic spring-like or tube-like devices called “stents” at the site of the blockage. The implanted stent serves as a scaffold that keeps the artery open. However, the restenosis rate, the recurrence of stenosis, a narrowing of a blood vessel, leading to restricted blood flow continuously increases after corrective surgery due to deposition of excessive plateaus (platelets) on the inner wall of the stent. As a result, patients have to repeatedly undergo coronary angioplasty surgery. Accordingly, increasing interest is concentrated on developing methods that will substantially lower the rate of restenosis. 
     Restenosis, the recurrence of abnormal narrowing of a coronary artery from scar tissue and cholesterol build-up after corrective surgery increases exponentially as the duration of time from surgery increases and eventually plateau percentages reach nearly 75% as shown in  FIG. 1 . 
     Angioplasty, the surgical removal of material build-up in a coronary artery and subsequent implant of a coronary stent, poses two significant disadvantages: the widened surface of the artery becomes uneven due to the uneven expansion of the catheter tube, and the inner surface of the artery displays recoil by springing back to its original position to a certain degree after the catheter has been removed, increasing the risk of arterial blockage from material build-up. 
     The disadvantages of angioplasty lead to several issues in present clinical settings: (1) the repeated, dangerously detailed replacement of a coronary stent, (2) the extreme inefficiency of the stent, and consequently, (3) the dramatically increased cost for the patients and practitioners alike. In light of this, the research community is focused on developing an improved stent design and the present investigation forms a part of such an effort. 
     Efforts have been made to diminish the adverse side effects of conventional stents. Various specialized stents were formulated to target a specific disadvantage of the results from an angioplasty. The bare metal stent (BMS) (shown in  FIG. 2 ), a tubular wired mesh stent with no coating, is used to lower the rate of thrombosis (formation of blood clot) once tissue regrowth covered the stent. However, there are several side effects for its use, including arterial perforation or rupture, coronary artery spasm, cerebrovascular accident, heightened rate of restenosis, and unstable angina pectoris. 
     The drug-eluting stent (DES) (also shown in  FIG. 2 ), consists of a metallic backbone, a situation-specific anti-proliferative drug, and a vehicle polymer that controls drug release rate, reduces restenosis and revascularization. This stent releases a drug geared toward inhibition of neointima, which causes restenosis. However, utilization of the drug-eluting stent induces a lengthy duration (approximately twelve months) of dual antiplatelet therapy (a combination of Aspirin and P2Y12 receptor blocker) in order to preclude an already higher rate of thrombosis. 
     Some commercially available bioengineered dual therapy stents (DTS) specifically target arteries of patients with contraindications for the dual antiplatelet therapy that is a part of the drug-eluting stent. One example of such a stent is coated with an antibody that captures CD34+ endothelial progenitor cells to the stent and the subsequently formed endothelial layer protects against thrombosis and decreases restenosis. A major disability in this stent is its lack of rigidity. Thus, DTS combines the benefit of DES and bio-engineered stents and is the only stent to contain a drug with active healing technology. Compared to these bioengineered stents, others embody more structure within their frames, restricting restenosis and supporting the internal arterial walls. 
     Biodegradable vascular scaffold stents (BVS) (shown in  FIG. 3 ) are a type of drug-eluting stent on a dissolvable scaffold platform. One such stent is coated with paclitaxel which is released from a polymer and both are absorbed by the body as time progresses, reducing irritation of the arterial lumen. The scaffold itself is absorbed over time. Unlike with the DTS, there is no active element to promote artery healing. The biodegradable vascular scaffold stent contains thicker struts compared to the bare metal stents. This causes the stent to bear less tolerance for the possible overexpansion of the mesh. 
     Finally, the dual therapy stents are considered to be the most advanced model because of their drug-release mechanism that lead to reduction in inflammation, and arterial healing. A biodegradable polymer releases a drug that significantly reduces restenosis. However, similar to the bioengineered stents, the dual therapy stents also exhibit increased rigidity within the structure thereby inhibiting their ability to accommodate the artery&#39;s intrinsic flexibility. 
     All of the current state-of-the-art stents demonstrate common disadvantages such as inefficiency, instability, and higher cost. Thus, improved stent design in order to control restenosis in a feasible manner is still being explored. 
     SUMMARY 
     The present disclosure relates to an innovative dimpled stent design and its fluid flow characteristics. Its geometrical characteristics, namely dimple width and depth are likely to generate localized turbulence and thrust within the blood flow site specific to the dimple, a direct result of the Magnus Effect to keep the plateaus (platelets) flowing with the blood stream without sticking to and the depositing on the wall of stent as scar tissue and cholesterol. Such a physical phenomenon is mathematically expressed as 
     
       
         
           
             
               
                 
                   
                     
                       F 
                       M 
                     
                     → 
                   
                   = 
                   
                     
                       1 
                       2 
                     
                     ⁢ 
                     
                       C 
                       L 
                     
                     ⁢ 
                     ρ 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     
                       
                         Aυ 
                         2 
                       
                       ⁡ 
                       
                         ( 
                         
                           
                             ω 
                             ^ 
                           
                           × 
                           
                             v 
                             ^ 
                           
                         
                         ) 
                       
                     
                   
                 
               
               
                 
                   ( 
                   1 
                   ) 
                 
               
             
           
         
       
     
