Theranostic digital twins: Concept, framework and roadmap towards personalized radiopharmaceutical therapies.

Radiopharmaceutical therapy (RPT) is a rapidly developing field of nuclear medicine, with several RPTs already well established in the treatment of several different types of cancers. However, the current approaches to RPTs often follow a somewhat inflexible "one size fits all" paradigm, where patients are administered the same amount of radioactivity per cycle regardless of their individual characteristics and features. This approach fails to consider inter-patient variations in radiopharmacokinetics, radiation biology, and immunological factors, which can significantly impact treatment outcomes. To address this limitation, we propose the development of theranostic digital twins (TDTs) to personalize RPTs based on actual patient data. Our proposed roadmap outlines the steps needed to create and refine TDTs that can optimize radiation dose to tumors while minimizing toxicity to organs at risk. The TDT models incorporate physiologically-based radiopharmacokinetic (PBRPK) models, which are additionally linked to a radiobiological optimizer and an immunological modulator, taking into account factors that influence RPT response. By using TDT models, we envisage the ability to perform virtual clinical trials, selecting therapies towards improved treatment outcomes while minimizing risks associated with secondary effects. This framework could empower practitioners to ultimately develop tailored RPT solutions for subgroups and individual patients, thus improving the precision, accuracy, and efficacy of treatments while minimizing risks to patients. By incorporating TDT models into RPTs, we can pave the way for a new era of precision medicine in cancer treatment.

Advancements in tissue engineering for cardiovascular health: a biomedical engineering perspective.

Myocardial infarction (MI) stands as a prominent contributor to global cardiovascular disease (CVD) mortality rates. Acute MI (AMI) can result in the loss of a large number of cardiomyocytes (CMs), which the adult heart struggles to replenish due to its limited regenerative capacity. Consequently, this deficit in CMs often precipitates severe complications such as heart failure (HF), with whole heart transplantation remaining the sole definitive treatment option, albeit constrained by inherent limitations. In response to these challenges, the integration of bio-functional materials within cardiac tissue engineering has emerged as a groundbreaking approach with significant potential for cardiac tissue replacement. Bioengineering strategies entail fortifying or substituting biological tissues through the orchestrated interplay of cells, engineering methodologies, and innovative materials. Biomaterial scaffolds, crucial in this paradigm, provide the essential microenvironment conducive to the assembly of functional cardiac tissue by encapsulating contracting cells. Indeed, the field of cardiac tissue engineering has witnessed remarkable strides, largely owing to the application of biomaterial scaffolds. However, inherent complexities persist, necessitating further exploration and innovation. This review delves into the pivotal role of biomaterial scaffolds in cardiac tissue engineering, shedding light on their utilization, challenges encountered, and promising avenues for future advancement. By critically examining the current landscape, we aim to catalyze progress toward more effective solutions for cardiac tissue regeneration and ultimately, improved outcomes for patients grappling with cardiovascular ailments.

Localized radiotherapy of solid tumors using radiopharmaceutical loaded implantable system: insights from a mathematical model.

Introduction: Computational models yield valuable insights into biological interactions not fully elucidated by experimental approaches. This study investigates an innovative spatiotemporal model for simulating the controlled release and dispersion of radiopharmaceutical therapy (RPT) using 177Lu-PSMA, a prostate-specific membrane antigen (PSMA) targeted radiopharmaceutical, within solid tumors via a dual-release implantable delivery system. Local delivery of anticancer agents presents a strategic approach to mitigate adverse effects while optimizing therapeutic outcomes. Methods: This study evaluates various factors impacting RPT efficacy, including hypoxia region extension, binding affinity, and initial drug dosage, employing a novel 3-dimensional computational model. Analysis gauges the influence of these factors on radiopharmaceutical agent concentration within the tumor microenvironment. Furthermore, spatial and temporal radiopharmaceutical distribution within both the tumor and surrounding tissue is explored. Results: Analysis indicates a significantly higher total concentration area under the curve within the tumor region compared to surrounding normal tissue. Moreover, drug distribution exhibits notably superior efficacy compared to the radiation source. Additionally, low microvascular density in extended hypoxia regions enhances drug availability, facilitating improved binding to PSMA receptors and enhancing therapeutic effectiveness. Reductions in the dissociation constant (KD) lead to heightened binding affinity and increased internalized drug concentration. Evaluation of initial radioactivities (7.1×107, 7.1×108, and 7.1×109 [Bq]) indicates that an activity of 7.1×108 [Bq] offers a favorable balance between tumor cell elimination and minimal impact on normal tissues. Discussion: These findings underscore the potential of localized radiopharmaceutical delivery strategies and emphasize the crucial role of released drugs relative to the radiation source (implant) in effective tumor treatment. Decreasing the proximity of the drug to the microvascular network and enhancing its distribution within the tumor promote a more effective therapeutic outcome. The study furnishes valuable insights for future experimental investigations and clinical trials, aiming to refine medication protocols and minimize reliance on in vivo testing.

