The relationship between compartment models and their stochastic counterparts:A comparative study with examples of the COVID-19 epidemic modeling

Deterministic compartment models(CMs)and stochastic models,including stochastic CMs and agent-based models,are widely utilized in epidemic modeling.However,the relationship between CMs and their corresponding stochastic models is not well understood.The present study aimed to address this gap by conducting a comparative study using the susceptible,exposed,infectious,and recovered(SEIR)model and its extended CMs from the coronavirus disease 2019 modeling literature.We demonstrated the equivalence of the numerical solution of CMs using the Euler scheme and their stochastic counterparts through theoretical analysis and simulations.Based on this equivalence,we proposed an efficient model calibration method that could replicate the exact solution of CMs in the corresponding stochastic models through parameter adjustment.The advancement in calibration techniques enhanced the accuracy of stochastic modeling in capturing the dynamics of epidemics.However,it should be noted that discrete-time stochastic models cannot perfectly reproduce the exact solution of continuous-time CMs.Additionally,we proposed a new stochastic compartment and agent mixed model as an alternative to agent-based models for large-scale population simulations with a limited number of agents.This model offered a balance between computational efficiency and accuracy.The results of this research contributed to the comparison and unification of deterministic CMs and stochastic models in epidemic modeling.Furthermore,the results had implications for the development of hybrid models that integrated the strengths of both frameworks.Overall,the present study has provided valuable epidemic modeling techniques and their practical applications for understanding and controlling the spread of infectious diseases.

A benchtop brain injury model using resected donor tissue from patients with Chiari malformation

The use of live animal models for testing new therapies for brain and spinal cord repair is a controversial area. Live animal models have associated ethical issues and scientific concerns regarding the predictability of human responses. Alternative models that replicate the 3 D architecture of the central nervous system have prompted the development of organotypic neural injury models. However, the lack of reliable means to access normal human neural tissue has driven reliance on pathological or post-mortem tissue which limits their biological utility. We have established a protocol to use donor cerebellar tonsillar tissue surgically resected from patients with Chiari malformation(cerebellar herniation towards the foramen magnum, with ectopic rather than diseased tissue) to develop an in vitro organotypic model of traumatic brain injury. Viable tissue was maintained for approximately 2 weeks with all the major neural cell types detected. Traumatic injuries could be introduced into the slices with some cardinal features of post-injury pathology evident. Biomaterial placement was also feasible within the in vitro lesions. Accordingly, this ‘proof-of-concept’ study demonstrates that the model offers potential as an alternative to the use of animal tissue for preclinical testing in neural tissue engineering. To our knowledge, this is the first demonstration that donor tissue from patients with Chiari malformation can be used to develop a benchtop model of traumatic brain injury. However, significant challenges in relation to the clinical availability of tissue were encountered, and we discuss logistical issues that must be considered for model scale-up.

PERTURBATION SOLUTION FOR COMPARTMENT MODEL OF VARIABLE EXTRACELLULAR VOLUME

提出了细胞外室体积随时间变化的两室模型并求出了其摄动解．与解析解相比，摄动解形式简单，经用两种解对肌酐（Ｃｒ）、尿素氮（ＢＵＮ）进行模拟计算后发现，简单的二级近似即可以得到足够的精度且计算速度较解析解快１０４倍，从而为迅速、准确地制定临床方案提供了理论依据．

GLOBAL DYNAMICS OF AN SEIR EPIDEMIC MODEL WITH IMMIGRATION OF DIFFERENT COMPARTMENTS

The SEIR epidemic model studied here includes constant inflows of new susceptibles, exposeds, infectives, and recovereds. This model also incorporates a population size dependent contact rate and a disease-related death. As the infected fraction cannot be eliminated from the population, this kind of model has only the unique endemic equilibrium that is globally asymptotically stable. Under the special case where the new members of immigration are all susceptible, the model considered here shows a threshold phenomenon and a sharp threshold has been obtained. In order to prove the global asymptotical stability of the endemic equilibrium, the authors introduce the change of variable, which can reduce our four-dimensional system to a three-dimensional asymptotical autonomous system with limit equation.

