For drug dispersion throughout the biological environment, drug diffusion is a vital mechanism. Thera- peutic compounds have different sizes and shapes and hence it is difficult to predict the varied diffusion coefficients. Molecular diffusion is also hindered by various resistances presented by the biological tissues. Drugs diffusing through a tissue interact with tissue elements which may be non-specific as binding with extracellular matrix (ECM) sites or highly specific such as ligand-receptor interactions.
Binding of ligand to cell surface receptors was on focus in direct experimental research for the past two decades which was mainly based on equilibrium binding properties. After that recognition of highly dynamic property of receptor binding phenomena instigated interest in binding kinetics. Some back- ground texts may be studied to get the details of experimental research on cell surface binding events [84, 64]. Binding of ligands such as drugs with cell surface receptors lead to internalization of both receptors and drugs by endocytosis. Endocytosis results in accumulation of ligand in lysosomes which lead to drug degradation. Endocytosis helps the cells to internalize a variety of compounds such as serum proteins, viruses, growth factors and many others, as observed by Mukherjee et al. . Ligand- receptor complexes formed as a result of interaction between ligand and receptors at the cell surface, are internalized into the cell intracellular region and stored into common endosomes (cf. ). It is an accepted fact that trafficking plays an important part in receptor-mediated cell response. Internaliza- tion of receptors can lead to cellular response generation as observed by Bretcher  or attenuation of a response as remarked by Zigmond . Cell surface receptor generation may get enhanced on exposure to stimuli which demonstrates that receptor concentration regulation may be significant in cellular responses. Thus, in order to increase drug efficacy and its therapeutic efficiency, the endocytic trafficking cycle should be studied and investigated in details. Two levels of mathematical models are mainly used to deal with endocytic trafficking cycle, firstly, the models that demonstrate the kinetics of receptor / drug interactions throughout the whole cellular region and secondly, the models dealing with specific endocytic mechanism. Whole-cell kinetic mathematical models predict receptor and drug states in connection to cell behavorial functions. On the other hand, mechanistic mathematical models deal with trafficking parameters in accordance with biophysical and biochemical properties of endo-
2. LITERATURE REVIEW 21 cytic cycle components. A combined apprehension of both types of mathematical models can relate molecular properties and cell functions effectively. The chemical interactions between a drug and a binding site lead to drug response, which can be observed from the work conducted by Salahudeen and Nishtala . Their work focussed on modelling of drug binding phenomenon, where it was concluded that drug response was dependent on the receptor occupancy by the drug particles, but de- terministic modelling was not done by them. The basic fundamental mathematical models of drug diffusion in the biological tissue, specific and non-specific interactions of drug with cell receptors and ECM sites were well illustrated by Lauffenburger, Linderman and Saltzman [79, 125]
2.2.1 Drug transport in solid tumour Transport within blood vessel
Drug particles begin to circulate in systemic plasma throughout the body just after the initial dose is injected. Drug properties along within vivobody environment regulate the process of drug transport within blood stream. During their transport through blood, drugs may get discharged into the tis- sues while passing by. Moreover, various organs of the body can take active part in filtering plasma, thereby eliminating drugs from systemic circulation, biologically termed as plasma clearance. The drug dosage, way of its administration into the circulatory system and plasma clearance together deter- mine the plasma drug concentration. This function of renal excretion may vary according to the drug type .
Transport through blood vessels
While transported in systemic plasma, some drugs get dispersed into tumour plasma via blood perfu- sion due to advective and diffusive transport. These drugs can be extravasated into the interstitial fluid due to high permeability of tumour vasculature. Across the vessel wall, drug transport by fluid flux follows advection which is the outcome of hydrostatic and osmotic pressure difference between lumen and interstitium. On the other hand, diffusive drug transport is the outcome of concentration gradient between blood and interstitial fluid along with vasculature permeability and area for drug exchange.
Hence, if the gradient alters in opposite direction, drug may get discharged back into the plasma. Here, the main modes of transport are diffusion and advection. Drug uptake by endothelial cells, that is, tran- scytosis is having negligible effect in comparison to diffusion and advection . Deen  presented a review work based on studies conducted by various researchers on hindered transport through pores available on membranes.