     Where {right arrow over (F M )} is the Magnus force, {circumflex over (ω)} is the vector representing an axis of rotation, {right arrow over (ν)} is the velocity vector of the flow, C L  is the lift coefficient, ρ is the density of the blood, A is the cross-sectional area of the platelet, v is the platelet velocity. 
     A dimpled stent design mirrors the working principle of a golf ball. Drag on a golf ball results mainly from air pressure forces, arising when the pressure in front of the ball is significantly higher than that behind the ball. The only practical way of reducing this difference is to design the ball surface to attract the main stream of air flowing by it as close to the surface of the ball as possible. This situation is achieved by the golf ball&#39;s dimples, which augment the turbulence close to the surface, bringing the high-speed air stream closer and increasing the pressure behind the ball. The effect is plotted in the chart, which shows that for Reynolds numbers (Re) achievable by hitting the ball with a club (10 5 ), the coefficient of drag C D  is much lower for the dimpled ball, as shown in  FIG. 4 . With the decreased drag of the golf ball, the golf ball projects further and the air flow around it accelerates. 
     Similar to the mechanics behind a golf ball&#39;s dimples and the surrounding fluid flow, the fluid flow in proximity of the inner stent surface dimples accelerate just enough to overcome the threshold that increases the rate of restenosis due to accumulation of decelerated platelets. The dimpled stent design simultaneously grants the possibility of extending the life of the stent while maintaining a stable and healthy blood velocity. 
     Based on the dimpled golf ball concept, a similar design is used for a stent application. Such a design based on basic fluid flow concepts would create a high pressure (thrust) zone and an Eddy zone within the dimpled region of the stent, as shown in  FIG. 5 . Furthermore, such a fluid flow would cause the platelets to flush away from the stent walls providing a possibility to prolong the stent life, as shown in  FIG. 6 . Moreover, the concept and working principle of a single dimple stent design can be extended to a multi-dimple design. 
     The dimpled stent design provides a fundamental improvement within the structure of state-of-the-art stents, allowing new possibilities to be explored in terms of sustainability in the field of cardiology. The new ability to reduce or eliminate restenosis will allow physicians to focus on efficient treatment of angina rather than attempting to prevent its recurrence. The focus can shift, for example, from restenosis prevention to drug optimization. As drug optimization is just one example, the extent of new capabilities presented by engineering of the dimpled stent is essentially boundless in that any stent can be personalized to the patients&#39; conditions. The combination of the drug release and its Ti6Al4V base metal allow for non-toxic, bio-friendly metals, ensuring the safety of the patient. 
     It is notable that the turbulence in fluid flow resides chiefly within the dimple, causing minimal disturbance in the main flow. Thus, the dimple generates just enough turbulence to ultimately restrain restenosis without potentially causing discomfort for the patient. 
     Different patterns and diverse architecture of dimples can be utilized. These include staggered, diagonal, in-lined, and spiral patterns in addition to the lay outs illustrated in  FIG. 7 . The various patterns listed differ in three key aspects: pitch P, the spacing between centers of two consecutive (adjacent) dimples in a given linear or spiral row of dimples, pitch R, the spacing between centers of two consecutive (adjacent) dimples in two given consecutive (adjacent) linear or spiral rows of dimples respectively, and orientation θ, the angle between pitch P and pitch R. Specifically, the staggered and spiral arrangements will display longer pitches compared to the in-lined and diagonal arrangements. The subsequent differences in pitches affect the fluid flow around each individual dimple through turbulence and friction factors. 
     The laser ablation of coronary stents to produce dimples on the inner surface essentially is a cost-effective, stable, and adept method to eliminate arterial narrowing recurrences after corrective surgery. The dimpled stent design deals with the issues such as inefficiency, instability, and the cost of repeated coronary angioplasty surgery currently unsolved by state-of-the-art stents. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       The following drawings form part of the present specification and are included to further demonstrate certain aspects of the present invention. The invention may be better understood by reference to one or more of these drawings in combination with the detailed description of specific embodiments presented herein. 
         FIG. 1  shows restenosis rates in coronary arteries at 8 months and 4 years following corrective surgeries (courtesy of Jorgensen et al. 2009). 
         FIG. 2  shows a diagram of thrombus formation in an artery having a drug-eluting stent (DES) and restenosis in an artery having a bare-metal stent (BMS) (courtesy of Shah 2003). 
         FIG. 3  shows a schematic of a biodegradable vascular scaffold (BVS) and the events that occur after insertion of the scaffold (courtesy of Balachandran et al. 2015). 
         FIG. 4  shows variation in drag coefficient (C D ) of a smooth surface ball, rough surface balls and a golf ball as a function of Reynolds number (Re) where s is the sand grain roughness height and m is the ball diameter (courtesy of Bearman et al. 1976). 
         FIG. 5  shows a schematic of a blood flow pattern in a dimpled stent having a dimple width w and depth d with high pressure and eddy zones within the dimple. 
         FIG. 6  shows a schematic of flushing of platelets in a dimpled stent having dimple diameter d where the platelets do not stick to the wall due to the turbulent flow and thrust generated within the dimple. 
         FIG. 7  shows schematics of (a) and (b), two exemplary placements (or layouts) of dimples in a stent design in accordance with preferred embodiments described herein, and (c) exemplary employment of dimples of various diameters in a stent design in accordance with preferred embodiments described herein. 
         FIG. 8  shows a computational simulation of a dimple produced on Ti6Al4V surface with a laser of 500 W and 0.12 s exposure time including (A) evolution of the ablation depth and (B) corresponding time temperature profiles. 
         FIG. 9  shows a computational simulation of a dimple produced on Ti6Al4V surface with a laser of 700 W and 0.12 s exposure time, including (A) evolution of the ablation depth and (B) corresponding time temperature profiles. 
         FIG. 10  shows a computational simulation of a dimple produced on Ti6Al4V surface with a laser of 900 W and 0.12 s exposure time, including (A) evolution of the ablation depth and (B) corresponding time temperature profiles. 
         FIG. 11  shows a computational simulation of a dimple produced on Ti6Al4V surface with a laser of 1800 W and 0.12 s exposure time, including (A) evolution of the ablation depth and (B) corresponding time temperature profiles. 
         FIG. 12  shows vaporization depths within the dimple of a stent material as a function of laser input power for constant beam residence time of 0.12 s. 
         FIG. 13A  shows a side view of a dimpled stent design in accordance with a preferred embodiment. 
         FIG. 13B  shows an end view of a dimpled stent design in accordance with a preferred embodiment. 
         FIG. 14  shows a schematic of an experimental setup used for evaluating gravity fed SBF flow characteristics of exemplary dimpled stent material. 
         FIG. 15  shows different times of fluid (SBF) flow characteristics under various test conditions. 
         FIG. 16  shows average fluid flow velocity for various test conditions. 
     