A dynamic cellular vertex model of growing epithelial tissues

Intercellular interactions play a significant role in a wide range of biological functions and processes at both the cellular and tissue scales, for example, embryogenesis, organogenesis, and cancer invasion. In this paper, a dynamic cellular vertex model is presented to study the morphomechanics of a growing epithelial monolayer. The regulating role of stresses in soft tissue growth is revealed. It is found that the cells originating from the same parent cell in the monolayer can orchestrate into clustering patterns as the tissue grows. Collective cell migration exhibits a feature of spatial correlation across multiple cells. Dynamic intercellular interactions can engender a variety of distinct tissue behaviors in a social context. Uniform cell proliferation may render high and heterogeneous residual compressive stresses, while stress-regulated proliferation can effectively release the stresses, reducing the stress heterogeneity in the tissue. The results highlight the critical role of mechanical factors in the growth and morphogenesis of epithelial tissues and help understand the development and invasion of epithelial tumors.

Reconstructing in vivo spatially offset Raman spectroscopy of human skin tissue using a GPU-accelerated Monte Carlo platform

As one type of spatially offset Raman spectroscopy(SORS), inverse SORS is particularly suited to in vivo biomedical measurements due to its ring-shaped illumination scheme. To explain inhomogeneous Raman scattering during in vivo inverse SORS measurements, the light–tissue interactions when excitation and regenerated Raman photons propagate in skin tissue were studied using Monte Carlo simulation. An eight-layered skin model was first built based on the latest transmission parameters. Then, an open-source platform, Monte Carlo e Xtreme(MCX), was adapted to study the distribution of 785 nm excitation photons inside the model with an inverse spatially shifted annular beam. The excitation photons were converted to emission photons by an inverse distribution method based on excitation flux with spatial offsets Δs of 1 mm, 2 mm, 3 mm and 5 mm. The intrinsic Raman spectra from separated skin layers were measured by continuous linear scanning to improve the simulation accuracy. The obtained results explain why the spectral detection depth gradually increases with increasing spatial offset, and address how the intrinsic Raman spectrum from deep skin layers is distorted by the reabsorption and scattering of the superficial tissue constituents. Meanwhile, it is demonstrated that the spectral contribution from subcutaneous fat will be improved when the offset increases to 5 mm, and the highest detection efficiency for dermal layer spectral detection could be achieved when Δs = 2 mm. Reasonably good matching between the calculated spectrum and the measured in vivo inverse SORS was achieved, thus demonstrating great utility of our modeling method and an approach to help understand the clinical measurements.

Real-Time Analytical Solutions as Series Formulas and Heaviside off/on Switch Functions for Multiple Intermittent Intravenous Infusions in One- and Two-Compartment Models

Pharmacokinetic compartment models are the only models that can extract pharmacokinetic parameters from data collected in clinical studies but their estimates lack accuracy, explanations and physiological significance. The objective of this work was to develop particular solutions to drug concentration and AUC in the form of mathematical series and Heaviside functions for repetitive intermittent infusions in the one- and two-compartment models, as a function of dose number and total time using differential calculus. It was demonstrated that the central and peripheral compartment volumes determined from regression analysis of the aminoglycoside antibiotic Sisomicin concentration in plasma represent the actual physiological body fluid volumes accessible by the drug. The drug peak time and peak concentration in the peripheral compartment were also calculated as a function of dose number. It is also shown that the time of intercompartmental momentary distribution equilibrium can be used to determine the drug’s apparent volume of distribution within any dosing interval in multi-compartment models. These estimates were used to carry out simulations of plasma drug concentration with time in the one-compartment model. In conclusion, the two-compartment open mammillary pharmacokinetic model was fully explained for the aminoglycoside antibiotic sisomicin through the new concept of the apparent volume of distribution.