Programmable intratumoral drug delivery to breast cancer using wireless bioelectronic device with electrochemical actuation.

OBJECTIVE: Breast cancer is a global health concern that demands attention. In our contribution to addressing this disease, our study focuses on investigating a wireless micro-device for intratumoral drug delivery, utilizing electrochemical actuation. Microdevices have emerged as a promising approach in this field due to their ability to enable controlled injections in various applications. METHODS: Our study is conducted within a computational framework, employing models that simulate the behavior of the microdevice and drug discharge based on the principles of the ideal gas law. Furthermore, the distribution of the drug within the tissue is simulated, considering both diffusion and convection mechanisms. To predict the therapeutic response, a pharmacodynamic model is utilized, considering the chemotherapeutic effects and cell proliferation. RESULTS: The findings demonstrate that an effective current of 3 mA, along with an initial gas volume equal to the drug volume in the microdevice, optimizes drug delivery. Microdevices with multiple injection capabilities exhibit enhanced therapeutic efficacy, effectively suppressing cell proliferation. Additionally, tumors with lower microvascular density experience higher drug concentrations in the extracellular space, resulting in significant cell death in hypoxic regions. CONCLUSIONS: Achieving an efficient therapeutic response involves considering both the characteristics of the tumor microenvironment and the frequency of injections within a specific time frame.

Improving tumor treatment through intratumoral injection of drug-loaded magnetic nanoparticles and low-intensity ultrasound.

The intratumoral injection of therapeutic agents responsive to external stimuli has gained considerable interest in treating accessible tumors due to its biocompatibility and capacity to reduce side effects. For the first time, a novel approach is explored to investigate the feasibility of utilizing low-intensity ultrasound in combination with intratumoral injection of drug-loaded magnetic nanoparticles (MNPs) to thermal necrosis and chemotherapy with the objective of maximizing tumor damage while avoiding harm to surrounding healthy tissue. In this study, a mathematical framework is proposed based on a multi-compartment model to evaluate the effects of ultrasound transducer's specifications, MNPs size and distribution, and drug release in response to the tumor microenvironment characteristics. The results indicate that while a higher injection rate may increase interstitial fluid pressure, it also simultaneously enhances the concentration of the therapeutic agent. Moreover, by increasing the power and frequency of the transducer, the acoustic pressure and intensity can be enhanced. This, in turn, increases the impact on accumulated MNPs, resulting in a rise in temperature and localized heat generation. Results have demonstrated that smaller MNPs have a lower capacity to generate heat compared to larger MNPs, primarily due to the impact of sound waves on them. It is worth noting that smaller MNPs have been observed to have enhanced diffusion, allowing them to effectively spread within the tumor. However, their smaller size also leads to rapid elimination from the extracellular space into the bloodstream. To summarize, this study demonstrated that the local injection of MNPs carrying drugs not only enables localized chemotherapy but also enhances the effectiveness of low-intensity ultrasound in inducing tissue thermal necrosis. The findings of this study can serve as a valuable and reliable resource for future research in this field and contribute to the development of personalized medicine.

Image-Based Modeling of Drug Delivery during Intraperitoneal Chemotherapy in a Heterogeneous Tumor Nodule.