    
    
     DETAILED DESCRIPTION 
     The present disclosure pertains to a stent having a dimpled texture which helps to eliminate arterial narrowing recurrences after corrective surgery. 
       FIG. 7  shows schematics of three types of placements (lay outs) of dimples in preferred embodiments of a stent design. D is the diameter of the stent, d is the depth of the dimple, w is the width of the dimple, and the pitch P is the spacing between centers of two consecutive (adjacent) dimples in a given linear or spiral row of dimples. P preferably ranges between 1.8 w and 2.2 w to maintain the required turbulence and the thrust. The pitch R is the spacing between centers of two consecutive (adjacent) dimples in two given consecutive (adjacent) linear or spiral rows of dimples, where R preferably ranges between 1.8 w and 2.2 w. In case of the placement with dimples of two different widths of w and w′ in each consecutive (adjacent) linear row or spiral row, P ranges between 1.8 times (w+w′) and 2.2 times (w+w′).  FIG. 7( a )  shows a preferred embodiment of a dimpled stent  10  having dimples  101  in a stent material  105  with a dimple placement where θ=90° where θ is the angle between P and R vectors and ranges between 0° and 90°.  FIG. 7( b )  shows a preferred embodiment of a dimpled stent  20  having dimples  201  in a stent material  205  with a dimple placement where θ=67.5°. Combinations of orientation θ between P and R, along with w, w′, P, and R would yield various embodiments of stent designs. The parameters such as center to center pitch of the dimple placement (P), center to center spacing between horizontal stent rows (R) and orientation (θ) between P and R can be varied to generate various combinations of dimple placements (layout) on the stent surface.  FIGS. 7( a ) and 7( b )  show the embodiments of dimpled stents  10  and  20  in both a folded tube shape and in an unfolded dimpled stent sheet, which would be formed into a tube sheet to create the dimpled stent.  FIG. 7( c )  provides one such specific layout for a dimpled stent  30  with different widths (w and w′) and depths (d and d′) in alternate rows of dimples  301  in a stent material  305  and the orientation, θ, between pitches P and R equal to 67.5°. 
     The magnitude of dimple site specific turbulence and thrust within the blood flow depends on several parameters such as but not limited to dimple morphology: spherical (width and depth) or elliptical (major and minor axes and depth); geometric layout of the dimple pattern; and number of dimples. These parameters can be precisely fabricated and controlled via the laser ablation of Ti6Al4V (a commonly used biocompatible titanium alloy), while employing a variety of laser processing parameters, including laser power, traverse speed, and laser beam diameter on the surface of the material which together provide desired input laser fluence. 
     The disparate architectural dimensions of the dimples that were modeled through the Finite Element (FE) based Multiphysics computational platform display correlation between the presence of dimples of required morphology (width and depth in case of the spherical dimple) for increased fluid (blood) flow and thrust that in turn drastically decrease the adhesion of platelets and formation of plaque in the interior wall. During in vivo study, the above dimensions of the stent dimples accelerated the overall flow of simulated body fluid (SBF) (a solution consisting of the same chemical composition as that of blood without the plasma), thereby providing a way to potentially substantially diminish the rate of restenosis. The innovative approach adopted is expected to increase the efficiency and lifespan of the stent enhancing the life of patients. 
     A computational model was developed in house and employed to model the interaction between the heat source (laser) and the titanium alloy (Ti6Al4V) surface during creation of a dimple of desired spherical geometry (width and depth). During laser processing (dimpling), material experiences various physical phenomena such as phase transition from solid-to-liquid-to-vaporization and material loss during evaporation. In addition, the material surrounding dimpled region also experiences the transition dependent effects such as thermal expansion during heating, recoil pressure during vaporization, and Marangoni convection and surface tension during phase transition. In order to simulate such complex laser dimpling mechanism, the present model was designed and developed using multistep and Multiphysics computational modeling approach for multidimensional (3D) laser dimpling process on a finite-element (FE) platform. The computational model based on the Multiphysics approach combines heat transfer, fluid flow, and structural mechanics for thermo-mechanical coupling (temperature and thermal expansion coefficient) along with several forces such as body force (gravitational force) and surface forces (viscosity/shear forces, recoil pressure) to investigate the combinatorial effects of these physical phenomena on evolution of physical attributes/surface topography (depth, width, and geometry) of a dimple. The selective governing equation based on heat transfer for a preferred Multiphysics computational model is presented in Eq. (2). 
     
       
         
           
             
               
                 
                   
                     ρ 
                     ⁢ 
                     
                       
                         
                           C 
                           p 
                         
                         ⁡ 
                         
                           [ 
                           
                             
                               ∂ 
                               T 
                             
                             
                               ∂ 
                               L 
                             
                           
                           ] 
                         
                       
                       
                         ( 
                         
                           x 
                           , 
                           y 
                           , 
                           z 
                         
                         ) 
                       
                     
                   
                   = 
                   
                     k 
                     ⁢ 
                     
                       { 
                       
                         
                           
                             [ 
                             
                               
                                 
                                   ∂ 
                                   2 
                                 
                                 ⁢ 
                                 T 
                               
                               
                                 ∂ 
                                 
                                   x 
                                   2 
                                 
                               
                             
                             ] 
                           
                           
                             ( 
                             
                               y 
                               , 
                               z 
                               , 
                               t 
                             
                             ) 
                           
                         
                         + 
                         
                           
                             [ 
                             
                               
                                 
                                   ∂ 
                                   2 
                                 
                                 ⁢ 
                                 T 
                               
                               
                                 ∂ 
                                 
                                   y 
                                   2 
                                 
                               
                             
                             ] 
                           
                           
                             ( 
                             
                               z 
                               , 
                               x 
                               , 
                               t 
                             
                             ) 
                           
                         
                         + 
                         
                           
                             [ 
                             
                               
                                 
                                   ∂ 
                                   2 
                                 
                                 ⁢ 
                                 T 
                               
                               
                                 ∂ 
                                 
                                   z 
                                   2 
                                 
                               
                             
                             ] 
                           
                           
                             ( 
                             
                               x 
                               , 
                               y 
                               , 
                               t 
                             
                             ) 
                           
                         
                       
                       } 
                     
                   
                 
               
               
                 
                   ( 
                   2 
                   ) 
                 
               
             
           
         
       
     
     Here, k is the thermal conductivity, C p  is the specific heat and ρ is the density of the material. Furthermore, the laser material interaction region is assigned a heat flux boundary with a moving laser beam defined by Eq. (3). 
     