A Reevaluation of Prazosin Pharmacokinetics in a Two-Compartment Model, the Apparent Volume of Distribution and Comparative Simulations in the One-Compartment Model

Published clinical data of Prazosin were reevaluated pharmacokinetically using explicit solutions to drug concentration as a function of total time for IV bolus injection, intermittent intravenous infusion and oral routes of administration in an open two-compartment model. In a novel way, the apparent volume of distribution was estimated from a two-compartment model and found to be close to the total body water suggesting that Prazosin is distributed in all tissues both extracellularly and intracellularly. In addition, extracting the value of the apparent volume of distribution from a two-compartment model allowed comparative simulations in the one-compartment model. It is shown that dosage calculations of Prazosin intermittent infusion can be safely performed using the simpler one-compartment model equations. Lastly, several additional time-dependent pharmacokinetic parameters e.g., the peak time in the central and peripheral compartment and non-steady state and steady state peak concentration and AUC were determined using series equations for all three routes of administration, as a function of dose number and total time upon multiple drug administrations in the two-compartment model. It is also the first time that steady-state plasma drug concentration equations were derived in a two-compartment mammillary model.

Local icariin application enhanced periodontal tissue regeneration and relieved local inflammation in a minipig model of periodontitis

Periodontitis is an inflammatory autoimmune disease. Treatment should alleviate inflammation, regulate the immune reaction and promote periodontal tissue regeneration. Icariin is the main active ingredient of Epimedii Folium, and it is a promising compound for the enhancement of mesenchymal stem cell function, promotion of bone formation, inhibition of bone resorption, alleviation of inflammation and regulation of immunity. The study investigated the effect of icariin on periodontal tissue regeneration in a minipig model of periodontitis. The minipig model of periodontitis was established. Icariin was injected locally. The periodontal clinical assessment index, a computed tomography(CT) scan, histopathology and enzyme-linked immune sorbent assay(ELISA)were used to evaluate the effects of icariin. Quantitative analysis results 12 weeks post-injection demonstrated that probing depth,gingival recession, attachment loss and alveolar bone regeneration values were(3.72 ± 1.18) mm vs.(6.56 ± 1.47) mm,(1.67 ± 0.59)mm vs.(2.38 ± 0.61) mm,(5.56 ± 1.29) mm vs.(8.61 ± 1.72) mm, and(25.65 ± 5.13) mm3 vs.(9.48 ± 1.78) mm3 in the icariin group and0.9% NaCl group, respectively. The clinical assessment, CT scan, and histopathology results demonstrated significant enhancement of periodontal tissue regeneration in the icariin group compared to the 0.9% NaCl group. The ELISA results suggested that the concentration of interleukin-1 beta(IL-1β) in the icariin group was downregulated compared to the 0.9% NaCl group, which indicates that local injection of icariin relieved local inflammation in a minipig model of periodontitis. Local injection of icariin promoted periodontal tissue regeneration and exerted anti-inflammatory and immunomodulatory function. These results support the application of icariin for the clinical treatment of periodontitis.

Soft Tissue Deformation Model Based on Marquardt Algorithm and Enrichment Function

In order to solve the problem of high computing cost and low simulation accuracy caused by discontinuity of incision in traditional meshless model,this paper proposes a soft tissue deformation model based on the Marquardt algorithm and enrichment function.The model is based on the element-free Galerkin method,in which Kelvin viscoelastic model and adjustment function are integrated.Marquardt algorithm is applied to fit the relation between force and displacement caused by surface deformation,and the enrichment function is applied to deal with the discontinuity in the meshless method.To verify the validity of the model,the Sensable Phantom Omni force tactile interactive device is used to simulate the deformations of stomach and heart.Experimental results show that the proposed model improves the real-time performance and accuracy of soft tissue deformation simulation,which provides a new perspective for the application of the meshless method in virtual surgery.