Intraperitoneal (IP) chemotherapy is a promising treatment approach for patients diagnosed with peritoneal carcinomatosis, allowing the direct delivery of therapeutic agents to the tumor site within the abdominal cavity. Nevertheless, limited drug penetration into the tumor remains a primary drawback of this method. The process of delivering drugs to the tumor entails numerous complications, primarily stemming from the specific pathophysiology of the tumor. Investigating drug delivery during IP chemotherapy and studying the parameters affecting it are challenging due to the limitations of experimental studies. In contrast, mathematical modeling, with its capabilities such as enabling single-parameter studies, and cost and time efficiency, emerges as a potent tool for this purpose. In this study, we developed a numerical model to investigate IP chemotherapy by incorporating an actual image of a tumor with heterogeneous vasculature. The tumor's geometry is reconstructed using image processing techniques. The model also incorporates drug binding and uptake by cancer cells. After 60 min of IP treatment with Doxorubicin, the area under the curve (AUC) of the average free drug concentration versus time curve, serving as an indicator of drug availability to the tumor, reached 295.18 mol·m-3·s-1. Additionally, the half-width parameter W1/2, which reflects drug penetration into the tumor, ranged from 0.11 to 0.14 mm. Furthermore, the treatment resulted in a fraction of killed cells reaching 20.4% by the end of the procedure. Analyzing the spatial distribution of interstitial fluid velocity, pressure, and drug concentration in the tumor revealed that the heterogeneous distribution of tumor vasculature influences the drug delivery process. Our findings underscore the significance of considering the specific vascular network of a tumor when modeling intraperitoneal chemotherapy. The proposed methodology holds promise for application in patient-specific studies.

In-silico investigations of haemodynamic parameters for a blunt thoracic aortic injury case.

Accounting for 1.5% of thoracic trauma, blunt thoracic aortic injury (BTAI) is a rare disease with a high mortality rate that nowadays is treated mostly via thoracic endovascular aortic repair (TEVAR). Personalised computational models based on fluid-solid interaction (FSI) principals not only support clinical researchers in studying virtual therapy response, but also are capable of predicting eventual outcomes. The present work studies the variation of key haemodynamic parameters in a clinical case of BTAI after successful TEVAR, using a two-way FSI model. The three-dimensional (3D) patient-specific geometries of the patient were coupled with three-element Windkessel model for both prior and post intervention cases, forcing a correct prediction of blood flow over each section. Results showed significant improvement in velocity and pressure distribution after stenting. High oscillatory, low magnitude shear (HOLMES) regions require careful examination in future follow-ups, since thrombus formation was confirmed in some previously clinically reported cases of BTAI treated with TEVAR. The strength of swirling flows along aorta was also damped after stent deployment. Highlighting the importance of haemodynamic parameters in case-specific therapies. In future studies, compromising motion of aortic wall due to excessive cost of FSI simulations can be considered and should be based on the objectives of studies to achieve a more clinical-friendly patient-specific CFD model.

Nanomedicine: New Frontiers in Fighting Microbial Infections.

Microbes have dominated life on Earth for the past two billion years, despite facing a variety of obstacles. In the 20th century, antibiotics and immunizations brought about these changes. Since then, microorganisms have acquired resistance, and various infectious diseases have been able to avoid being treated with traditionally developed vaccines. Antibiotic resistance and pathogenicity have surpassed antibiotic discovery in terms of importance over the course of the past few decades. These shifts have resulted in tremendous economic and health repercussions across the board for all socioeconomic levels; thus, we require ground-breaking innovations to effectively manage microbial infections and to provide long-term solutions. The pharmaceutical and biotechnology sectors have been radically altered as a result of nanomedicine, and this trend is now spreading to the antibacterial research community. Here, we examine the role that nanomedicine plays in the prevention of microbial infections, including topics such as diagnosis, antimicrobial therapy, pharmaceutical administration, and immunizations, as well as the opportunities and challenges that lie ahead.

Recent Advances of Utilizing Artificial Intelligence in Lab on a Chip for Diagnosis and Treatment.

Nowadays, artificial intelligence (AI) creates numerous promising opportunities in the life sciences. AI methods can be significantly advantageous for analyzing the massive datasets provided by biotechnology systems for biological and biomedical applications. Microfluidics, with the developments in controlled reaction chambers, high-throughput arrays, and positioning systems, generate big data that is not necessarily analyzed successfully. Integrating AI and microfluidics can pave the way for both experimental and analytical throughputs in biotechnology research. Microfluidics enhances the experimental methods and reduces the cost and scale, while AI methods significantly improve the analysis of huge datasets obtained from high-throughput and multiplexed microfluidics. This review briefly presents a survey of the role of AI and microfluidics in biotechnology. Also, the incorporation of AI with microfluidics is comprehensively investigated. Specifically, recent studies that perform flow cytometry cell classification, cell isolation, and a combination of them by gaining from both AI methods and microfluidic techniques are covered. Despite all current challenges, various fields of biotechnology can be remarkably affected by the combination of AI and microfluidic technologies. Some of these fields include point-of-care systems, precision, personalized medicine, regenerative medicine, prognostics, diagnostics, and treatment of oncology and non-oncology-related diseases.