       
         
           
             
               
                 
                   
                     k 
                     ⁡ 
                     
                       [ 
                       
                         
                           ( 
                           
                             
                               ∂ 
                               T 
                             
                             
                               ∂ 
                               x 
                             
                           
                           ) 
                         
                         + 
                         
                           ( 
                           
                             
                               ∂ 
                               T 
                             
                             
                               ∂ 
                               y 
                             
                           
                           ) 
                         
                         + 
                         
                           ( 
                           
                             
                               ∂ 
                               T 
                             
                             
                               ∂ 
                               z 
                             
                           
                           ) 
                         
                       
                       ] 
                     
                   
                   = 
                   
                     
                       P 
                       X 
                     
                     - 
                     
                       { 
                       
                         
                           h 
                           ⁡ 
                           
                             [ 
                             
                               T 
                               - 
                               
                                 T 
                                 0 
                               
                             
                             ] 
                           
                         
                         + 
                         
                           ɛ 
                           ⁢ 
                           
                             σ 
                             ⁡ 
                             
                               [ 
                               
                                 
                                   T 
                                   4 
                                 
                                 - 
                                 
                                   T 
                                   0 
                                   4 
                                 
                               
                               ] 
                             
                           
                         
                       
                       } 
                     
                   
                 
               
               
                 
                   ( 
                   3 
                   ) 
                 
               
             
           
         
       
     
     Here, h is heat transfer coefficient, ε is emissivity, σ is Stefan-Boltzman constant, T 0  is ambient temperature, and P X  is the input laser power intensity distribution. Such a heat source, P, can have Gaussian or top hat or a dumbbell shaped beam profile in terms of spatial distribution of the power as expressed in the following set of equations. 
     
       
         
           
             
               
                 
                   
                     P 
                     g 
                   
                   = 
                   
                     
                       
                         P 
                         0 
                       
                       
                         π 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         
                           r 
                           0 
                           2 
                         
                       
                     
                     ⁢ 
                     
                       exp 
                       
                         - 
                         
                           ⌊ 
                           
                             
                               
                                 x 
                                 2 
                               
                               + 
                               
                                 y 
                                 2 
                               
                             
                             
                               r 
                               0 
                               2 
                             
                           
                           ⌋ 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   4 
                   ) 
                 
               
             
             
               
                 
                   
                     P 
                     th 
                   
                   = 
                   
                     
                       
                         P 
                         0 
                       
                       
                         π 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         
                           r 
                           0 
                           2 
                         
                       
                     
                     ⁢ 
                     
                       
                         exp 
                         
                           - 
                           
                             
                               
                                 ( 
                                 
                                   
                                     x 
                                     2 
                                   
                                   + 
                                   
                                     y 
                                     2 
                                   
                                 
                                 ) 
                               
                               n 
                             
                             
                               r 
                               0 
                               2 
                             
                           
                         
                       
                       ⁡ 
                       
                         ( 
                         
                           
                             where 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             n 
                           
                           ⁢ 
                           
                               
                           
                           -&gt; 
                           ∞ 
                         
                         ) 
                       
                     
                   
                 
               
               
                 
                   ( 
                   5 
                   ) 
                 
               
             
             
               
                 
                   
                     P 
                     db 
                   
                   = 
                   
                     
                       
                         2 
                         ⁢ 
                         
                           P 
                           0 
                         
                       
                       
                         π 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         
                           r 
                           0 
                           2 
                         
                       
                     
                     ⁢ 
                     
                       
                         ( 
                         
                           
                             x 
                             + 
                             y 
                           
                           
                             r 
                             0 
                           
                         
                         ) 
                       
                       2 
                     
                     ⁢ 
                     
                       exp 
                       
                         - 
                         
                           
                             
                               ( 
                               
                                 
                                   x 
                                   2 
                                 
                                 + 
                                 
                                   y 
                                   2 
                                 
                               
                               ) 
                             
                             n 
                           
                           
                             r 
                             0 
                             2 
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   6 
                   ) 
                 
               
             
           
         
       
     
     Where P g  is the Gaussian heat flux, P th  is the top hat heat flux, P db  is the dumbbell heat flux, P 0  is laser input power, r 0  is the radius of beam at which laser power transverse intensity decreases to 1/e 2 , and x, y, z are the Cartesian coordinates with y along the axis of the beam and x and z are in the plane orthogonal to the axis of the beam and the beam intensity distribution is considered axisymmetric in x-z plane. 
     All other surfaces are assigned convective cooling and surface to ambient radiation boundary conditions given by the following relationship (Eq. (7)): 
     
       
         
           
             
               
                 
                   
                     - 
                     
                       k 
                       ⁡ 
                       
                         [ 
                         
                           
                             ( 
                             
                               
                                 ∂ 
                                 T 
                               
                               
                                 ∂ 
                                 x 
                               
                             
                             ) 
                           
                           + 
                           
                             ( 
                             
                               
                                 ∂ 
                                 T 
                               
                               
                                 ∂ 
                                 y 
                               
                             
                             ) 
                           
                           + 
                           
                             ( 
                             
                               
                                 ∂ 
                                 T 
                               
                               
                                 ∂ 
                                 z 
                               
                             
                             ) 
                           
                         
                         ] 
                       
                     
                   
                   = 
                   
                     
                       h 
                       ⁡ 
                       
                         [ 
                         
                           T 
                           - 
                           
                             T 
                             0 
                           
                         
                         ] 
                       
                     
                     + 
                     
                       ɛ 
                       ⁢ 
                       
                         σ 
                         ⁡ 
                         
                           [ 
                           
                             
                               T 
                               4 
                             
                             - 
                             
                               T 
                               0 
                               4 
                             
                           
                           ] 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   7 
                   ) 
                 
               
             
           
         
       
     
     Moreover, there are various types of lasers available commercially which could be employed for stent surface ablation to produce a dimpled texture on it. These lasers have various wavelengths within the electromagnetic spectrum. Moreover, depending upon the laser type under consideration, a pulsed and/or continuous wave modes of operation can be adopted. In case of pulsed lasers, the pulse duration during interaction with the material can range from femtosecond (10 −15  s) to millisecond (10 −3  s). Such characteristics of commercial lasers that can be adopted in laser dimpling of the stent are tabulated below in Table 1. The basic classification of such lasers in infrared and ultraviolet type is based on the wavelength range in which they operate. 
     