Fabrication of paper-based devices for in vitro tissue modeling

Paper devices have recently attracted considerable attention as a class of cost-effective cell culture substrates for various biomedical applications.The paper biomaterial can be used to partially mimic the in vivo cell microenvironments mainly due to its natural three-dimensional characteristic.The paper-based devices provide precise control over their structures as well as cell distributions,allowing recapitulation of certain interactions between the cells and the extracellular matrix.These features have shown great potential for the development of normal and diseased human tissue models.In this review,we discuss the fabrication of paper-based devices for in vitro tissue modeling,as well as the applications of these devices toward drug screening and personalized medicine.It is believed that paper as a biomaterial will play an essential role in the field of tissue model engineering due to its unique performances,such as good biocompatibility,eco-friendliness,cost-effectiveness,and amenability to various biodesign and manufacturing needs.

Angiogenesis in a 3D model containing adipose tissue stem cells and endothelial cells is mediated by canonical Wnt signaling

Adipose-derived stromal cells （ASCs） have gained great attention in regenerative medicine. Progress in our understanding of adult neovascularization further suggests the potential of ASCs in promoting vascular regeneration, although the specific cues that stimulate their angiogenic behavior remain controversial In this study, we established a three-dimensional （3D） angiogenesis model by co-culturing ASCs and endothelial cells （ECs） in collagen gel and found that ASC-EC-instructed angiogenesis was regulated by the canonical Wnt pathway. Furthermore, the angiogenesis that occurred in implants collected after injections of our collagen gel- based 3D angiogenesis model into nude mice was confirmed to be functional and also regulated by the canonical Wnt pathway. Wnt regulation of angiogenesis involving changes in vessel length, vessel density, vessel sprout, and connection numbers occurred in our system. Wnt signaling was then shown to regulate ASC- mediated paracrine signaling during angiogenesis through the nuclear translocation of β-catenin after its cytoplasmic accumulation in both ASCs and ECs. This translocation enhanced the expression of nuclear cofactor Lef-1 and cyclin D1 and activated the angiogenic transcription of vascular endothelial growth factor A （VEGFA）, basic fibroblast growth factor （bFGF）, and insulin-like growth factor 1 （IGF-1）. The angiogenesis process in the 3D collagen model appeared to follow canonical Wnt signaling, and this model can help us understand the importance of the canonical Wnt pathway in the use of ASCs in vascular regeneration.

A New Model to Study Healing of a Complex Femur Fracture with Concurrent Soft Tissue Injury in Sheep

High energy bone fractures resulting from impact trauma are often accompanied by subcutaneous soft tissue injuries, even if the skin remains intact. There is evidence that such closed soft tissue injuries affect the healing of bone fractures, and vice versa. Despite this knowledge, most impact trauma studies in animals have focussed on bone fractures or soft tissue trauma in isolation. However, given the simultaneous impact on both tissues a better understanding of the interaction between these two injuries is necessary to optimise clinical treatment. The aim of this study was therefore to develop a new experimental model and characterise, for the first time, the healing of a complex fracture with concurrent closed soft tissue trauma in sheep. A pendulum impact device was designed to deliver a defined and standardised impact to the distal thigh of sheep, causing a reproducible contusion injury to the subcutaneous soft tissues. In a subsequent procedure, a reproducible femoral butterfly fracture (AO C3-type) was created at the sheep’s femur, which was initially stabilised for 5 days by an external fixator construct to allow for soft tissue swelling to recede, and ultimately in a bridging construct using locking plates. The combined injuries were applied to twelve sheep and the healing observed for four or eight weeks (six animals per group) until sacrifice. The pendulum impact led to a moderate to severe circumferential soft tissue injury with significant bruising, haematomas and partial muscle disruptions. Posttraumatic measurements showed elevated intra-compartmental pressure and circulatory tissue breakdown markers, with recovery to normal, pre-injury values within four days. Clinically, no neurovascular deficiencies were observed. Bi-weekly radiological analysis of the healing fractures showed progressive callus healing over time, with the average number of callus bridges increasing from 0.4 at two weeks to 4.2 at eight weeks. Biomechanical testing after sacrifice showed in- creasing torsional stiffness between four and eight weeks healing time from 10% to 100%, and increasing ultimate torsional strength from 10% to 64% (relative to the contralateral control limb). Our results demonstrate the robust healing of a complex femur fracture in the presence of a severe soft tissue contusion injury in sheep and demonstrate the establishment of a clinically relevant experimental model, for research aimed at improving the treatment of bone fractures accompanied by closed soft tissue injuries.