3D Printed Hydrogels for Ocular Wound Healing.

Corneal disease is one of the most significant causes of blindness around the world. Presently, corneal transplantation is the only way to treat cornea blindness. It should be noted that the amount of cornea that people donate is so much less than that required (1:70). Therefore, scientists have tried to resolve this problem with tissue engineering and regenerative medicine. Fabricating cornea with traditional methods is difficult due to their unique properties, such as transparency and geometry. Bioprinting is a technology based on additive manufacturing that can use different biomaterials as bioink for tissue engineering, and the emergence of 3D bioprinting presents a clear possibility to overcome this problem. This new technology requires special materials for printing scaffolds with acceptable biocompatibility. Hydrogels have received significant attention in the past 50 years, and they have been distinguished from other materials because of their unique and outstanding properties. Therefore, hydrogels could be a good bioink for the bioprinting of different scaffolds for corneal tissue engineering. In this review, we discuss the use of different types of hydrogel for bioink for corneal tissue engineering and various methods that have been used for bioprinting. Furthermore, the properties of hydrogels and different types of hydrogels are described.

Synthetic 18F-FDG PET Image Generation Using a Combination of Biomathematical Modeling and Machine Learning.

No previous works have attempted to combine generative adversarial network (GAN) architectures and the biomathematical modeling of positron emission tomography (PET) radiotracer uptake in tumors to generate extra training samples. Here, we developed a novel computational model to produce synthetic 18F-fluorodeoxyglucose (18F-FDG) PET images of solid tumors in different stages of progression and angiogenesis. First, a comprehensive biomathematical model is employed for creating tumor-induced angiogenesis, intravascular and extravascular fluid flow, as well as modeling of the transport phenomena and reaction processes of 18F-FDG in a tumor microenvironment. Then, a deep convolutional GAN (DCGAN) model is employed for producing synthetic PET images using 170 input images of 18F-FDG uptake in each of 10 different tumor microvascular networks. The interstitial fluid parameters and spatiotemporal distribution of 18F-FDG uptake in tumor and healthy tissues have been compared against previously published numerical and experimental studies, indicating the accuracy of the model. The structural similarity index measure (SSIM) and peak signal-to-noise ratio (PSNR) of the generated PET sample and the experimental one are 0.72 and 28.53, respectively. Our results demonstrate that a combination of biomathematical modeling and GAN-based augmentation models provides a robust framework for the non-invasive and accurate generation of synthetic PET images of solid tumors in different stages.

Modeling the efficacy of different anti-angiogenic drugs on treatment of solid tumors using 3D computational modeling and machine learning.

Accurate simulation of tumor growth during chemotherapy has significant potential to alleviate the risk of unknown side effects and optimize clinical trials. In this study, a 3D simulation model encompassing angiogenesis and tumor growth was developed to identify the vascular endothelial growth factor (VEGF) concentration and visualize the formation of a microvascular network. Accordingly, three anti-angiogenic drugs (Bevacizumab, Ranibizumab, and Brolucizumab) at different concentrations were evaluated in terms of their efficacy. Moreover, comprehensive mechanisms of tumor cell proliferation and endothelial cell angiogenesis are proposed to provide accurate predictions for optimizing drug treatments. The evaluation of simulation output data can extract additional features such as tumor volume, tumor cell number, and the length of new vessels using machine learning (ML) techniques. These were investigated to examine the different stages of tumor growth and the efficacy of different drugs. The results indicate that brolucizuman has the best efficacy by decreasing the length of sprouting new vessels by up to 16%. The optimal concentration was obtained at 10 mol m-3 with an effectiveness percentage of 42% at 20 days post-treatment. Furthermore, by performing comparative analysis, the best ML method (matching the performance of the reference simulations) was identified as reinforcement learning with a 3.3% mean absolute error (MAE) and an average accuracy of 94.3%.

Formulation and Characterization of Poly (Ethylene Glycol)-Coated Core-Shell Methionine Magnetic Nanoparticles as a Carrier for Naproxen Delivery: Growth Inhibition of Cancer Cells.