       
         
           
               
             
               
                 TABLE 1 
               
             
            
               
                   
               
               
                 Various types of lasers and their characteristics 
               
               
                 suitable for producing dimpled stent material 
               
            
           
           
               
               
               
            
               
                 Type of laser 
                 Wavelength (nm) 
                 Interaction time 
               
               
                   
               
            
           
           
               
            
               
                 Infrared Lasers 
               
            
           
           
               
               
               
            
               
                 CO 2   
                 9600-10600 
                 micro seconds to 
               
               
                   
                   
                 continuous wave 
               
               
                 YAG 
                 232, 532, 1064 
                 fempto seconds to 
               
               
                 (eg: Nd: YAG, Er: 
                   
                 continuous wave 
               
               
                 YAG, and NdCrYAG) 
               
               
                 Ti: Sapphire 
                 650-1100 
                 fempto seconds to 
               
               
                   
                   
                 continuous wave 
               
               
                 Diode laser 
                 900-1100 
                 mili seconds to 
               
               
                   
                   
                 continuous wave 
               
               
                 Free electron laser 
                 tunable wavelength 
                 Micro to mili 
               
               
                   
                   
                 seconds 
               
            
           
           
               
            
               
                 Ultraviolet lasers 
               
            
           
           
               
               
               
            
               
                 Excimer lasers 
                 Ultraviolet range including 
                 fempto to nano 
               
               
                 (eg: ArF, KrF, 
                 157, 248, 282, 308, 351 
                 seconds 
               
               
                 XeBr, and XeCl) 
                 depending upon the gaseous 
               
               
                   
                 laser medium employed 
               
               
                   
               
            
           
         
       
     
     During the present preliminary efforts, feasibility of the suitable laser processing parameters for laser-based dimpling of the stent material (Ti6Al4V) was established through the computational model. The evolution of the dimple morphology was established through a time-dependent model parameters for the discrete laser residence time (the length of time of laser-material interaction) of 0.12 seconds by incorporating material properties such as density, specific heat, and thermal conductivity along with consideration to the physical phenomena such as the temperature dependent transition of material from solid to liquid to gas. Thus, with the computational model based on FE simulation, the depth and width of the dimples were estimated for laser powers of 500 W, 700 W, 900 W, and 1800 W and laser residence time of 0.12 seconds. These computational estimations also included the optical energy density (laser fluence) delivered per unit area under these conditions. The laser fluences for the input powers used in the current work with increasing order of the power were 212, 297, 382, and 763 J/mm 2  respectively. The transient effects during laser dimpling are realized through computational estimations of temperature at the surface and below the surface at depths of 0.095 mm, 0.190 mm, 0.370 mm, 0.550 mm, and 0.720 mm. Some of these depths represent the exact boundaries of phase changes (solid to liquid and liquid to vapor). The boundary between the liquid phase and vapor phase represents the profile of the final dimple depth. The dimple being part of a circular geometry, the width and depth of this boundary are the dimensions of the resultant dimple. These computational simulations indicated that the formation of dimples of various morphologies (depth and width) under the laser input powers employed in the current efforts in the range of 500 W-1800 W (with corresponding laser fluence range of 212 J/mm 2 -763 J/mm 2 ) occur during laser beam residence time of 0.12 seconds (shown in  FIGS. 8, 9, 10, and 11 ). The depth and width ranges of the dimples formed is between 0.25 mm-0.57 mm and 0.9 mm-3.2 mm respectively (shown in  FIG. 8-12 ). Thus, the computational model assisted in designing a combination of the process parameters (laser power, laser-material interaction time) and desired/resultant dimple parameters (depth and width). Furthermore, it has been reported in the literature that the optimum ratio of dimple depth (d or d′) to dimple width (w or w′) is in the range of 0.15-0.30. In the current set of experimental conditions, laser input power of 1800 W, laser beam residence time of 0.12 seconds (corresponding laser fluence of 763 J/mm 2 ) possessed a dimple depth to width ratio of ˜0.0.18 pointing towards potentially optimum performance. In addition, the optimum relative pitch, Q, defined as ratio of dimple spacing or pitch, P, and dimple width is reported to be in the range of 0.81-1.21. For the laser operating power of 1800 W and laser beam residence time of 0.12 seconds (laser fluence: 763 J/mm 2 ), the estimated dimple spacing or pitch, P, has value of 3.8 mm for the Q value of 1.21. Moreover, dimples of the various widths can be employed provided the ratio of dimple width (w or w′) to dimple depth (d or d′) and pitch, Q, of the dimple are maintained in the range of 0.15-0.3 and 0.81-1.21 respectively, as shown in  FIG. 7 ( c ) . 
       FIGS. 13A and 13B  show preferred embodiments of the present invention relating to a stent  100  having circumferential walls  110  enclosing a generally cylindrical inner space  120  surrounding a central axis  130 .  FIG. 13A  shows a view from the side of stent  100 , while  FIG. 13B  shows a view of an end of stent  100 , looking along central axis  130 . The circumferential walls  110  have one or more laser produced dimples  140  protruding outwardly away from the central axis  130  to create dimpled spaces  150  in outer edges of the cylindrical inner space  120 . When body fluid such as blood passes through the cylindrical inner space  120  it encounters the dimpled spaces  150  in the laser produced dimples  130  and becomes turbulent in those spaces, resulting in a decreased tendency for build-up of circulating material such as platelets against the inside of the circumferential walls  110  of the stent. 
     In preferred embodiments, the dimpled stent is made of any suitable material having good corrosion resistance and biocompatibility, such as a titanium alloy, cobalt-chrome alloys (MP35N), cobalt-nickel-chromium-molybdenum (CoNiCrMo) alloy, cobalt-chromium-tungsten-nickel (CoCrWNi) alloy known as L-605, stainless steel, Nitinol and biopolymers such as poly-lactic acid (PLLA), tyrosine polycarbonate, poly (anhydride ester) salicyclic acid and polytyrosine. In additional preferred embodiments, the dimpled stent is about 30 mm long, about 3.5 mm in diameter, and the circumferential walls are about 0.2 mm thick. The dimples can preferably have a depth of about 0.12 mm and a width of about 0.6 mm. 
     Additional preferred embodiments include a method for creating a dimpled stent. A flat coupon of stent material is preferably dimpled at one or more selected locations using a laser having a selected power and pulse interaction time to generate one or more dimples having a particular depth and width, with various spatial lay outs and various combinations of values for pitches P and R and orientation θ. The laser may be a Neodymium-Doped Yttrium Aluminum Garnet (Nd:Y 3 Al 5 O 12 ) or Nd:YAG laser having a 1.064 μm wavelength and fiber optic beam delivery with pulse interaction time of about 0.12 seconds and power ranging from about 500 W to 1800 W. Any other lasers listed in Table 1 can also be employed for this purpose and in that case power and interaction time can be varied in the rage of 100 W to 2000 W and 10 ns to 0.12 s, respectively. During laser processing, at a high level, the stent material contacted by the laser is partially ablated and the surrounding material changes shape into a generally dome-shaped dimple (having either spherical or ellipsoidal dome shape). After dimpling, the flat coupon of stent material, now dimpled, is mechanically formed into a cylindrical shape with the dimples protruding outwardly and two free edges of the cylindrically formed tube are precision laser butt welded (joined), for placement in a patient. Preferred applications involve use in coronary arteries following corrective surgery. Additional applications include implantation in native coronary arteries of the appropriate size, as well as implantation in a particular lesion such as proximal, non-angulated lesions, lesions of tortuous anatomy and complex situations including ostial lesions, bifurcation lesions, and calcified lesions. 
     In preferred embodiments, during the dimpling process, the laser material interaction region is assigned a heat flux boundary with a moving laser beam defined by: 
     