Engineering biomimetic intestinal topological features in 3D tissue models: retrospects and prospects

Conventional 2D intestinal models cannot precisely recapitulate biomimetic features in vitro and thus are unsuitable for various pharmacokinetic applications,development of disease models,and understanding the host-microbiome interactions.Thus,recently,efforts have been directed toward recreating in vitro models with intestine-associated unique 3D crypt-villus(for small intestine)or crypt-lumen(for large intestine)architectures.This review comprehensively delineates the current advancements in this research area in terms of the different microfabrication technologies(photolithography,laser ablation,and 3D bioprinting)employed and the physiological relevance of the obtained models in mimicking the features of native intestinal tissue.A major thrust of the manuscript is also on highlighting the dynamic interplay between intestinal cells(both the stem cells and differentiated ones)and different biophysical,biochemical,and mechanobiological cues along with interaction with other cell types and intestinal microbiome,providing goals for the future developments in this sphere.The article also manifests an outlook toward the application of induced pluripotent stem cells in the context of intestinal tissue models.On a concluding note,challenges and prospects for clinical translation of 3D patterned intestinal tissue models have been discussed.

<i>In Vitro</i>Evaluation System of Pharmacokinetics and Irradiation Effect in Boron Neutron Capture Therapy (BNCT) Using Three-Dimensional Artificial Human Tumor Tissue Model

Boron neutron capture therapy (BNCT) is based on the incorporation of boron-containing drugs to cancer cells and the nuclear reaction of 10B atoms by thermal neutron irradiation results in tumor degeneration. For the development of this therapy, currently, long time and high cost consuming experiments using many animals are required. In this study, we constructed a new in vitro evaluation system for BNCT by combination of an artificial tumor tissue model, comprised of normal human dermal-derived fibroblast (NHDF) and human pancreatic cancer cell line BxPC3, and the optical plastic material CR-39 as a solid state nuclear track detector. Administration of boronophenylalanine (10BPA) as a boron-containing drug and neutron irradiation up to 2.52 × 1012 n/cm2 to the control tissue constructed by NHDF (NHDF3D) and BxPC3 cell loaded tissue (NHDF3D/BxPC3) resulted in detection of 1.6 times higher number of α-ray/recoiled Li particle tracks in NHDF3D/BxPC3 in comparison to NHDF3D, demonstrating that putative irradiation damage to cancer cells can be evaluated by this system. On a cellular level, the hit number of α-ray/recoiled Li particle tracks per single BxPC3 cells and NHDF was evaluated as 5.46 and 1.71, respectively. The tumor and normal tissue ratio (T/N ratio) was 3.19, which was corresponded with those of BPA as 2 - 4 that reported in the previous studies. This new in vitro evaluation system may provide a useful tool for a low cost, labor-saving, and non-animal method for the development of new boron-containing drugs or improvement of BNCT conditions.