An efficient and selective drug delivery vehicle for cancer cells can remarkably improve therapeutic approaches. In this study, we focused on the synthesis and characterization of magnetic Ni1-xCoxFe2O4 nanoparticles (NPs) coated with two layers of methionine and polyethylene glycol to increase the loading capacity and lower toxicity to serve as an efficient drug carrier. Ni1-xCoxFe2O4@Methionine@PEG NPs were synthesized by a reflux method then characterized by FTIR, XRD, FESEM, TEM, and VSM. Naproxen was used as a model drug and its loading and release in the vehicles were evaluated. The results for loading efficiency showed 1 mg of Ni1-xCoxFe2O4@Methionine@PEG NPs could load 0.51 mg of the naproxen. Interestingly, Ni1-xCoxFe2O4@Methionine@PEG showed a gradual release of the drug, achieving a time-release up to 5 days, and demonstrated that a pH 5 release of the drug was about 20% higher than Ni1-xCoxFe2O4@Methionine NPs, which could enhance the intracellular drug release following endocytosis. At pH 7.4, the release of the drug was slower than Ni1-xCoxFe2O4@Methionine NPs; demonstrating the potential to minimize the adverse effects of anticancer drugs on normal tissues. Moreover, naproxen loaded onto the Ni1-xCoxFe2O4@Methionine@PEG NPs for breast cancer cell lines MDA-MB-231 and MCF-7 showed more significant cell death than the free drug, which was measured by an MTT assay. When comparing both cancer cells, we demonstrated that naproxen loaded onto the Ni1-xCoxFe2O4@Methionine@PEG NPs exhibited greater cell death effects on the MCF-7 cells compared with the MDA-MB-231 cells. The results of the hemolysis test also showed good hemocompatibility. The results indicated that the prepared magnetic nanocarrier could be suitable for controlled anticancer drug delivery.

A multiscale cell-based model of tumor growth for chemotherapy assessment and tumor-targeted therapy through a 3D computational approach.

OBJECTIVES: Computational modeling of biological systems is a powerful tool to clarify diverse processes contributing to cancer. The aim is to clarify the complex biochemical and mechanical interactions between cells, the relevance of intracellular signaling pathways in tumor progression and related events to the cancer treatments, which are largely ignored in previous studies. MATERIALS AND METHODS: A three-dimensional multiscale cell-based model is developed, covering multiple time and spatial scales, including intracellular, cellular, and extracellular processes. The model generates a realistic representation of the processes involved from an implementation of the signaling transduction network. RESULTS: Considering a benign tumor development, results are in good agreement with the experimental ones, which identify three different phases in tumor growth. Simulating tumor vascular growth, results predict a highly vascularized tumor morphology in a lobulated form, a consequence of cells' motile behavior. A novel systematic study of chemotherapy intervention, in combination with targeted therapy, is presented to address the capability of the model to evaluate typical clinical protocols. The model also performs a dose comparison study in order to optimize treatment efficacy and surveys the effect of chemotherapy initiation delays and different regimens. CONCLUSIONS: Results not only provide detailed insights into tumor progression, but also support suggestions for clinical implementation. This is a major step toward the goal of predicting the effects of not only traditional chemotherapy but also tumor-targeted therapies.

Theranostic digital twins for personalized radiopharmaceutical therapies: Reimagining theranostics via computational nuclear oncology.

This work emphasizes that patient data, including images, are not operable (clinically), but that digital twins are. Based on the former, the latter can be created. Subsequently, virtual clinical operations can be performed towards selection of optimal therapies. Digital twins are beginning to emerge in the field of medicine. We suggest that theranostic digital twins (TDTs) are amongst the most natural and feasible flavors of digitals twins. We elaborate on the importance of TDTs in a future where 'one-size-fits-all' therapeutic schemes, as prevalent nowadays, are transcended in radiopharmaceutical therapies (RPTs). Personalized RPTs will be deployed, including optimized intervention parameters. Examples include optimization of injected radioactivities, sites of injection, injection intervals and profiles, and combination therapies. Multi-modal multi-scale images, combined with other data and aided by artificial intelligence (AI) techniques, will be utilized towards routine digital twinning of our patients, and will enable improved deliveries of RPTs and overall healthcare.

The Effects of Curcumin Nanoparticles Incorporated into Collagen-Alginate Scaffold on Wound Healing of Skin Tissue in Trauma Patients.