       
         
           
             
               k 
               ⁡ 
               
                 [ 
                 
                   
                     ( 
                     
                       
                         ∂ 
                         T 
                       
                       
                         ∂ 
                         x 
                       
                     
                     ) 
                   
                   + 
                   
                     ( 
                     
                       
                         ∂ 
                         T 
                       
                       
                         ∂ 
                         y 
                       
                     
                     ) 
                   
                   + 
                   
                     ( 
                     
                       
                         ∂ 
                         T 
                       
                       
                         ∂ 
                         z 
                       
                     
                     ) 
                   
                 
                 ] 
               
             
             = 
             
               
                 P 
                 X 
               
               - 
               
                 { 
                 
                   
                     h 
                     ⁡ 
                     
                       [ 
                       
                         T 
                         - 
                         
                           T 
                           0 
                         
                       
                       ] 
                     
                   
                   + 
                   
                     ɛ 
                     ⁢ 
                     
                       σ 
                       ⁡ 
                       
                         [ 
                         
                           
                             T 
                             4 
                           
                           - 
                           
                             T 
                             0 
                             4 
                           
                         
                         ] 
                       
                     
                   
                 
                 } 
               
             
           
         
       
     
     where h is heat transfer coefficient, ε is emissivity, σ is Stefan-Boltzman constant, T 0  is ambient temperature, and P X  is the input laser power intensity distribution. Such a heat source, P x  can have Gaussian or top hat or a dumbbell shaped beam profile in terms of spatial distribution of the power as expressed in the following set of equations. 
     
       
         
           
             
               
                 
                   
                     P 
                     g 
                   
                   = 
                   
                     
                       
                         P 
                         0 
                       
                       
                         π 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         
                           r 
                           0 
                           2 
                         
                       
                     
                     ⁢ 
                     
                       exp 
                       
                         - 
                         
                           ⌊ 
                           
                             
                               
                                 x 
                                 2 
                               
                               + 
                               
                                 y 
                                 2 
                               
                             
                             
                               r 
                               0 
                               2 
                             
                           
                           ⌋ 
                         
                       
                     
                   
                 
               
             
             
               
                 
                   
                     P 
                     th 
                   
                   = 
                   
                     
                       
                         P 
                         0 
                       
                       
                         π 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         
                           r 
                           0 
                           2 
                         
                       
                     
                     ⁢ 
                     
                       
                         exp 
                         
                           - 
                           
                             
                               
                                 ( 
                                 
                                   
                                     x 
                                     2 
                                   
                                   + 
                                   
                                     y 
                                     2 
                                   
                                 
                                 ) 
                               
                               n 
                             
                             
                               r 
                               0 
                               2 
                             
                           
                         
                       
                       ⁡ 
                       
                         ( 
                         
                           
                             where 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             n 
                           
                           ⁢ 
                           
                               
                           
                           -&gt; 
                           ∞ 
                         
                         ) 
                       
                     
                   
                 
               
             
             
               
                 
                   
                     P 
                     db 
                   
                   = 
                   
                     
                       
                         2 
                         ⁢ 
                         
                           P 
                           0 
                         
                       
                       
                         π 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         
                           r 
                           0 
                           2 
                         
                       
                     
                     ⁢ 
                     
                       
                         ( 
                         
                           
                             x 
                             + 
                             y 
                           
                           
                             r 
                             0 
                           
                         
                         ) 
                       
                       2 
                     
                     ⁢ 
                     
                       exp 
                       
                         - 
                         
                           
                             
                               ( 
                               
                                 
                                   x 
                                   2 
                                 
                                 + 
                                 
                                   y 
                                   2 
                                 
                               
                               ) 
                             
                             n 
                           
                           
                             r 
                             0 
                             2 
                           
                         
                       
                     
                   
                 
               
             
           