Transport in interstitial fluid
The extracellular matrix and intense non-uniformity in vasculature distribution generate a compli- cated tumour interstitial space . The tumour pressure may go beyond the atmospheric pressure [125, 15], which is the result of inefficient lymphatics, increased tumour vasculature permeability and cell proliferation in a restricted tumour volume leading to vasculature collapse . An effec-
tive mathematical model was derived by Baxter and Jain  for transvascular exchange in addition to extravascular fluid and macromolecular transport in tumour. Moreover, in the study of Baxter and Jain, interstitial space was considered as a porous medium where Darcy’s law was utilized. In order to reach the targeted tumour cells, the drugs pass through the interstitial fluid by advection and diffusion depending on interstitial fluid pressure and interstitial fluid velocity within tumour. The extracellular space composition affects the diffusivity of drugs due to the presence of proteins. Diffusivity is also affected by the tissue geometry which leads to the difference in diffusion coefficient of a particular drug in tumour and normal tissue .
In this chapter, general literature survey is carried out and underlying physical phenomena are discussed so that the readers get an overview of the advancement of study of drug release and drug transport with time. In the following chapters where various problems are focussed and elucidated, problem specific literature reviews are provided at the beginning of the chapters for readers’ ease.
DRUG RELEASE FROM MICROPARTICLES
Sometimes patients consciously or unconsciously change their prescribed drug dosage schedules and many a time physicians are not informed of this. Forgetfulness is one of the major reasons behind this non-compliance by the patients, which leads to serious consequences in their treatment. New drug delivery systems certainly offer the opportunity to reduce patient non-compliance by tailoring some of the conventional dosage forms. Not only non-compliance by the patients, but also drug distribution, absorption and metabolism vary among individuals. Controlled drug release mechanism provides much relief to these problems. It increases patient’s comfort by reducing the frequency of doses. A major advantage of controlled drug release is that besides prolonging the action of the drug, it maintains drug levels within the therapeutic windows (range of drug dosages that can treat diseases effectively while staying within the safety range) of the drug. One of the most common practices to get controlled release is to encapsulate a drug in microparticles or any matrix to enhance or reduce the kinetics behind drug release mechanism depending on the anticipated healing target.
Drug encapsulating microparticles have the potential to spend an extended time in the body relative to that for naked drug. Hence, they have the ability to circulate for a prolonged duration of time in the vicinity of the organ at which they are targeted. Due to biocompatibility and biodegradability of the microparticles, particularly those with polymeric coating such as polylactic acid (PLA), polyglycolic acid (PGA) and polylactic-co-glycolic acid (PLGA), they are reliably used in recent years as potential drug delivery devices. There are several advantages of using microparticles as controlled drug release devices . First, particle size and the characteristics of the surface can be varied according to the necessity to have both passive and active self-programmed controlled release system. In passively programmed system, the release rate of drug is predetermined and it does not depend on any external biological stimuli. In actively programmed system, the release rate can be controlled by some external mechanism. Secondly, since microparticles have biodegradable polymeric coating, they are particu-
3. DRUG RELEASE FROM MICROPARTICLES 24 larly attractive for use in drug delivery, as once introduced into the body the microparticle matrix is degraded into non-toxic by-products leading to reduction of side effects. Thirdly, encapsulation of drug in a polymeric matrix is done in such a way that the drug and its polymeric coating are mutually inert, thus preserving the chemical stability of the drug and its biological activities. Moreover, these microparticles can be used through various paths of administration, including oral, nasal etc.
Mathematical modelling of drug release process is a subject of recent medical progress. Due to the advancement in computational science, the models have become easier to apply. Theoretical results should predict the effects of processing parameters, not only on the pharmacokinetic aspect, but also on the resulting pharmacodynamics. An extremely helpful, yet challenging aspect is to have such type of mathematical modelling for formulating drug transport in the living cells . Besides, controlled drug release is also an important part of the recent medical research, many attempts have been made to control drug release through various approaches and different theories. An important work is done by Pontrelli and Monte , where drug association / dissociation aspect is taken into account while dealing with transdermal drug delivery. A work of Casalini et al.  on drug release process is described as —water penetrates inside the polymeric microparticle and wets drug crystals, allowing solubilisation of the drug, which diffuses through the microparticle. There is an assumption that no significant recrystallization of solubilised drug occurs during its release. In the present study, an im- proved model of controlled drug release is proposed. In this improved model, some of the simplifying assumptions made in the works of Pontrelli and Monte  and Casalini et al.  are not taken into account which make the model a more realistic one. The process of drug release is described by taking into account the solubilisation dynamics of drug crystallites and diffusion of the solubilised drug through the microparticle. The reversible drug binding process both in the microparticle and in tissue is also addressed. An important aspect of this type of modelling is to have correct judgement of the main parameters, such as diffusion coefficient, mass transfer coefficient, drug association and dissociation rates. A significant perspective of the present work is that the model is solved analytically.
The numerical results and their graphical representations provide trustworthy predictions about various aspects of controlled drug release kinetics, which can be utilised by pharmacists to revive their ideas and make few tweaks to the prevailing drug delivery technique.