Interventional effect of hirudin on the expression of microtubule-associated protein 2 in peripheral tissue of hematom of model rats with acute intracerebral hemorrhage

BACKGROUND： It is suspected that dissociation, destruction or synthetic disorder of microtubule-associated protein 2 （MAP-2） may participate in secondary injury of intracerebral hemorrhage （ICH）, and the reason may be related to thrombin in high concentration after ICH; therefore, the mechanism should be studied further. OBJECTIVE： To explore the effect of hirudin on expression of MAP-2 in peripheral tissue of hematom after ICH and changes of water content in brain tissue and analyze pathogenesis of thrombin in secondary injury after ICH. DESIGN ： Completely randomized grouping design and controlled animal study SEn-ING ： Department of Neurology, the First Affiliated Hospital of Jilin University MATERIALS ： The experiment was carried out in the Neurological Laboratory of the First Affiliated Hospital of Jilin University from April 2003 to April 2004. A number of 80 healthy Wistar rats, of both genders, aged 3-4 months, weighing 250-350 g, were randomly divided into 8 groups： normal control group, 6-hour ICH group, 1-day ICH group, 2-day ICH group, 3-day ICH group, 7-day ICH group, 3-day hirudin group and 7-day hirudin group with 10 in each group. Five rats from each group were selected to measure their water content, and the others were undertaken immunohistochemical stain. Hirudin was produced by Sigma Company, USA, and MAP-2 rabbit-rat polyclonal antibody was provided by Fuzhou Maixin Biotechnology Company Limited. METHODS： ① Model establishing and grouping intervention： Rats in simple ICH group were collected their blood from tails and then inserted with 50 μL non-anticoagulant auto-arterial blood into the cauda of the putamen in right brain within 5 minutes. Rats in hirudin groups were inserted with 10 U hirudin （which was diluted with saline to 20 μL） into local hematom regions within 5 minutes, and the needle was pulled out after 10 minutes. Rats in normal control group were untouched. ② Water content in peripheral tissue of hematom： Based on the ratio between dry weight and wet weight, brain tissue at bleeding side and in right frontal lobe was selected to measure dry and wet weights so as to calculate the water content [（wet weight - dry weight） /wet weight] × 100%.③ Positive expression of MAP-2： Based on immunohistochemical stain, positive MAP-2 cells were regarded as neurons and they were buffy morphological. Positive rate of MAP-2 was calculated, i.e., percentage of positive cells in each sight to total cells in all sights. ④ Statistical analysis： Data among groups were compared with one-way analysis of variance, averages were compared with SNK-q test by each other, and relation between water content and MAP-2 was analyzed with linear regression technique. MAIN OUTCOME MEASURES： Changes of water content and MAP-2 expression in peripheral tissue of hematorn at various time points after ICH and intervention of hirudin. RESULTS： All 80 rats were involved in the final analysis. ①Water content： Water content was increased at day 1, reached peak at day 3 and decreased at day 7. It was （72.31±0.32）%, （77.42±0.53）%, （78.44±0.28）%, （74.10±0.13）%, （74.85±0.51）% and （70.07±0.36）%, respectively in 1-day, 2-day, 3-day and 7-day ICH groups and 3-day and 7-day hirudin groups, which was higher than that in normal control group （63.85±0.41, q=-4.684 3 to -7.262 0, P〈 0.05）; that in 2-day and 3-day ICH groups was higher than that in 7-day ICH group （q=-3.053 4, -3.727 0, P 〈 0.05）; and that in 3-day and 7-day ICH groups was higher than that in hirudin groups at the same time points （q=-2.965 6, -2.726 4, P 〈 0.05）. ②Positive expression of MAP-2： Positive expression of MAP-2 was decreased at 6 hours after ICH, reached the lowest value at day 3 and increased at day 7. Positive rate was （78.60±0.42）%, （60.56±0.74）%, （44.60±0.26）%, （25.45±0.85）%, （32.55±0.64）%, （37.69＋0.76）%, （41.75±0.68）%, respectively in 6-hour, 1-day, 2-day, 3-day and 7-day ICH groups and 3-day and 7-day hirudin groups, which was lower than that in normal control group [（96.50±0.33）%, q= -3.074 5 to -8.128 5, P 〈 0.05]. In addition, positive cells of MAP-2 disappeared plentifully at 3-7 days after ICH, stain of positive cells were light, and only stain of plasma was positive. That in 3-day and 7-day hirudin groups was higher than that in ICH groups at the same time points （q= -3.391 8, -2.967 9, P 〈 0.05）. Moreover, positive cells of MAP-2 was formed slightly but deeply stained. ③ Results of linear regression： Water content was negatively related to MAP-2 changes at 7 days after ICH （r= -0.894 9, P〈 0.01）, i.e., water content was increased with decrease of MAP-2 expression. CONCLUSION ： The deterioration of MAP-2 may be involved in the pathogenesis of thrombin within the first week after ICH, and the local administration of hirudin can protect neurons.