         
       
     
     where P g  is the Gaussian heat flux, P th  is the top hat heat flux, P db  is the dumbbell heat flux, P 0  is laser input power, r 0  is the radius of beam at which laser power transverse intensity decreases to 1/e 2 , and x, y, z are the Cartesisan coordinates with y along the axis of the beam and x and z are in the plane orthogonal to the axis of the beam and the beam intensity distribution is considered axisymmetric in x-z plane. 
     EXAMPLES 
     The following examples are included to demonstrate preferred embodiments of the invention. It should be appreciated by those of skill in the art that the techniques disclosed in the examples that follow present techniques discovered by the inventor to function well in the practice of the invention, and thus can be considered to constitute preferred modes for its practice. However, those of skill in the art should, in light of the present disclosure, appreciate that many changes can be made in the specific embodiments that are disclosed and still obtain a like or similar result without departing from the spirit and scope of the invention. 
     Example 1 
     Laser Fabrication of Dimpled Surface 
     For laser-engineering the dimples on stent material, the flat coupons Ti6Al4V alloy of dimensions 2.5×1.0×0.375 cm 3  were cut on the slow speed diamond saw. The coupons were ground on 600 grit SiC emery paper for flatness and uniform average surface roughness of 4 μm. The coupons were cleaned with deionized water followed by alcohol prior to laser dimpling experiments. The dimples were created on these coupons using Neodymium-Doped Yttrium Aluminum Garnet; Nd:Y 3 Al 5 O 12  laser (1.064 μm wavelength and fiber optic beam delivery) with pulse interaction time (0.12 seconds) and powers (500, 700, 900, and 1800 W) as stated above. Only single dimples were produced under laser power-laser beam interaction (laser fluence) combination to just verify the effects of presence of a dimple and its geometry (width and depth) on the fluid flow characteristics. This approach was adopted to reveal/realize and verify the increased turbulence and thrust based flow due to the presence of a dimple on the surface compared to a flat surface (absence of dimple) of the stent material. 
     In Vivo Evaluation in Simulated Body Fluid 
     The effectiveness of creation of dimples on the surface of Ti6Al4V was in vivo evaluated with the flow of simulated body fluid (SBF). The detailed method of SBF preparation is state of the art and discussed in the publication by Tadashi Kokubo and Hiroaki Takadama., “How useful is SBF in predicting in vivo bone bioactivity?”, Biomaterials, 27, (2006): 2907-2915, incorporated by reference herein. The chemical composition of the SBF solution is presented in Table 2 below. A Tris (Tris-hydroxymethyl aminomethane) chemical was added as a stabilizer until the entire solution reached a stable pH of 7.45. 
     
       
         
           
               
             
               
                 TABLE 2 
               
             
            
               
                   
               
               
                 Reagents for SBF preparation from Kokubo and Takadama 
               
            
           
           
               
               
               
               
               
            
               
                   
                 Reagent 
                   
                 Amount 
                 Formula Weight 
               
               
                   
                   
               
            
           
           
               
               
               
               
               
            
               
                   
                 NaCl 
                 8.035 
                 g 
                 58.4430 
               
               
                   
                 NaHCO 3   
                 0.355 
                 g 
                 84.0068 
               
               
                   
                 KCl 
                 0.225 
                 g 
                 74.5515 
               
               
                   
                 K 2 HPO 4 •3H 2 O 
                 0.231 
                 g 
                 228.2220 
               
               
                   
                 MgCl 2 •6H 2 O 
                 0.311 
                 g 
                 203.3034 
               
               
                   
                 CaCl 2   
                 0.292 
                 g 
                 110.9848 
               
               
                   
                 Na 2 SO 4   
                 0.072 
                 g 
                 142.0428 
               
               
                   
                 1.0 M -HCl 
                 5 
                 ml 
                 — 
               
               
                   
                   
               
            
           
         
       