Wound healing is a biological process that is mainly crucial for the rehabilitation of injured tissue. The incorporation of curcumin (Cur) into a hydrogel system is used to treat skin wounds in different diseases due to its hydrophobic character. In this study, sodium alginate and collagen, which possess hydrophilic, low toxic, and biocompatible properties, were utilized. Collagen/alginate scaffolds were synthesized, and nanocurcumin was incorporated inside them; their interaction was evaluated by FTIR spectroscopy. Morphological studies investigated structures of the samples studied by FE-SEM. The release profile of curcumin was detected, and the cytotoxic test was determined on the L929 cell line using an MTT assay. Analysis of tissue wound healing was performed by H&E staining. Nanocurcumin was spherical, its average particle size was 45 nm, and the structure of COL/ALG scaffold was visible. The cell viability of samples was recorded in cells after 24 h incubation. Results of in vivo wound healing remarkably showed CUR-COL/ALG scaffold at about 90% (p < 0.001), which is better than that of COL/ALG, 80% (p < 0.001), and the control 73.4% (p < 0.01) groups at 14 days/ The results of the samples' FTIR indicated that nanocurcumin was well-entrapped into the scaffold, which led to improving the wound-healing process. Our results revealed the potential of nanocurcumin incorporated in COL/ALG scaffolds for the wound healing of skin tissue in trauma patients.

Computational modeling of thermal combination therapies by magneto-ultrasonic heating to enhance drug delivery to solid tumors.

For the first time, inspired by magnetic resonance imaging-guidance high intensity focused ultrasound (MR-HIFU) technology, i.e., medication therapy and thermal ablation in one session, in a preclinical setting based on a developed mathematical model, the performance of doxorubicin (Dox) and its encapsulation have been investigated in this study. Five different treatment methods, that combine medication therapy with mild hyperthermia by MRI contrast ([Formula: see text]) and thermal ablation via HIFU, are investigated in detail. A comparison between classical chemotherapy and thermochemistry shows that temperature can improve the therapeutic outcome by stimulating biological properties. On the other hand, the intravascular release of ThermoDox increases the concentration of free drug by 2.6 times compared to classical chemotherapy. The transport of drug in interstitium relies mainly on the diffusion mechanism to be able to penetrate deeper and reach the cancer cells in the inner regions of the tumor. Due to the low drug penetration into the tumor center, thermal ablation has been used for necrosis of the central areas before thermochemotherapy and ThermoDox therapy. Perfusion of the region around the necrotic zone is found to be damaged, while cells in the region are alive and not affected by medication therapy; so, there is a risk of tumor recurrence. Therefore, it is recommended that ablation be performed after the medication therapy. Our model describes a comprehensive assessment of MR-HIFU technology, taking into account many effective details, which can be a reliable guide towards the optimal use of drug delivery systems.

Mathematical simulation and prediction of tumor volume using RBF artificial neural network at different circumstances in the tumor microenvironment.

Uncontrolled proliferation of cells in a tissue caused by genetic mutations inside a cell is referred to as a tumor. A tumor which grows rapidly encounters a barrier when it grows to a certain size in presence of preexisting vasculature. This is the time when it has to find a way to go on the growth. The tumor starts to secrete tumor angiogenic factors (TAFs) and stimulate preexisting vessels to grow new sprouts. These new sprouts will find their way to the tumor in the extracellular matrix (ECM) by the gradient of TAF. As these new capillaries anastomose and reach tumor, fresh oxygen is available for the tumor and it will reinitiate the growth. Number of initial sprouts, distance of initial tumor cells from the vessel(s) and initial density of the tumor at the time of sprout formation are questions which are to be investigated. In the present study, the aim is to find the response of tumor cells and vessels to the reciprocal effects of each other in different circumstances in the tissue. Together with a mathematical formulation, a radial basis function (RBF) neural network is established to predict the number of tumor cells at different circumstances including size and distance of initial tumors from the parent vessel. A final formulation is given for the final number of tumor cells as a function of initial tumor size and distance between a parent vessel and a tumor. Results of this simulation demonstrate that, increasing the distance between a tumor and a parent vessel decreases the number of final tumor cells. Specially, this decrement becomes faster beyond a certain distance. Moreover, initial tumors in bigger domains must become much bigger before inducing angiogenesis which makes it harder for them to survive.