Study and Modeling of Human Biological Tissue Exposed to High Frequency Electromagnetic Waves

The main objective of this proposed article is to provide explanations to justify the validity of the results of the studies of the interaction between the electromagnetic fields and the human body. It can also find direct applications in the characterization and modeling of the macroscopic electrical properties of the biological media for assessing the effects of fields induced by electromagnetic radiation sources in the human body to set up new standards on the Human exposure to electromagnetic fields. To do this, we have taken into account the different physical phenomena of propagation of a hyper-frequency electromagnetic plane wave and on the other hand, the experimental values in order to model the electrical behavior of human biological tissues based on an equivalent electronic circuit model composed of capacities, resistance and reel, which assimilates the biological tissues of the skin, grease, blood. This model using the characteristic impedance of the dielectric support makes it possible to evaluate the voltage induced by the electromagnetic waves of the hyper-frequencies in the studied biological system. The results of the simulations obtained from computer tools demonstrate that the hyper-frequency electromagnetic waves can result in an elevation of the electrical potential of the biological tissues. Despite this potential is a decreasing function of the penetration depth.

A NEW TWO-COMPARTMENT MODEL OF PATIENT-ARTIFICIAL KIDNEY SYSTEM INCLUDING CSF COMPARTMENT

A two-compartment model of patient-artificial kidney system consisting of a cerebrospinalfluid(CSF)and a body liquor compartments have been presented.With the model,the mechanism ofdisequilibrium syndrome occurred in a patient undergoing hemodialysis has been discussed to simulatethe CSF pressure transients.Urea,as an uretic toxin,was injected into dogs and in vivohemodialysis experiments have been performed under clinical conditions.The parameters in the sol-ution,G and K,have been determinde from experiments and are in good agreement with those re-ported under normal physiological conditions and in previous investigations.

A local high-resolution deformation model of soft tissue based on element-free Galerkin method

In order to solve the problem that the existing meshless models are of high computational complexity and are difficult to express the biomechanical characteristics of real soft tissue, a local high-resolution deformation model of soft tissue based on element-free Galerkin method is proposed. The proposed model applies an element-free Galerkin method to establish the model, and integrates Kelvin viscoelastic model and adjustment function to simulate nonlinear viscoelasticity of soft tissue. Meanwhile, a local high-resolution algorithm is applied to sample and render the deformed region of the model to reduce the computational complexity. To verify the effectiveness of the model,liver and brain tumor deformation simulation experiments are carried out. The experimental results show that compared with the existing meshless models, the proposed model well reflects the biomechanical characteristics of soft tissue, and is of high authenticity, which can provide better visual feedback to users while reducing computational cost.

The Presence of Phases and the Inability of the Classical Compartment Models to Provide Pharmacokinetic Parameters of Physiological Significance for Lipophilic Drugs

The first biphasic open one-compartment pharmacokinetic model is described. Its analytical solutions to drug concentration were developed from parameters of an open two-compartment pharmacokinetic model. The model is used to explain the unusually large compartment volumes and apparent volumes of distribution of lipophilic drugs, as well as to identify which of the pharmacokinetic parameters of the classical compartment models are biologically relevant.