     
     The measure of SBF flow characteristics was conducted following the general principle explained in the work of Soltani Bozchalooi, A. Careaga Houck, J. M. AlGhamdi, and K. Youcef-Toumi, “Design and control of multi-actuated atomic force microscope for large-range and high-speed imaging”, Ultramicroscopy, 160 (2016): 213-224, incorporated by reference herein. Generally, an experimental set up was designed for in vivo evaluation of SBF flow under the gravitational force over a dimpled sample, shown in  FIG. 14 . This assembly was put into a rubber hose to mimic the artery with the real life ratio between the length of the left subclavian artery (22-27.5 cm) and the stent (9-21 mm), averaging approximately 27:1 in size. Hence, the plastic mimic vessel used was 70 cm long, compared to the stent length of 2.5 cm. The fluid flow characteristics of gravitationally fed SBF were evaluated for time required for a given volume of SBF to flow over the sample surface of the given dimensions. For comparison, the time of flow characteristics were evaluated for three different samples of identical dimensions: (1) untreated stent material, (2) surface dimpled stent material, and (3) no stent material (empty vessel). The time for a given amount of SBF to flow through plastic mimic vessel for three different conditions of samples listed above was accurately measured using a digital watch integrated with the experimental set up. The watch accurately measured the time between the times of starting and end of fluid flow of the given volume through the mimic vessel. Total of five readings of time were recorded for each sample condition. The time of flow in combination with the distance travelled within the mimic vessel was further utilized to calculate experimentally observed SBF flow velocity. 
     The laser ablated volume of a dimple (dimensions) was expected to increase with increase in power from 500 W to 1800 W. In light of this, the largest dimensions (width and depth) of the dimple made with 1800 W were expected to experience the most significant changes in the fluid flow. Hence, gravitationally fed fluid flow measurements were conducted only on the samples with the dimple produced at 1800 W. 
     The results from the three conditions displayed clear differences in the SBF flow characteristics. As expected, the vessel with no stent displayed the shortest average time of 32.59 seconds for the SBF to flow through, shown in  FIG. 15 . On the other hand, the vessel with untreated stent had the average time of 34.55 seconds whereas the vessel with laser dimpled stent resulted in an average time of 32.88 seconds, also shown in  FIG. 15 . Thus, there was a difference of ˜2 seconds between the SBF flow in the vessel containing untreated and no stent materials. Such a difference in time was further significantly reduced to 0.3 seconds for the vessel containing laser dimpled stent. These results were encouraging with respect to the original concept and provided a possibility of deployment of the dimpled stent. 
     The dimensions of the dimple produced with 1800 W were predicted using computational approach described earlier. These computed dimensions were 1.62 mm and 0.60 mm for width and depth respectively. The improved fluid flow characteristic of the laser dimpled sample at 1800 W compared to non-laser treated stent material is considered to be due to increased fluid flow and thrust and decreased friction within the dimple. Such fluid flow characteristics are result of the improved theoretical fluid flow efficiency and can be realized through the formation of the vortex at the underside of the dimple and the uneven distribution of pressure inside of the dimple, both of which generate turbulence in the fluid (as shown in  FIG. 5 ). Some portion of fluid in the dimpled zone is not easily driven by the upper main flow, and instead form an “eddy zone” that prohibits the escape of fluid (also as shown in  FIG. 5 ). The friction factor is expected to decrease as the fluid approaches the center of the dimple and finally reaches a minimum value at the bottom. The remaining fluid in the dimpled zone that can escape is mixed with the main flow adequately. As a result of the mixing of the escaped fluid, there is a high-pressure region (see  FIG. 5 ) at the backside of the dimpled zone causing the friction factor to reach a maximum value. The maximum friction factor value is sufficient enough to counter the sticking forces of the platelets and make them flow with the bloodstream without sticking to the stent wall as shown in  FIG. 6 . All of these factors are expected to result in the slight increase of fluid flow velocity in the dimpled surface in comparison to the untreated surface, shown in  FIG. 16 . 
     The preliminary efforts indicate: (1) improvement in SBF flow characteristics of the dimpled stent design compared to an untreated stent, (2) by increasing the fluid flow and thrust, the possibility of plaque formation on the stent wall can be substantially reduced, and (3) by imprinting ideal dimple dimensions and dimple spatial layout, the anti-sticking properties within the stent, the acceleration of platelets, and the subsequent decrease in the tendency for restenosis of the stent can be achieved. Although each dimple contributes to improved flow characteristics (velocity), the optimal stent dimensions and spatial layout of the dimples are critical parameters for the smoothest and most rapid blood flow (shown in  FIG. 16 ). Furthermore, the dimpled stent can provide immensely cost-efficient disease-preventing capabilities. In conjunction with efficiency, stability, and potential minimal costs, the study indicates that laser ablation is the ideal method to fabricate a dimpled stent surface to prevent plaque formation. The reduction or the elimination of arterial blockage is expected to impact those affected by angina (chest pain) by increasing the lifetime of the stent and the patient. This design and approach are further expected to decrease the costs involved in bypass revision surgeries and improve the quality of life for the patient. 
     REFERENCES CITED 
     The following references, to the extent that they provide exemplary procedural or other details supplementary to those set forth herein, are specifically incorporated herein by reference.
     Jørgensen, Erik, Steffen Helqvist, Lene Klovgaard, Jens Kastrup, Peter Clemmensen, Lene Holmvang, Thomas Engstrom, Kari Saunamaki, and Henning Kelbæk. “Restenosis in coronary bare metal stents. Importance of time to follow-up: A comparison of coronary angiograms 6 months and 4 years after implantation.” Scandinavian Cardiovascular Journal, 43, (2009): 87-93.   Sardi. (2006). Coronary Stents. www.pages.drexel.edu/˜sr335/Background.html.   Shah, S. N. (2014). Coronary Bare-Metal Stent. emedicine.medscape.com/article/2009987-overview#a8   Shah, P. K “Inflammation, neointimal hyperplasia, and restenosis: as the leukocytes roll, the arteries thicken.” Circulation, 107 (2003): 2175-2177.   Balachandran, K., &amp; Zambahari, R. (2015). Absorb Bioresorbable Vascular Scaffold.  Institut Jantung Negara National Heart Institute.      Cottone, Robert J., G. Lawrence Thatcher, Sherry P. Parker, Laurence Hanks, David A. Kujawa, Stephen M. Rowland, Marco Costa, Robert S. Schwartz, and Yoshinobu Onuma. “OrbusNeich fully absorbable coronary stent platform incorporating dual partitioned coatings.” Euro Intervention 5, no. Suppl F (2009): F65-71   Colombo, Antonio, Goran Stankovic, and Jeffrey W. Moses. “Selection of coronary stents.” Journal of the American College of Cardiology 40, no. 6 (2002): 1021-1033.   P. W. Bearman and J. K. Harvey, “Golf ball aerodynamics”, Aeronaut., 27 (1976) 112-122.   Jin Choi, Woo-Pyung Jeon, and Haecheon Choi, “Mechanism of drag reduction by dimples on a sphere”, Physics of Fluids, 18 (2006) 041702.   Rabindra D. Mehta, “Aerodynamics of sports balls”, Ann. Rev. Fluid Mech., 17 (1983) 151-189.   Jeffrey Ryan Kensrud, “Determining aerodynamic properties of sports ball in situ”, Master of Science in Mechanical Engineering Thesis, Washington State University, 2010.   Koechner, W., Solid-state Laser Engineering (6 th  Edition), Springer, Berlin (2005).   Kastrati, Adnan, Julinda Mehilli, Josef Dirschinger, Franz Dotzer, Helmut Schuhlen, Franz-Josef Neumann, Martin Fleckenstein, Conrad Pfafferott, Melchior Seyfarth, and Albert Schomig. “Intracoronary stenting and angiographic results.” Circulation 103, no. 23 (2001): 2816-2821.   Willstrand, O., Intensity distribution conversion from Gaussian to Top-Hat in a single-mode fiber connector (Master&#39;s Thesis) in University of  18 (2006), 041702 . Lund Reports on Atomic Physics , (2013).   Paschotta, R. (2010). Fluence. www.rp-photonics.com/fluence.html.   Tadashi Kokubo, Hiroaki Takadama., “How useful is SBF in predicting in vivo bone bioactivity?”, Biomaterials, 27, (2006): 2907-2915.   Silva, Carlos, and Doseo Park. “Optimization of fin performance in a laminar channel flow through dimpled surfaces.” Journal of Heat Transfer 131, no. 2 (2009): 021702.   Soltani Bozchalooi, A. Careaga Houck, J. M. AlGhamdi, and K. Youcef-Toumi, “Design and control of multi-actuated atomic force microscope for large-range and high-speed imaging”, Ultramicroscopy, 160 (2016): 213-224.   Sangtarash, Farhad, and Hossein Shokuhmand. “Experimental and numerical investigation of heat transfer, temperature distribution, and louver efficiency on the dimpled louvers fin banks.” Advances in Mechanical Engineering 7, (2015): 1687814015573825